tag:blogger.com,1999:blog-31772603147908376022024-02-19T08:46:39.557-08:00MEDIA ILMU PENGETAHUANAnonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.comBlogger23125tag:blogger.com,1999:blog-3177260314790837602.post-76600278140335265362012-05-10T06:14:00.002-07:002012-05-10T06:14:53.232-07:00<span style="color: #333333; font-family: Verdana, sans-serif; font-size: x-small;"><span style="line-height: 20px;"><b><br style="background-color: white; text-align: justify;" /></b></span></span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">• “Waspadalah terhadap tiga orang: pengkhianat, pelaku zalim, dan pengadu domba. Sebab, seorang yang berkhianat demi dirimu, ia akan berkhianat terhadapmu dan seorang yang berbuat zalim demi dirimu, ia akan berbuat zalim terhadapmu. Juga seorang yang mengadu domba demi dirimu, ia pun akan melakukan hal yang sama terhadapmu.”</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">• “Tiga manusia adalah sumber kebaikan: manusia yang mengutamakan diam (tidak banyak bicara), manusia yang tidak melakukan ancaman, dan manusia yang banyak berzikir kepada Allah.”</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">• “Sesungguhnya puncak keteguhan adalah tawadhu’.” Salah seorang bertanya kepada Imam, “Apakah tanda-tanda tawadhu’ itu?” Beliau menjawab, “Hendaknya kau senang pada majlis yang tidak memuliakanmu, memberi salam kepada orang yang kau jumpai, dan meninggalkan perdebatan sekalipun engkau di atas kebenaran.”</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">• Seorang laki-laki seringkali mendatangi Imam Ja‘far as, kemudian dia tidak pernah lagi datang. Tatkala Imam as menanyakan keadaannya, seseorang menjawab dengan nada sinis, “Dia seorang penggali sumur.” Imam as membalasnya, “Hakekat seorang lelaki ada pada akal budinya, kehormatannya ada pada agamanya, kemuliannya ada pada ketakwaannya, dan semua manusia sama-sama sebagai Bani Adam.” </span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">• “Hati-hatilah terhadap orang yang teraniaya, karena doanya akan terangkat sampai ke langit.”</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">• “Ulama adalah kepercayaan para rasul. Dan bila kau temukan mereka telah percaya pada penguasa, maka curigailah ketakwaan mereka.”</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">• “Tiga perkara dapat mengeruhkan kehidupan: penguasa zalim, tetangga yang buruk, dan perempuan pencarut. Dan tiga perkara yang tidak akan damai dunia ini tanpanya, yaitu keamanan, keadilan, dan kemakmuran.”</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">=========================================</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata-kata mutiara Islam dari Imam Baqir a.s.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">=========================================</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">1. Jiwa yang agung</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Kuwasiatkan lima hal kepadamu: (1) jika engkau dizalimi, jangan berbuat zalim, (2) jika mereka mengkhianatimu, janganlah engkau berkhianat, (3) jika engkau dianggap pembohong, janganlah marah, (4) jika engkau dipuji, janganlah gembira, dan (5) jika engkau dicela, kontrollah dirimu”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">2.Akibat baik dan buruk</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Alangkah mungkin orang yang tamak kepada dunia akan mendapatkannya di dunia. Akan tetapi, ketika ia mendapatkan seluruhnya, dunia itu akan menjadi bala` baginya dan ia menjadi sengsara karenanya. Dan alangkah mungkin seorang membenci urusan akhirat. Akan tetapi, ia dapat menggapainya kemudian dan ia hidup bahagia karenanya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">3. Keutamaan terbaik dan jihad terbaik</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Tiada keutamaan seperti jihad dan tiada jihad seperti menentang hawa nafsu”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">4. Ambillah nasihat yang baik</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Ambillah nasihat baik dari orang yang mengucapkannya meskipun ia tidak mengamalkannya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">5. Indahnya kesabaran yang disertai dengan ilmu</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“(Jika sesuatu digabung dengan yang lain), tidak ada gabungan yang lebih indah dari kesabaran yang digabung dengan ilmu”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">6. Kesempurnaan yang paling sempurna</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Kesempurnaan yang paling sempurna adalah tafakkuh (mendalami) agama, sabar menghadapi musibah dan ekonomis dalam mengeluarkan biaya hidup”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">7. Tiga kriteria agung</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Tiga hal adalah kemuliaan dunia dan akhirat: memaafkan orang yang menzalimimu, menyambung tali persaudaraan terhadap orang yang memutuskannya, dan sabar ketika engkau diperlakukan sebagai orang bodoh”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">8. Kontinyu dalam berdoa</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Sesungguhnya Allah membenci seseorang yang meminta-minta kepada orang lain berkenaan dengan kebutuhannya, dan menyukai hal itu (jika ia meminta kepada)-Nya. Sesungguhnya Ia suka untuk diminta setiap yang dimiliki-Nya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">9. Keutamaan orang alim atas ‘abid</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Seorang alim yang dapat dimanfaatkan ilmunya lebih utama dari tujuh puluh ribu ‘abid”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">10. Dua karakter orang alim</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Seorang hamba bisa dikatakan alim jika ia tidak iri kepada orang yang berada di atasnya dan tidak menghina orang yang berada di bawahnya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">11. Tiga pahala</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Jika mulut seseorang berkata jujur, maka perilakunya akan bersih, jika niatnya baik, maka rezekinya akan ditambah, dan jika ia berbuat baik kepada keluarganya, maka umurnya akan ditambah”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">12. Tinggalkanlah kemalasan</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Janganlah malas dan suka marah, karena keduanya adalah kunci segala keburukan. Barang siapa yang malas, ia tidak akan dapat melaksanakan hak (orang lain), dan barang siapa yang suka marah, maka ia tidak akan sabar mengemban kebenaran”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">13. Penyesalan di hari kiamat</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Orang yang paling menyesal di hari kiamat adalah orang yang berbicara keadilan dan ia sendiri tidak melaksanakannya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">14. Buah silaturahmi</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Silaturahmi dapat membersihkan amalan, memperbanyak harta, menghindarkan bala`, mempermudah hisab (di hari kiamat) dan menunda ajal tiba”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">15. Berucap ramah dengan orang lain</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Ucapkanlah kepada orang lain kata-kata terbaik yang kalian senang jika mereka mengatakan itu kepadamu”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">16. Hadiah Ilahi</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Allah akan memberikan hadiah bala` kepada hamba-Nya yang mukmin sebagaimana orang yang bepergian akan selalu membawa hadiah bagi keluarganya, dan menjaganya dari (godaan) dunia sebagaimana seorang dokter menjaga orang yang sakit”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">17. Jujur dan melaksanakan amanat</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Bersikaplah wara’, berusahalah selalu, jujurlah, dan berikanlah amanat kepada orangnya, baik ia adalah orang baik maupun orang fasik. Seandainya pembunuh Ali bin Abi Thalib a.s. menitipkan amanat kepadaku, niscaya akan kuberikan kepadanya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">18. Perbedaan antara ghibah dan tuduhan</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Ghibah adalah engkau membicarakan aib (yang dimiliki oleh saudaramu) yang Allah telah menutupnya (sehingga tidak diketahui oleh orang lain), dan menuduh adalah engkau membicarakan aib yang tidak dimiliki olehnya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">19. Pencela dibenci Allah</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Allah membenci pencela yang tidak memiliki harga diri”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">20. Tanda-tanda rendah hati</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“(Engkau dapat dikatakan rendah hati jika) engkau rela duduk di sebuah majelis yang lebih rendah dari kedudukanmu, mengucapkan salam kepada orang yang kau jumpai, dan menghindari debat meskipun engkau benar”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">21. Menjaga harga diri adalah ibadah terbaik</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Ibadah yang terbaik adalah menjaga perut dan kemaluan”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">22. Sumber dosa adalah tidak kenal Allah</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Tidak akan bermaksiat kepada Allah orang yang mengenal-Nya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">24. Akal adalah makhluk Allah terbaik</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Ketika Allah menciptakan akal, Ia berfirman kepadanya: “Kemarilah!” Ia pun menghadap. Ia berfirman kembali: “Mundurlah!” Ia pun mundur. Kemudian Ia berfirman: “Demi kemuliaan dan keagungan-Ku, Aku tidak pernah menciptakan makhluk yang lebih Kucintai darimu, dan Aku tidak akan menyempurnakanmu kecuali bagi orang yang Kucintai. Semua perintah, larangan, siksa dan pahala-Ku tertuju kepadamu”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">25. Hisab atas dasar akal</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Sesungguhnya Allah akan menghisab hamba-hamba-Nya pada hari kiamat sesuai dengan kadar akal yang telah dianugerahkan kepada mereka di dunia.”</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">26. Pahala guru dan murid</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Sesungguhnya pahala orang yang mengajarkan ilmu adalah seperti pahala orang yang belajar darinya, dan ia masih memiliki kelebihan darinya. Oleh karena itu, pelajarilah ilmu dari ahlinya dan ajarkanlah kepada saudara-saudaramu sebagaimana ulama telah mengajarkannya kepadamu”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">27. Dosa mufti yang tidak berilmu</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Barang siapa yang mengeluarkan fatwa tanpa ilmu yang cukup, maka ia akan dilaknat oleh malaikat rahmat dan azab serta dosa orang yang mengamalkan fatwanya akan dipikul olehnya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">28. Ulama neraka</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Orang yang mencari ilmu dengan tujuan mendebat ulama (lain), mempermalukan orang-orang bodoh atau mencari perhatian manusia, maka bersiap-siaplah untuk menempati neraka. Kepemimpinan tidak berhak dimiliki kecuali oleh ahlinya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">29. Tanda-tanda seorang faqih</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Faqih yang sebenarnya adalah orang yang zahid terhadap dunia, rindu akhirat dan berpegang teguh kepada sunnah Rasulullah SAWW”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">30. Bergurau tanpa mencela</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Sesungguhnya Allah azza wa jalla menyukai orang-orang yang suka bergurau dengan orang lain dengan syarat tanpa cela-mencela”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">31. Azab untuk tiga kriteria</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Tiga kriteria yang penyandangnya tidak akan meninggal dunia kecuali ia telah merasakan siksanya: kezaliman, memutuskan tali silaturahmi dan bersumpah bohong, yang dengan sumpah tersebut berarti ia telah berperang melawan Allah”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">32. Yang disukai Allah</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Sesuatu yang paling utama di sisi Allah adalah engkau meminta segala yang dimiliki-Nya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">33. Kontinyu dalam doa</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Demi Allah, seorang hamba tidak berdoa kepada-Nya terus menerus kecuali Ia akan mengabulkannya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">34. Berdoa di waktu sahar</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Sesungguhnya Allah mencintai hamba yang banyak berdoa. Oleh karena itu, berdoalah pada waktu ashar hingga matahari terbit, karena pada waktu itu pintu-pintu langit terbuka, rezeki-rezeki dibagikan dan hajat-hajat penting dikabulkan”</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">35. Berdoa untuk orang lain</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Doa yang paling cepat dikabulkan adalah doa seorang hamba untuk saudaranya tanpa sepengetahuannya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">36. Mata-mata yang tidak akan menangis</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Semua mata pasti akan menangis pada hari kiamat kecuali tiga mata: mata yang bangun malam di jalan Allah, mata yang menangis karena takut kepada-Nya dan mata yang tidak pernah melihat hal-hal yang diharamkan oleh Allah”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">37. Orang yang tamak bak ulat sutra</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Perumpamaan orang yang tamak bagaikan ulat sutra. Ketika sutra yang melilitnya bertambah banyak, sangat jauh kemungkinan baginya untuk bisa keluar sehingga ia akan mati kesedihan di dalam sarangnya sendiri”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Bijak Islami</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">38. Jangan berwajah dua</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">“Hamba yang paling celaka adalah hamba yang berwajah dan bermulut dua; ia memuji saudaranya di hadapannya dan menghibahnya di belakangnya, jika saudaranya itu dianugerahi nikmat, ia iri dan jika ia ditimpa musibah, ia menghinanya”.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Perbanyaklah kamu mengingat mati, karena hal itu bisa membersihkan dosa dan menyebabkan kamu zuhud atau tidak cinta kepada dunia.(Rasulullah)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Keluarlah dari dirimu dan serahkanlah semuanya pada Allah, lalu penuhi hatimu dengan Allah. Patuhilah kepada perintahNya, dan larikanlah dirimu dari laranganNya, supaya nafsu badaniahmu tidak memasuki hatimu, setelah itu keluar, untuk membuang nafsu-nafsu badaniah dari hatimu, kamu harus berjuang dan jangan menyerah kepadanya dalam keadaan bgaimanapun juga dan dalam tempo kapanpun juga.(Syekh Abdul Qodir al-Jaelani)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Berteman dengan orang bodoh yang tidak mengikuti ajakan hawa nafsunya adalah lebih baik bagi kalian, daripada berteman dengan orang alim tapi selalu suka terhadap hawa nafsunya.(Ibnu Attailllah as Sakandari)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Orang yang suka berkata jujur akan mendapatkan 3 hal, yaitu : KEPERCAYAN, CINTA dan RASA HORMAT (Sayidina Ali bin Abi Thalib)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Ketahuilah bahwa sabar, jika dipandang dalam permasalahan seseorang adalah ibarat kepala dari suatu tubuh. Jika kepalanya hilang maka keseluruhan tubuh itu akan membusuk. Sama halnya, jika kesabaran hilang, maka seluruh permasalahan akan rusak.</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">(Sayidina Ali bin Abi Thalib)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kejahatan yang dibalas dengan kejahatan pula adalah sebuah akhlaq ular, dan kalau kebajikan dibalas dengan kejahatan itulah akhlaq buaya, lalu bila kebajikan dibalas dengan kebajkan adalah akhlaq anjing, tetapi kalau kejahatan dibalas dengan kebajikan itulah akhlaq manusia.(Nasirin)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Ilmu itu lebih baik daripada harta. Ilmu akan menjaga engkau dan engkau menjaga harta. Ilmu itu penghukum (hakim) sedangkan harta terhukum. Kalau harta itu akan berkurang apabila dibelanjakan, tetapi ilmu akan bertambah apabila dibelanjakan.(Sayidina Ali bin Abi Thalib)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Sabar memiliki dua sisi, sisi yang satu adalah sabar, sisi yang lain adalah bersyukur kepada Allah. (Ibnu Mas’ud)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Takutlah kamu akan perbuatan dosa di saat sendirian, di saat inilah saksimu adalah juga hakimmu. (Ali bin Abi Thalib)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Orang yang paling aku sukai adalah dia yang menunjukkan kesalahanku.(Umar bin Khattab)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Niat adalah ukuran dalam menilai benarnya suatu perbuatan, oleh karenanya, ketika niatnya benar, maka perbuatan itu benar, dan jika niatnya buruk, maka perbuatan itu buruk. (Imam An Nawawi)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Aku mengamati semua sahabat, dan tidak menemukan sahabat yang lebih baik daripada menjaga lidah. Saya memikirkan tentang semua pakaian, tetapi tidak menemukan pakaian yang lebih baik daripada takwa. Aku merenungkan tentang segala jenis amal baik, namun tidak mendapatkan yang lebih baik daripada memberi nasihat baik. Aku mencari segala bentuk rezki, tapi tidak menemukan rezki yang lebih baik daripada sabar. (Umar bin Kattab)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Dia yang menciptakan mata nyamuk adalah Dzat yang menciptakan matahari.(Bediuzzaman Said Nursi)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Penderitaan jiwa mengarahkan keburukan. Putus asa adalah sumber kesesatan; dan kegelapan hati, pangkal penderitaan jiwa.(Bediuzzaman Said Nursi)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kebersamaan dalam suatu masyarakat menghasilkan ketenangan dalam segala kegiatan masyarakat itu, sedangkan saling bermusuhan menyebabkan seluruh kegiatan itu mandeg.(Bediuzzaman Said Nursi)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Menghidupkan kembali agama berarti menghidupkan suatu bangsa. Hidupnya agama berarti cahaya kehidupan.(Bediuzzaman Said Nur)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Orang yang terkaya adalah orang yang menerima pembagian (taqdir) dari Allah dengan senang hati.(Ali bin Husein)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Seseorang yang melihat kebaikan dalam berbagai hal berarti memiliki pikiran yang baik. Dan seseoran yang memiliki pikiran yang baik mendapatkan kenikmatan dari hidup.(Bediuzzaman Said Nur)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Pangkal dai semua kebaikan di dunia maupun di akhirat adalah taqwa kepada Allah.(Abu Sualeman Addarani)</span><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><b style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Kata Mutiara Islam</b><br style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;" /><span style="background-color: white; color: #333333; font-family: Verdana, sans-serif; font-size: 13px; line-height: 20px; text-align: justify;">Barang siapa tidak dicoba dengan bencana atau kesusahan, maka tidak ada sebuah kebahagiaan pun disisi Allah.(Adh-Dhahhak)</span>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-26167916354436603562012-01-15T02:42:00.000-08:002012-01-16T07:11:49.332-08:00Rumus Volume dan Luas Permukaan Bangun Ruang<br />
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<b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">Bangun
Ruang Sisi Lengkung</span></b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><o:p></o:p></span></div>
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<b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">a. Tabung
(Silinder )<o:p></o:p></span></b></div>
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<span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
Dalam tabung (silinder) berlaku rumus-rumus:<br />
i. d = 2r atau r = ½ d<br />
ii. La= Lb= πr 2 = ¼d2<br />
iii. L s= 2πrt = πdt<br />
iv. L p= L a+ Lb + L s= 2πr (r + t) = π d (d + t)<br />
v. V= Lb t = L a t = π r 2 t</span></div>
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<img src="http://t0.gstatic.com/images?q=tbn:ANd9GcQ_Wj0A69c-rReDaVYen8WhDmmj2b4KavXmJqJhDBToAz_zpYFq" /> <span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
dengan:<br />
r = jari-jari atas/alas tabung<br />
d = diameter atas/ alas tabung<br />
t= tinggi tabung<br />
La = luas bidang atas tabung<br />
Lb = luas bidang bawah/ alas/ dasar tabung<br />
Ls = luas selimut/ selubung tabung<br />
Lp= luas permukaan tabung<br />
V = volume/ isi tabung<o:p></o:p></span></div>
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<b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">b. Kerucut</span></b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
Dalam kerucut berlaku rumus-rumus:<br />
i. d = 2r atau r = ½ d<br />
ii. s2= t 2+ r 2<br />
iii. Lb= πr 2 = ¼πd2<br />
iv. L s= πrp = ½πds<br />
v. L s= Lb + L s= πr (r + s) =½ πd (d + s)<br />
vi. V = π/3 r 2 t<br />
vii. φ = r/p x 360<o:p></o:p></span></div>
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<img src="http://t1.gstatic.com/images?q=tbn:ANd9GcQ9ZnXr9vxcF5PLmgsvGy1PujMBZU7iam0reQB6vvx04weeN_uX" />
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<span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"></span><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">dengan:<br />
r= jari-jari alas kerucut<br />
d= diameter alas kerucut<br />
t = tinggi kerucut<br />s = panjang garis pelukis atau apotema<br />
Lb = luas bidang bawah/ alas/ dasar kerucut<br />
Ls = luas selimut/ selubung kerucut<br />
Ls= luas permukaan kerucut<br />
V = volume/ isi kerucut<br />
φ = sudut pusat rebahan<o:p></o:p></span></div>
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</span><b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">c. Kerucut Terpancung</span></b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
Dalam kerucut terpancung berlaku rumus-rumus:<br />
i. d1 = 2r1 atau r1 = ½ d 1<br />
ii. d2 = 2r2 atau r2 = ½ d 2<br />
iii. Lb= πr 12 = ¼ πd12<br />
iv. La= πr 22 = ¼ πd22<br />
v. L s= πp (r 1+ r 2)= ½πp (d1+ d2)<br />
vi. L p= Lb + La+ L s= πp(r 1+ r 2) + π p(r 12+ r 22)<br />
vii. V = π/3 t (r1 2+ r22 + r 1r2)</span></div>
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<img src="http://t3.gstatic.com/images?q=tbn:ANd9GcQMVIknHNKQ_FC_ibRoogSLOzjDIyO-Cd8bR-mnajOyu2UKfHRCFA" /> <span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
dengan:<br />
r1 = jari-jari bidang alas/ dasar/ bawah kerucut terpancung<br />
d1 = diameter bidang alas/ dasar/ bawah kerucut terpancung<br />
r2 = jari-jari bidang atas kerucut terpancung<br />
d2 = diameter bidang atas kerucut terpancung<br />
t = tinggi kerucut terpancung<br />
p = panjang garis pelukis atau apotema kerucut terpancung<br />
Lb = luas bidang bawah/ alas/ dasar kerucut terpancung<br />
La = luas bidang atas kerucut terpancung<br />
Ls = luas selimut/ selubung kerucut terpancung<br />
Lp = luas permukaan kerucut terpancung<br />
V = volume/ isi kerucut terpancung<o:p></o:p></span></div>
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<b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">d. Bola</span></b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
Dalam bola berlaku rumus-rumus:<br />
i. D = 2R atau R= ½ D<br />
ii. d = 2r atau r = ½ d<br />
iii. R2 = h2+ r 2<br />
iv. Lt = 2πRt = πDt<br />
v. L p= 4πR 2= πD2<br />
vi. V = 4π/ 3 R3= π/ 3D3<br />
vii. Vt= πt2 (3R- t)</span></div>
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<img src="http://t0.gstatic.com/images?q=tbn:ANd9GcSRi1nVmbdX71eBWpEfo_y8ZckxbSJz_vlLD73Le2YqzlEjJf1W8w" /> <span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
dengan:<br />
R = jari-jari bola<br />
D = diameter bola<br />
r = jari-jari bidang lingkaran<br />
d = diameter bidang lingkaran<br />
h = jarak pusat bola ke bidang lingkaran<br />
t = jarak dari pusat bidang lingkaran ke kulit bola<br />
Lp = luas permukaan bola<br />
Lt = luas bidang lengkung tembereng<br />
V = volume/ isi bola<br />
Vt = volume/ isi tembereng bola<o:p></o:p></span></div>
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<b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">2. Bangun
Ruang Sisi Datar<o:p></o:p></span></b></div>
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<b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">a. Kubus</span></b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
Dalam kubus berlaku rumus:<br />
ds= a √2<br />
dr= a √3<br />
Lp= 6 a 2<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">V = a^ 3<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">dengan:<br />
a = panjang rusuk kubus<br />
ds = panjang diagonal sisi kubus<br />
dr = panjang diagonal ruang kubus<br />
Lp = luas permukaan kubus<br />
V = volume/ isi kubuS<o:p></o:p></span></div>
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<b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">b. Balok</span></b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
Dalam balok berlaku rumus-rumus:<br />
d1= √ (p2 + l2)<br />
d2= √ (p2 + t2)<br />
d3= √ (l2 + t2)<br />
dr= √ (p2 + l2+ t2)<br />
Ls= 2 (p + l )t<br />
Lp= 2 (pl + pt + lt)<br />
V = plt<br />
dengan :<br />
p = panjang balok<br />
l = lebar balok<br />
t = tinggi balok<br />
d1 = panjang diagonal sisi alas/ atas<br />
d2 = panjang diagonal sisi depan/ belakang<br />
d3 = panjang diagonal sisi samping kiri/ kanan<br />
dr = panjang diagonal ruang balok<br />
Ls = luas selimut/ selubung balok<br />
Lp = luas permukaan balok<br />
V = volume/ isi balok<o:p></o:p></span></div>
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<b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">c. Prisma
Tegak</span></b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
Dalam prisma tegak berlaku rumus-rumus:<br />
Luas selimut/ selubung prisma tegak = keliling alas x panjang rusuk tegak<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">Luas permukaan prisma tegak<br />
Luas permukaan prisma tegak =<br />
luas selimut + luas bidang alas + luas bidang atas<br />
= luas selimut + 2 x luas bidang alas<br />
= luas selimut + 2 x luas bidang atas<br />
Volume prisma tegak= luas bidang bawah/ alas/ dasar x panjang rusuk tegak
(tinggi)<br />
= luas bidang atas x panjang rusuk tegak (tinggi)<o:p></o:p></span></div>
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<b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;">d. Limas
(Piramida)</span></b><span style="color: #333333; font-family: 'Arial Unicode MS', sans-serif; font-size: 10pt;"><br />
Dalam limas (piramida) berlaku rumus-rumus:<br />
Luas permukaan limas = luas alas + jumlah sisi tegak = luas alas + n x luas
sisi tegak<br />
Lp = Lb + n x L<br />
Volume limas = 1/3 luas alas x tinggi<br />
V = 1/3 Lb x t<o:p></o:p></span></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-33913732039894008972012-01-12T21:13:00.000-08:002012-01-16T07:12:16.462-08:00Persamaan Lingkaran , SMA<br />
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<span style="color: black;"><br />
<b>Persamaan Lingkaran :</b><o:p></o:p></span></div>
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<span style="color: black;"><b><br /></b></span></div>
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<a href="http://t0.gstatic.com/images?q=tbn:ANd9GcR6ZoeCzSHENYxLsSJiP7nV1gsWsjE8dICLWyMfzOLUaTEO5jI" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="http://t0.gstatic.com/images?q=tbn:ANd9GcR6ZoeCzSHENYxLsSJiP7nV1gsWsjE8dICLWyMfzOLUaTEO5jI" width="190" /></a><span class="Apple-style-span" style="color: #338813;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXiV46oFv7pLSljlTSAndMWEUGeLpH3Asw3O9dYN4RA72pbOs58Ln1Ic8bh6OJi-W_w2Bp8W1bd-rQ_BFvRNEnvPRMTD0qdY49hpH6qlchvcYDXZYOXit2DJhtdEgmbrrE1MIWG7Y3YygK/s1600/CodeCogsEqn%25281%2529.gif" /></span><br />
<b style="color: black;">Pusat = ( a,b)</b><br />
<b style="color: black;">Jari-jari = r</b><br />
<br />
Jika bentuk yang dalam kurung dikuadratkan maka.....<o:p></o:p></div>
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<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWXZw-kxWOyZeWXiV1cLi-1PhuRlwQlcWREMjLED96TyilUPBXqVwQoAuXld93niVwM-cE7L_0bJ080TDDTyPlJq3sb3rgADYp8_7V38nHQjtV6lmlEoMca4ojRKfZYRJP0qASqaLSpfOX/s1600/CodeCogsEqn%25282%2529.gif"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
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<span style="color: black;"><br />
<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWXZw-kxWOyZeWXiV1cLi-1PhuRlwQlcWREMjLED96TyilUPBXqVwQoAuXld93niVwM-cE7L_0bJ080TDDTyPlJq3sb3rgADYp8_7V38nHQjtV6lmlEoMca4ojRKfZYRJP0qASqaLSpfOX/s1600/CodeCogsEqn%25282%2529.gif" /><br />
<br />
<b>Pusat (P) dan jari-jari r :</b><o:p></o:p></span></div>
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<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixIBQw8d3K33vuB_W-b_3nUUVVB8DnGlpmj1skWzgJehj9aLbTNr4g5eMmFBY0gprNwQpg5Xf6WSFcrel2schOvtWrRXuQtTH6OTmkeAU7JyqqZ59nqcqlxF4xk5KDVbTXnNS2EOebYEQw/s1600/CodeCogsEqn%25283%2529.gif" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
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<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUpDND9UWpgHrPhvgQ1tZvV7OifNRV6ZD8yWa4yFFihhm0LYQvKEsEatNsoi3zuUyOsw53arznaZ8ASsc9uvqfzj8TVsbQiuQ2WsdBHC4HiqqGbD9fKca1LQDCxhCQ3sjV9TgvUekfh0Z0/s1600/CodeCogsEqn%25284%2529.gif" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
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<span style="color: black;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixIBQw8d3K33vuB_W-b_3nUUVVB8DnGlpmj1skWzgJehj9aLbTNr4g5eMmFBY0gprNwQpg5Xf6WSFcrel2schOvtWrRXuQtTH6OTmkeAU7JyqqZ59nqcqlxF4xk5KDVbTXnNS2EOebYEQw/s1600/CodeCogsEqn%25283%2529.gif" /><br />
<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUpDND9UWpgHrPhvgQ1tZvV7OifNRV6ZD8yWa4yFFihhm0LYQvKEsEatNsoi3zuUyOsw53arznaZ8ASsc9uvqfzj8TVsbQiuQ2WsdBHC4HiqqGbD9fKca1LQDCxhCQ3sjV9TgvUekfh0Z0/s1600/CodeCogsEqn%25284%2529.gif" /><br />
</span><br />
<a name='more'></a><span style="color: black;"><br />
<b>Catatan :</b><br />
dalam menentukan persamaan lingkaran sering digunakan rumus<b> </b><br />
<br />
<b>1. Jarak titik (x<sub>1</sub>,<sub>y1</sub>) ke titik (<sub>x2</sub>,<sub>y2</sub>)
adalah d maka :</b><br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFUDvBUx3XfkG6q3LQFxjAbCOAwKqdFIKIXpKtaM8WYHi69x3cgdRxfsYIwCJgGP_zki6gErlH4zXebBuO8Q8JY28Mu4xVN_X9so94rMqZ-pvjrXOEIapHt-D1MWIRPWFYhXRrlIuvHq-F/s1600/CodeCogsEqn%25285%2529.gif" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><br />
<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFUDvBUx3XfkG6q3LQFxjAbCOAwKqdFIKIXpKtaM8WYHi69x3cgdRxfsYIwCJgGP_zki6gErlH4zXebBuO8Q8JY28Mu4xVN_X9so94rMqZ-pvjrXOEIapHt-D1MWIRPWFYhXRrlIuvHq-F/s1600/CodeCogsEqn%25285%2529.gif" /><br />
<br />
<br />
<b>2. Jarak titik (p,q) ke garis Ax + By + C = 0 adalah d maka :</b><o:p></o:p></span></div>
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</div>
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</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJjXSSf5m2ks-yS5zQ4WLJwyhwW9FrMFB-ZxW1ClvPcy3lqQjVe8-7026rZbquLqXqhHOqBIaZVha6O0WAVb3JyfPDcRyvddnEPAOpwwNIOQ5Euwzyb6V4w_2FSysTUcDtwHl7IBnxNl9P/s1600/CodeCogsEqn%25286%2529.gif" imageanchor="1" style="float: left;"><span class="Apple-style-span" style="color: black;"><br /></span></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJjXSSf5m2ks-yS5zQ4WLJwyhwW9FrMFB-ZxW1ClvPcy3lqQjVe8-7026rZbquLqXqhHOqBIaZVha6O0WAVb3JyfPDcRyvddnEPAOpwwNIOQ5Euwzyb6V4w_2FSysTUcDtwHl7IBnxNl9P/s1600/CodeCogsEqn%25286%2529.gif" imageanchor="1" style="float: left;"><span class="Apple-style-span" style="color: black;"><br /></span></a><o:p></o:p></div>
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<span style="color: black;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJjXSSf5m2ks-yS5zQ4WLJwyhwW9FrMFB-ZxW1ClvPcy3lqQjVe8-7026rZbquLqXqhHOqBIaZVha6O0WAVb3JyfPDcRyvddnEPAOpwwNIOQ5Euwzyb6V4w_2FSysTUcDtwHl7IBnxNl9P/s1600/CodeCogsEqn%25286%2529.gif" /><br />
<br />
<br />
<b>Hubungan Lingkaran dengan Garis Lurus</b><br />
<br />
Persamaan garis<span class="apple-converted-space"> </span><b>y = px + q<span class="apple-converted-space"> </span></b>disubtitusikan ke dalam persamaan
lingkaran untuk menggantikan variabel y sehingga diperoleh persamaan kuadrat<span class="apple-converted-space"><b> </b></span><b>ax<sup>2</sup><span class="apple-converted-space"> </span>+ bx + c = 0<span class="apple-converted-space"> </span></b><br />
<br />
Hubungan keduanya dapat ditentukan dengan nilai<span class="apple-converted-space"> </span><b>diskriminannya ( D )</b><o:p></o:p></span></div>
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<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1O6vGi9CGHkCvDxCcMMOxMHSUJsrChdk9nVcDDsCz1ZaGWjJsnSS8D-js3NGZ4acyEHqgFEju9afCbsC6SPJjxAX8L6z_iRAhGcQyHpuc7ryuM7aZAaSMkUU422X9c_FZTY6qmgkZPnlN/s1600/CodeCogsEqn%25287%2529.gif" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
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<span style="color: black;"><o:p> </o:p></span><span class="Apple-style-span" style="line-height: normal;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1O6vGi9CGHkCvDxCcMMOxMHSUJsrChdk9nVcDDsCz1ZaGWjJsnSS8D-js3NGZ4acyEHqgFEju9afCbsC6SPJjxAX8L6z_iRAhGcQyHpuc7ryuM7aZAaSMkUU422X9c_FZTY6qmgkZPnlN/s1600/CodeCogsEqn%25287%2529.gif" /></span></div>
<ul type="disc">
<li class="MsoNormal" style="color: black; line-height: 19.2pt; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;">Jika
D > 0 → Persamaan garis berpotongan dengan lingkaran di dua titik<o:p></o:p></li>
<li class="MsoNormal" style="color: black; line-height: 19.2pt; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;">Jika
D = 0 → Persamaan garis bersinggungan dengan lingkaran<o:p></o:p></li>
<li class="MsoNormal" style="color: black; line-height: 19.2pt; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;">Jika
D < 0 → Persamaan raris tidak berpotongan/bersinggungan dengan
lingkaran<o:p></o:p></li>
</ul>
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<span style="color: black;"><br />
<b>Persamaan Garis Singgung Lingkaran</b><br />
<br />
1. Lingkaran<span class="apple-converted-space"><b> </b></span><b>( x - a )<sup>2</sup><span class="apple-converted-space"> </span>+ ( y - b )<sup>2</sup><span class="apple-converted-space"> </span>= r<sup>2</sup><span class="apple-converted-space"> </span></b>dengan gradien garis singgung<span class="apple-converted-space"> </span><b>m</b><o:p></o:p></span></div>
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<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz5XdAFr3q-Q-NmLFOoHrAz8dnW0Rh2cV4jq_iQRfSuM12WSY1nJuHjByuBuP5IH5dWUxBBxZG9AHcjH2kDmaznahTSMvqULfpX4IV-8_hBPUQaEJUC-_6-GbyFdRYFQDUfiBDZvJHYFP3/s1600/CodeCogsEqn%25288%2529.gif" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
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<span style="color: black;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz5XdAFr3q-Q-NmLFOoHrAz8dnW0Rh2cV4jq_iQRfSuM12WSY1nJuHjByuBuP5IH5dWUxBBxZG9AHcjH2kDmaznahTSMvqULfpX4IV-8_hBPUQaEJUC-_6-GbyFdRYFQDUfiBDZvJHYFP3/s1600/CodeCogsEqn%25288%2529.gif" /><br />
<br />
<br />
2. Persamaan garis singgung di titik<span class="apple-converted-space"><b> </b></span><b>(p,q)</b><span class="apple-converted-space"> </span>pada :<br />
a. Lingkaran<span class="apple-converted-space"> </span><b>( x - a )<sup>2</sup><span class="apple-converted-space"> </span>+ ( y - b )<sup>2</sup><span class="apple-converted-space"> </span>= r<sup>2</sup><span class="apple-converted-space"> </span></b>adalah :<o:p></o:p></span></div>
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<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5PlBzcK07yIA2KLOiVmHn2LBhpL6InHhd5ThtLaGcHqGtN-QAPf7UJkONqLj2opV0SPCwoCXp7ke7REI1f4kKEg_m9neX4wBz4-NUHJYDM-S5WSqmf0IGiddPrrOlMWnAWrUIgVlScjM-/s1600/CodeCogsEqn%252812%2529.gif" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
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<span style="color: black;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5PlBzcK07yIA2KLOiVmHn2LBhpL6InHhd5ThtLaGcHqGtN-QAPf7UJkONqLj2opV0SPCwoCXp7ke7REI1f4kKEg_m9neX4wBz4-NUHJYDM-S5WSqmf0IGiddPrrOlMWnAWrUIgVlScjM-/s320/CodeCogsEqn%252812%2529.gif" /><br />
<br />
<br />
b. Lingkaran<span class="apple-converted-space"> </span><b>x<sup>2</sup><span class="apple-converted-space"> </span>+ y<sup>2</sup><span class="apple-converted-space"> </span>+ Ax + By + C = 0</b><span class="apple-converted-space"> </span>adalah :<o:p></o:p></span></div>
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<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH9NvcSTZ49z1cycKBX6HjPzvqFf8AR43QNY-Wj6NSwrIEEJMUQOCI1DKBMW4qZM6rugGlepL_XMPfadHIY7RFXlhJT638hXnLCxf8FaYP6k2nYV7B8HYbfUYexJIwE5AZsYTlFYo5VqfU/s1600/CodeCogsEqn%252813%2529.gif" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH9NvcSTZ49z1cycKBX6HjPzvqFf8AR43QNY-Wj6NSwrIEEJMUQOCI1DKBMW4qZM6rugGlepL_XMPfadHIY7RFXlhJT638hXnLCxf8FaYP6k2nYV7B8HYbfUYexJIwE5AZsYTlFYo5VqfU/s320/CodeCogsEqn%252813%2529.gif" /><br />
<br />
<b>
</b><br />
<b>Sketsa Persamaan Lingkaran</b><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;">Seringkali
untuk menyelesaikan suatu persamaan lingkaran diperlukan kemampuan untuk
menggambarkan sketsanya sehinggga gambaran mengenai persamaan lingkaran
tersebut menjadi lebih jelas dan mudah difahami.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;">Coba
perhatikan penyelesaian soal - soal persamaan lingkaran di bawah ini :<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;">Tentukan
persamaan lingkaran yang :<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;">a.
berpusat di (2,-3) dan melalui titik (5,7)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;">b.
berpusat di (10,5) dan menyinggung sumbu y<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;">c.
berpusat di (-1,-2) dan menyinggung garis 4x + 3y + 5 = 0<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;">d.
pusatnya pada garis y = x - 3 dan menyinggung sumbu x di titik (5,0)<o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<b><span style="color: black;">Jawab
:</span></b><span style="color: black;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;">a.<o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal" style="line-height: 19.2pt; margin-bottom: 12.0pt;">
<span style="color: black;"><br />
<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZGwjGOIIVoIHeVGz7AjZJdHlY8a1VWj0Rbc6LBDMe6hD2Yj2bi-t3pcDsnZuPF-g694ku496H9LoE87f2iUq89YfhwNXnB-3GrKbm9GzFtdcMUNacW_yqfr-M4Gyq-7oJkF2rnbxdVvVK/s1600/mtk01.jpg" /><br />
<br />
<br />
Jari-jari lingkaran = r = jarak titik (2,-3) dengan titik (5,7)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibbsCzeKl3mbTcng31tzZtaGwdBEDabpZWAkpfUo-YbZ6qR8goQ6uVr7joyVAZyLKLNz3U2uhy5Ui1ltmMvId5AKZ5wiKH_vJHcU30xb8Q27jfy0v2MiLlID4BJwOF9mx2aGY9M3hpP-JO/s1600/CodeCogsEqn%252814%2529.gif" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibbsCzeKl3mbTcng31tzZtaGwdBEDabpZWAkpfUo-YbZ6qR8goQ6uVr7joyVAZyLKLNz3U2uhy5Ui1ltmMvId5AKZ5wiKH_vJHcU30xb8Q27jfy0v2MiLlID4BJwOF9mx2aGY9M3hpP-JO/s1600/CodeCogsEqn%252814%2529.gif" /><br />
<br />
<br />
sehingga persamaan lingkarannya :<br />
<br />
<b>( x - 2 )<sup>2</sup><span class="apple-converted-space"> </span>+ ( y +
3 )<sup>2</sup><span class="apple-converted-space"> </span>= 109<span class="apple-converted-space"> </span></b><br />
<br />
b.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnuTvHcmjcRifwfeiHwtWHReuX3TNfKxrrxSyTaYHknj9x161zGwM4ZZ6oevV0u0gTr9Ttt9A04dA6IxzsMa-PNY-v1szvY66oKZ6D0-pb_3bzEJc3FZOHCxHf5L01VOcTqD0iVB83EwNr/s1600/mtk02.jpg" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnuTvHcmjcRifwfeiHwtWHReuX3TNfKxrrxSyTaYHknj9x161zGwM4ZZ6oevV0u0gTr9Ttt9A04dA6IxzsMa-PNY-v1szvY66oKZ6D0-pb_3bzEJc3FZOHCxHf5L01VOcTqD0iVB83EwNr/s1600/mtk02.jpg" /><br />
karena menyinggung sumbu y maka jari-jarinya ( r) = absis (x) pusat
lingkarannya = 10<br />
<br />
sehingga persamaan lingkarannya :<br />
<br />
<b>( x - 10 )<sup>2</sup><span class="apple-converted-space"> </span>+ ( y -
5 )<sup>2</sup><span class="apple-converted-space"> </span>= 100</b><br />
<br />
<br />
c.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQJAaFmoJDn-PA9bxAV8jQM-yFdIsF8GN0VcQVc5duw7w06y8boOHGQkhULc-misLkPkJPO8uzvdHOBHBB0kcuEu6DRRitHM6Ul6Al8jUuPkwgXymO8bFvi3PbFMdS7HTCOjKNso_PsHog/s1600/mtk04.png" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"><br />
</span></a><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt; margin-bottom: 12.0pt;">
<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrhQ6P3rNjBADtn9vV1P8L1N4KYAgYmGjzHpsNVoIie8eDnisxRMSDUO9J8X2XOFVEoAGdjU14Wc2pzOTYrVNIiv_qPsDKMhUQ9d1EdUbzn-WWHef5aNCIlwrGpGlUoSjZ-Pd9-G-i0nkm/s1600/mtk04.jpg" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a>
<br />
<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrhQ6P3rNjBADtn9vV1P8L1N4KYAgYmGjzHpsNVoIie8eDnisxRMSDUO9J8X2XOFVEoAGdjU14Wc2pzOTYrVNIiv_qPsDKMhUQ9d1EdUbzn-WWHef5aNCIlwrGpGlUoSjZ-Pd9-G-i0nkm/s1600/mtk04.jpg" /><br />
<br />
<br />
<br />
r = jarak titik (-1,-2 ) ke garis 4x + 3y + 5 = 0<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAn_n3O9dJWetS2tGmdHbtE-UeBD9TEinzcPZBjcUNt9Gq7Lga29uEnQeUhV_ioo2MbrZHtmafH9fBphqtycDFbbdk9K8UYL-An7w5yTUYGP6QZjkpBo8_X1-eXd8kvNGXsGCxIkzC6V_h/s1600/CodeCogsEqn%252815%2529.gif" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt; margin-bottom: 12.0pt;">
<span style="color: black;"><br />
<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAn_n3O9dJWetS2tGmdHbtE-UeBD9TEinzcPZBjcUNt9Gq7Lga29uEnQeUhV_ioo2MbrZHtmafH9fBphqtycDFbbdk9K8UYL-An7w5yTUYGP6QZjkpBo8_X1-eXd8kvNGXsGCxIkzC6V_h/s1600/CodeCogsEqn%252815%2529.gif" /><br />
<br />
<br />
sehingga persamaan lingkarannya :<br />
<br />
<b>( x + 1 )<sup>2</sup><span class="apple-converted-space"> </span>+ ( y +
2 )<sup>2</sup><span class="apple-converted-space"> </span>= 1</b><br />
<br />
d.<o:p></o:p></span><span class="Apple-style-span" style="line-height: normal;"></span></div>
<div class="MsoNormal" style="line-height: 19.2pt; margin-bottom: 12.0pt;">
<span style="color: black;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0Mj2lSVfZ30CQPHqmWkHsLXJ0WBdOgaNo-LJ-bUrNcvzXreGNjJfce-3G6CbekQch7BdgZ28-tahnadhKPGycsNFllTKFk8Y7IoFAGcB95sUnKSbhzrRSSdYgip8ylynp6Bs9Pb-csYao/s320/mtk03.jpg" /></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0Mj2lSVfZ30CQPHqmWkHsLXJ0WBdOgaNo-LJ-bUrNcvzXreGNjJfce-3G6CbekQch7BdgZ28-tahnadhKPGycsNFllTKFk8Y7IoFAGcB95sUnKSbhzrRSSdYgip8ylynp6Bs9Pb-csYao/s1600/mtk03.jpg" imageanchor="1" style="float: left;"><span style="color: #338813; text-decoration: none;"></span></a><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.2pt;">
<span style="color: black;">dari
sketsa terlihat bahwa titik X pusatnya = titik singgungnya = 5<br />
kemudian dengan memasukkan nilai X = 5 ke persamaan garis y = x - 3 diperoleh
nilai Y pusatnya<br />
<br />
y = 5 - x = 5 - 3 = 2<br />
<br />
sehingga titik pusatnya = (5,2)<br />
<br />
karena menyinggung sumbu x maka jari-jarinya ( r) = ordinat (y) pusat
lingkarannya = 2<br />
<br />
sehingga persamaan lingkarannya :<br />
<br />
<b>( x - 5 )<sup>2</sup><span class="apple-converted-space"> </span>+ ( y -
2 )<sup>2</sup><span class="apple-converted-space"> </span>= 4</b><o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-16395622061697241012012-01-07T08:18:00.000-08:002012-01-16T07:12:36.162-08:00Persamaan Linier SMA<h3 class="post-title">
<br />
</h3>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; color: black; font-family: 'Times New Roman'; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
<b>Penyelesaian persamaan linier </b>dalam bentuk matriks dapat dilakukan melalui beberapa cara, yaitu dengan eliminasi Gauss atau dapat juga dengan cara eliminasi Gauss-Jordan. Namun, suatu sistem persamaan linier dapat diselesaikan dengan eliminasi Gauss untuk mengubah bentuk matriks teraugmentasi ke dalam bentuk eselon-baris tanpa menyederhanakannya. Cara ini disebut dengan substitusi balik.<b>Persamaan Linier<span class="Apple-converted-space"> </span></b>adalah salah satu materi matematika siswa SMA,</div>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; color: black; font-family: 'Times New Roman'; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
<br /></div>
<div class="separator" style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; clear: both; color: black; font-family: 'Times New Roman'; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; orphans: 2; text-align: center; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRZhquRdVr5ZvW-8TVPhP_TSXhAYdnFBtcnA6DOZbyUf0_vTO004I5Dz-SW2QOMo37iFFjK_WAgg9IJJyMidDvPVZftvonNM0q5lodgyxIe05jcFK33SmDD5p7Taac40nKjWOQgG7fFCMR/s1600/soal_matematika_Persamaan_linier.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRZhquRdVr5ZvW-8TVPhP_TSXhAYdnFBtcnA6DOZbyUf0_vTO004I5Dz-SW2QOMo37iFFjK_WAgg9IJJyMidDvPVZftvonNM0q5lodgyxIe05jcFK33SmDD5p7Taac40nKjWOQgG7fFCMR/s1600/soal_matematika_Persamaan_linier.png" style="cursor: move;" /></a></div>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; color: black; font-family: 'Times New Roman'; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
<br /></div>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; color: black; font-family: 'Times New Roman'; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b style="background-color: white; font-size: 13px; line-height: 19px;"><a href="http://www.blogger.com/goog_556700364">Persamaan linear</a></b><span class="Apple-style-span" style="background-color: white; font-size: 13px; line-height: 19px;"><a href="http://soaljawabanujian.blogspot.com/"> </a>adalah sebuah </span><b><a href="http://id.wikipedia.org/wiki/Persamaan" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: none; background-origin: initial; color: #0645ad; font-size: 13px; line-height: 19px; text-decoration: none;" title="Persamaan">persamaan</a><span class="Apple-style-span" style="background-color: white; font-size: 13px; line-height: 19px;"> </span><a href="http://id.wikipedia.org/wiki/Aljabar" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: none; background-origin: initial; color: #0645ad; font-size: 13px; line-height: 19px; text-decoration: none;" title="Aljabar">aljabar</a></b><span class="Apple-style-span" style="background-color: white; font-size: 13px; line-height: 19px;">, yang tiap sukunya mengandung konstanta, atau perkalian konstanta dengan </span><a href="http://id.wikipedia.org/wiki/Variabel" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: none; background-origin: initial; color: #0645ad; font-size: 13px; line-height: 19px; text-decoration: none;" title="Variabel">variabel</a><span class="Apple-style-span" style="background-color: white; font-size: 13px; line-height: 19px;"> tunggal. Persamaan ini dikatakan linear sebab hubungan matematis ini dapat digambarkan sebagai garis lurus dalam </span><a href="http://id.wikipedia.org/wiki/Sistem_koordinat_Kartesius" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: none; background-origin: initial; color: #0645ad; font-size: 13px; line-height: 19px; text-decoration: none;" title="Sistem koordinat Kartesius"><b>Sistem koordinat Kartesius</b></a><span class="Apple-style-span" style="background-color: white; font-size: 13px; line-height: 19px;">.</span></span></div>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; color: black; font-family: 'Times New Roman'; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
<span class="Apple-style-span" style="background-color: white; font-size: 13px; line-height: 19px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br />
</span></span></div>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; color: black; font-family: 'Times New Roman'; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
<br /></div>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: white; color: black; font-family: 'Times New Roman'; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; margin-bottom: 0.5em; margin-top: 0.4em; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Bentuk umum untuk persamaan linear adalah</span></div>
</div>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: white; color: black; font-family: 'Times New Roman'; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; margin-bottom: 0.5em; margin-top: 0.4em; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">y + mx =b </span></div>
</div>
<dl style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: white; color: black; font-family: 'Times New Roman'; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; margin-bottom: 0.5em; margin-top: 0.2em; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 2em;"><br />
<a name='more'></a><br /></dd></dl>
<div style="-webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: white; color: black; font-family: 'Times New Roman'; font-size: 13px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; margin-bottom: 0.5em; margin-top: 0.4em; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">
<div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Dalam
hal ini, konstanta m akan menggambarkan gradien garis, dan konstanta b
merupakan titik potong garis dengan sumbu-y. Persamaan lain, seperti <i>x</i><sup style="line-height: 1em;">3</sup>,<i>y</i><sup style="line-height: 1em;">1/2</sup>, dan <span class="texhtml" dir="ltr" style="font-size: 15px; line-height: 1em;"><i>x</i><i>y</i></span> bukanlah persamaan linear.</span></div>
</div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-19910866249734951642012-01-07T08:15:00.001-08:002012-01-16T07:14:02.435-08:00Prisma Bangun Ruang Rumus SD SMP SMA<h3 class="post-title">
<br />
</h3>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5FRL-qhf9nzBwwtQBhfsQcOVKQU3rL7PNRI6r5teunQPzmH2SggmkA0n2PII6hFNOXu6w625RUqWrKwNxiQI-uVyOo48ny07gB0xwR_FHEaU_n8qsLmqcRTl98411BWW6KvdxR9UZXcY/s1600/Prisma+tegak+segitiga.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5FRL-qhf9nzBwwtQBhfsQcOVKQU3rL7PNRI6r5teunQPzmH2SggmkA0n2PII6hFNOXu6w625RUqWrKwNxiQI-uVyOo48ny07gB0xwR_FHEaU_n8qsLmqcRTl98411BWW6KvdxR9UZXcY/s1600/Prisma+tegak+segitiga.jpg" /></a></div>
<br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;"><b><a href="http://soaljawabanujian.blogspot.com/" target="_blank">Prisma</a></b> adalah bangun ruang yang dibatasi oleh dua bidang berhadapan yang sama dan</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">sebangun atau kongruen dan sejajar, serta bidang - bidang lain yang berpotongan menurut</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">rusuk - rusuk yang sejajar.</span><br />
<br />
<b>Prisma Menurut Nama</b><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">Prisma diberi nama berdasarkan bentuk segi - n pada bidang alas atau bidang atas.</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">Contoh : Prisma segiempat, karena bidang alas dan atas berbentuk segiempat.</span><br />
<br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">Rusuk - rusuk pada prisma tegak lurus terhadap bidang alas mapun bidang atas, sehingga</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">disebut dengan </span><em style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">prisma tegak.</em><br />
<em style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;"></em><br />
<em style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;"></em><span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;"><b>Bidang - bidang tegak pada berbentuk persegi panjang</b></span><br />
<br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">Contoh : Prisma segienam ABCDEF.GHIIJKL</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">- Bidang ABCDEF merupakan bidang alas dan bidang GHIJKL merupakan bidang atas, </span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">berbentuk segienam.</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">- Bidang - bidang tegaknya adalah ABHG, BCIH, CDJI, DEKJ, EFLK, dan FAGL berbentuk</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">persegi panjang</span><br />
<a name='more'></a><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">- Rusuk - rusuk tegak adalah AG, HB, IC, JD, KE dan LF</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">- Rusuk - rusuk yang lainnya adalah AB< BC, CD. DE. EF. FA, GH, HI, IJ, JK, KL, dan LG</span><br />
<br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">Bidang diagonal dibentuk oleh dua pasang garis dan dua pasang diagonal bidang.</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">Bidang diagonal suatu prisma berbentuk persegi panjang.</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; text-align: left;">Contohnya : bidang ACJL, CFLI, dll</span>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-42341868013429480682012-01-07T08:13:00.000-08:002012-01-16T07:14:35.660-08:00LIMAS Bangun ruang Rumus SD, SMP, SMA<h3 class="post-title">
<br />
</h3>
<div class="separator" style="clear: both; text-align: center;">
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<span style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;"><b><br /></b></span><br />
<span style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;"><b>LIMAS</b></span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;"><b>limas </b>adalah bangun ruang yang dibatasi oleh sebuah <b>segitiga ataupun segibanyak </b>sebagai</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">alas dan beberapa buah bidang berbentuk segitiga sebagai bidang tegak yang bertemu pada</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">satu titik puncak.</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">limas diberi nama berdasarkan bentuk segi - n pada bidang alas.</span><br />
<br />
<a name='more'></a><br /><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">Contoh : <b>Limas segilima T.ABCDE</b></span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">- bidang ABCDE sebagai bidang alas berbentuk segilima dan titik T sebagai titik puncak.</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">- bidang tegaknya adalah bidang TAB, TBC, TCD, TDE, dan TAE berbentuk segitiga.</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">- Rusuk - rusukk tegaknya adalah TA, TB. TC, TD, dan TE</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">- Rusuk - rusuk lainnya adalah AB, BC, CD, DE, dan AE.</span><br />
<br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">Bidang - bidang diagonal suatu limas berbentuk segitiga.</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">Contoh : pada limas segiempat O.ABCD, Bidang BDO merupakan bidang diagonal.</span><br />
<span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">Bidang BDO dibentuk oleh rusuk BO dan DO serta diagonal bidanag BD</span><br />
<br />
<b style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">Luas Permukaan Limas</b><span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;"> = luas alas + jumlah luas segitiga bidang tegak</span><br />
<br />
<b style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;">Volume Limas</b><span class="Apple-style-span" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; line-height: 18px; text-align: left;"> = 1/3 x luas alas x tinggi</span>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-18280164464586244922012-01-07T08:04:00.001-08:002012-01-16T07:15:08.548-08:00Rumus dan SIfat Bangun Datar Segitiga<h3 class="post-title entry-title" style="background-color: white; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 5px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left;">
<span class="Apple-style-span" style="color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: xx-small;"><span class="Apple-style-span" style="line-height: 18px;"><br /></span></span></h3>
<div class="separator" style="clear: both; text-align: center;">
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<h3 class="post-title entry-title" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 16px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 5px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left;">
<span class="Apple-style-span" style="font-size: 13px; font-weight: normal; line-height: 18px;"><br /></span></h3>
<h3 class="post-title entry-title" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 16px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 5px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left;">
<span class="Apple-style-span" style="font-size: 13px; line-height: 18px;">Suatu segitiga</span><span class="Apple-style-span" style="font-size: 13px; font-weight: normal; line-height: 18px;"> dapat dilukis, jika diketahui :</span></h3>
<div class="post-body entry-content" style="background-color: white; color: #555555; font-family: tahoma, 'Trebuchet MS', lucida, helvetica, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 1em; margin-top: 5px; text-align: left;">
<div style="margin-bottom: 1em; margin-top: 5px;">
1. tiga buah sisinya (sisi, sisi, sisi)<br />
2. dua sisi dan satu sudut yang diapit sisi -sisi yang diketahui (sisi, sudut, sisi)<br />
3. dua sisi dan satu sudut yang menghadap salah satu sisi yang diketahui ( sisi, sisi, sudut)<br />
4. satu sisi dan dua sudut yang terletak pada sisi yang diketahui (sudut, sisi, sudut)<br />
<span class="fullpost" style="display: inline;"><br /><br /><br />Untuk setiap segitiga berlaku : <em><strong>jumlah dua sisi selalu lebih panjang dari sisi ketiga</strong></em><br /><strong><em></em></strong><br />Untuk setiap segitiga berlaku :<br />1. sudut terbesar menghadap sisi terpanjang<br />2. sudut terkecil menghadap sisi terpendek<br />3. sudut yang sedang menghadap sisi yang sedang.<br /><br />jenis - jenis segitiga<br />1. Ditinjau panjang sisi - sisinya<br />a. segiitiga sembarang<br />b. segitiga sama kaki<br />c. segitiga sama sisi</span><br />
<a name='more'></a><span class="fullpost" style="display: inline;"><br />2. Ditinjau dari besar sudutnya<br />a. segitiga lancip<br />b. segitiga siku - siku<br />c. segitiga tumpul<br /><br />Segitiga Istimewa<br />1. Segitiga samakaki<br />adalah segitiga yang memiliki dua sisi yang sama panjang<br />sifat - sifat :<br />a. memiliki dua sisi yang sama panjang<br />b. memiliki dua sudut yang sama besar<br /><br />2. Segitiga samasisi<br />adalah segitiga yang semua sisinya sama panjang.<br />sifat - sifat :<br />a. memiliki tiga sisi yang sama panjang<br />b. memiliki tiga sudut yang sama besar yaitu 60 derajat<br />Luas = 1/4 x s x akar 3<br /><br />Garis - garis Istimewa segitiga<br />1. Garis tinggi adalah garis yang ditarik dari titik sudut suatu segitiga dan tegak lurus<br />terhadap sisi di hadapannya.<br /><br />2. Garis Bagi adalah garis yang ditarik dari titik sudut suatu segitiga dan membagi sudut itu<br />menjadi dua bagian yang sama besar.<br /><br />3. Garis sumbu adalah garis yang ditarik dari pertengahan sisi suatu segitiga dan tegak lurus<br />dengan sisi itu.<br /><br />4. Garis Berat adalah garis yang ditarik dari titik sudut suatu segitiga ke pertengahn sisi<br />dihadapannya.<br /><br />Jumlah sudut dalam setiap segitiga adalah 180 derajat.<br /><br />Besar sudut luar segitiga sama dengan jumlah sudut dalam yang tidak berpelurus dengan<br />sudut tersebut.<br /><br />Keliling segitiga = jumlah ketiga sisi - sisinya.<br /><br />Luas segitiga = 1/2 x alas x tinggi<br /><br />Luas segitga sembarang = akar s x (s - a) x (s - b) x (s - c)<br /><br />Dimana s = 1/2 x keliling segitiga</span></div>
</div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-9700666849662458202011-12-27T21:53:00.000-08:002012-01-15T01:55:49.936-08:00Trik Perkalian<link href="file:///C:%5CUsers%5CHIDAYA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><link href="file:///C:%5CUsers%5CHIDAYA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CUsers%5CHIDAYA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link>
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<b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Trik
Perkalian 11 </span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Mungkin perkalian 1 x 11 sampai 9 x
11 sudah kalian hafal.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Karena itu sangat gampang, contoh:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">1 x 11 = 11<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">8 x 11 = 88<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">9 x 11 = 99<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Memang itu gampang, tetapi bagaimana
kalau perkalian 10 x 11 sampai 20 x 11?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Caranya:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">12 x 11<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Tulis angka yang akan dikalikan 11
tapi kosongkan tengahnya!<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">1_2 (Perhatikan. Di antara 1 dan 2
ada ruang kosong)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Maksud “_” adalah ruang kosong
antara 1 dan 2. Jadi bila menulis di buku, gantilah “_” dengan spasi / tempat
kosong<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Lalu coba jumlahkan kedua angka itu
( 1 + 2).<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Hasilnya pasti 3 kan?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Lalu taruh angka 3 di antara kedua
angka itu. Lalu itu akan menjadi seperti ini:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Sebelum = 1_2<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Sesudah = 132<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Tapi apabila perkalian 19 x 11
bagaimana caranya?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Caranya:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Isikan tempat kosong di antara 1 dan
9 (1_9).<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Lalu hitung 1 + 9.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Hasilnya pasti 10 kan? Tapi jangan
menjawab hasil dari 19 x 11 = 1109!<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Tapi caranya begini:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Tulis dahulu di kertas orak-orek
angka 10. Lalu masukan angka akhirnya (0) jadinya seperti ini: 109.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Tapi bagaimana dengan angka 1 nya?
Caranya tambahkan angka akhir dari 19 (1 nya) dengan angka 1 nya (sisanya).<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">1 + 1 tentu hasilnya 2 kan? Nah,
sekarang kita ganti angka terakhir dari 109 menjadi 2 dan hasilnya menjadi
seperti ini:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">209. Coba hitung dengan cara
menyusun. Hasilnya pasti 209. Gampangkan!</span></div>
<div class="MsoNormal" style="line-height: normal;">
<br /></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Trik
Perkalian 25 </span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Perkalian 25 memang sangat susah<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Tapi kalau memakai trik ini, pasti
lebih gampang!<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Triknya:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><yang akan dikalikan 25> : 4 x
100<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Apabila sisanya 0, angka 00nya tetap
menjadi 00<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Apabila sisanya 1, angka 00nya
menjadi 25<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Apabila sisanya 2, angka 00nya menjadi
50<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Apabila sisanya 3, angka 00nya
menjadi 75<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Contoh:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">25 x 12 = …….<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Caranya:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">12:4×100 =<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">3×100 = 300<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Karena sisa dari 12 dibagi 4 tidak
ada (0), maka 00 tetap menjadi 00<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Jadi hasilnya 300!<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Coba hitung dengan menyusun, pasti
benar<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Contoh 2:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">25 x 11 =….<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Caranya:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">11:4×100 =<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">2 (sisanya 3)x100 = 200<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Karena 11 dibagi 4 mempunyai sisa 3,
maka angka 00 dari bilangan 200 menjadi 75<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Jadi hasilnya 275!<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Coba hitung dengan menyusun, pasti
benar!!!!</span></div>
<div class="MsoNormal" style="line-height: normal;">
<br /></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Trik lainnya<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Tentu kita dapat menghitungnya
dengan cara seperti biasa. Kita juga dapat menyelesaikannya dengan kalkulator.
Tetapi apa kreatifnya? Apa asyiknya? Ini lah cara asyiknya! <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">54<sup>2</sup> = 2916<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">29 kita peroleh dari 25 + 4<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">16 kita peroleh dari 4<sup>2</sup> <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">56<sup>2</sup> = 3136<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">31 kita peroleh dari 25 + 6<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">36 kita peroleh dari 6<sup>2</sup> <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">57<sup>2</sup> = 3249<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">32 kita peroleh dari 25 + 7<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">49 kita peroleh dari 7<sup>2</sup><o:p></o:p></span></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-30466564746181258892011-12-27T21:44:00.001-08:002012-01-15T01:56:02.231-08:00Cara hitung cepat dengan angka 9<link href="file:///C:%5CUsers%5CHIDAYA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><link href="file:///C:%5CUsers%5CHIDAYA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CUsers%5CHIDAYA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link>
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<span style="color: black; font-family: 'Times New Roman', serif;">Karena setiap bilangan sembarang jika
dikalikan 9 maka jumlah hasilnya = 9<br />
maka :</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.3pt; margin-bottom: 0.0001pt;">
<span style="color: black; font-family: 'Times New Roman', serif;">1 x 9 = 9<br />
2 x 9 = 18, jumlah 1 + 8 = 9<br />
3 x 9 = 27, jumlah 2 + 7 = 9<br />
4 x 9 = 36, jumlah 3 + 6 = 9<br />
dan seterusnya......................</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.3pt; margin-bottom: 0.0001pt;">
<span style="color: black; font-family: 'Times New Roman', serif;"><br />
<b>Cara hitung cepat dengan angka 9 :</b><br />
Contoh : 22 x 9 = 198,<br />
( cara cepatnya 2 x 9 = 18, lalu selipkan angka 9 ditengah ), jadi jumlahnya
adalah <b>198</b></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.3pt; margin-bottom: 0.0001pt;">
<span style="color: black; font-family: 'Times New Roman', serif;">simak cara cepatnya berikut ini :<br />
33 x 9 = 297 ( cara cepat 3 x 9 = 27, selipkan 9 ditengah )<br />
44 x 9 = 3<b>9</b>6<br />
55 x 9 = 4<b>9</b>5<br />
66 x 9 = 5<b>9</b>4<br />
77 x 9 = 6<b>9</b>3<br />
88 x 9 = 7<b>9</b>2<br />
99 x 9 = 8<b>9</b>1<br />
lalu bagaimana jika dengan 3 angka kembar, selipkan saja angka 99
ditengahnya.<br />
Contoh :</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 19.3pt; margin-bottom: 0.0001pt;">
<span style="color: black; font-family: 'Times New Roman', serif;">222 x 9 = 1998 (cara cepat 2 x 9= 18, selipkan
99 ditengah )<br />
333 x 9 = 2<b>99</b>7<br />
444 x 9 = 3<b>99</b>6<br />
555 x 9 = 4<b>99</b>5</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
</div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-86161858416908208412011-12-25T03:16:00.000-08:002011-12-25T03:16:12.238-08:00Rumus Cepat Matematika (Aljabar) Menjadi Idaman<br />
<h3 style="background: white; margin-bottom: .0001pt; margin: 0in;">
<span style="color: blue;"><span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;"><span style="font-family: 'Kristen ITC';"><span style="font-weight: normal;"><br /></span></span></span></span></h3>
<div class="MsoNormal" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; margin-bottom: 0.0001pt;">
<span style="color: blue;"><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Anak-anak sangat menyukai matematika. Mereka minta terus dikasih
soal. Saya sendiri heran, mengapa mereka begitu semangat?<br />
“Lagi Pak. Kasih soal lagi Pak!” anak-anak menantang saya.<br />
“306 x 303 = …” saya keluarkan soal.<br />
“Sembilan…dua tujuh…delapan belas!” jawab mereka ramai-ramai.<br />
“Maksudnya berapa?”<br />
“92718”<br />
“Betul!”<br />
<br />
Anak-anak yang terdiri dari kelas 3 sampai kelas 5 SD itu senang menemukan cara
berhitung cepat perkalian ratusan kali ratusan. Bagi mereka itu adalah rumus
cepat matematika yang diidam-idamkan. Anak-anak SMA yang menjelang UN, SPMB,
dan UMPTN 2008 juga tidak kalah semangat. Jika mereka memperoleh rumus
matematika cepat untuk UN, SPMB, dan UMPTN maka matanya langsung
berbinar-binar. Wajahnya berseri-seri.<br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Saya sering mengatakan kepada mereka,</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">”Maukah kalian dapat soal bonus?”</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">”Apa itu soal bonus?”</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">”Soal UN, SPMB, atau UMPTN yang selalu dapat
kamu selesaikan dengan mudah.”</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">”Ya maulah…”</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">”Limit.”</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Limit kan sangat abstrak dan sulit? Bagaimana
bisa dikatakan sebagai bonus? Itulah intinya. Limit adalah ide fundamental
dalam kalkulus. Karena limit sangat kaya akan variasi dan abstrak bagi orang
awam, maka limit hanya diperkenalkan bagian dasar saja untuk anak tingkat SMA.
Jadi limit tingkat SMA tentu yang mudah-mudah saja. Limit adalah bonus. Rumus
cepat adalah terhormat.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Bagaimana jika terjadi komersialisasi rumus
cepat? Saya tidak tahu jawabannya. O iya, saya jadi ingat dengan berhitung
cepat yang paling awal tadi bagaimana caranya?</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Sekedar contoh rumus cepat untuk limit.
Kadang orang menyebut rumus cepat sebagai trik cepat, fastest solution, king of
fastest, atau rumus sesat. Boleh-boleh saja. Soal berikut ini sangat mudah.
Sudah pernah diujikan untuk tes masuk ITB sejak tahun 70-an. Tetapi entah
mengapa, soal limit tipe ini tetap sering diujikan sampai sekarang. Benar-benar
bonus untuk kita.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Untuk limit x menuju 0 hitunglah</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">(tg5x)/(sin3x) = …</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Bagi orang awam jawabannya sangat mudah yaitu
5/3.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Apakah Anda yakin itu jawaban yang benar?</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Banyak anak-anak karena ragu, karena dirasa
terlalu mudah, malah tidak mau menjawab dengan 5/3.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Mari kita diskusikan!</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Untuk membahasnya kita perlu ke dasar-dasar
limit trigonometri. Sudah banyak dibuktikan dalam buku-buku bahwa untuk limit x
menuju 0 berlaku:</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">(sinx)/x = 1;</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">(tgx)/x = 1;</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Biasanya anak-anak harus hafal rumus di atas.
Bagi saya rumus ini adalah rumus cepat limit. Tetapi rumus ini beruntung. Ia
tidak pernah disebut sebagai rumus sesat. Ia mendapat gelar kehormatan sebagai
rumus dasar limit trigonometri. Dengan rumus dasar limit trigonometri ini kita
akan memecahkan</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">(tg5x)/(sin3x) =</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">[(tg5x)(5x/5x)]/[(sin3x)(3x/3x)] =</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">[(tga)(a/a)]/[(sinb)(b/b)]</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">dengan a = 5x dan b = 3x;</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">gunakan rumus dasar trigonometri:</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">[1.a]/[1.b] =</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">[5x]/[3x] =</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">= 5/3 (Selesai)</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Kita peroleh jawaban 5/3 sesuai tebakan awal
kita.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Apakah kita selalu boleh melakukan tebakan
semacam itu? Boleh. Tebakan ini sah. Kita mendasarkan pada rumus dasar limit
trigonometri dengan menambah satu langkah implikasi.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Karena (sinx)/x = 1 maka (sinx) = x;</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">karena (tgx)/x = 1 maka (tgx) = x.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Jadi rumus dasar trigonometri yang kita hafal
adalah</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">sinx = x;</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">tgx = x.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Dengan sedikit mengubah cara pandang ini akan
membawa keberuntungan besar pada UN, SPMB, UMPTN 2008. Siswa-siswa SMA,
mestinya tidak asing dengan cara pandang ini. Kita telah memakai cara pandang
ini ketika menghitung interferensi gelombang Young dalam fenomena fisika.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Jadi bila kita terapkan ke soal di atas:</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">(tg5x)/(sin3x) = 5x/3x = 5/3 (Selesai).</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Rumus cepat di atas akan semakin bernilai
bila bentuk soalnya semakin rumit seperti</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">(2x + tg3x)/(x + sin7x) =…</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">(2x + 3x)/(x + 7x) = 5/8 (Selesai).</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Rumus cepat matematika bukan hal baru. Dalam
sejarah matematika tercatat bahwa masyarakat memang mengidolakan rumus-rumus
cepat matematika. Saat itu rumus-rumus cepat tidak dipandang sebagai rumus
sesat. Pun yang menguasai rumus-rumus cepat adalah para ahli matematika itu
sendiri.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Pada tahun 1535 Tartagtila mengikuti
pertandingan berhitung cepat. Ia melawan murid dari seorang profesor matematika
ternama. Tartagtila tidak begitu dikenal di dunia matematika waktu itu. Ia
mempelajari matematika nyaris secara mandiri. Tetapi Tartagtila memiliki
keistimewaan: ia memiliki rumus cepat untuk memecahkan persamaan polinom
pangkat 3.</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><br />
<br />
</span><span style="font-family: 'Kristen ITC'; font-size: 10.5pt;">Aturan pertandingan itu sederhana.
Masing-masing peserta menuliskan 30 soal matematika. Kemudian soal itu
diserahkan kepada lawan untuk diselesaikan. Siapa saja yang mampu menyelesaikan
soal lebih awal dan benar maka ia sebagai pemenang. Setelah 2 jam pertandingan
berlangsung. Tartagtila berhasil menyelesaikan seluruh 30 soal yang
dihadapinya. Sedangkan lawannya belum mampu menyelesaikan soal satu pun.
Tartagtila mampu menyelesaikannya karena menggunakan rumus cepat. Sedangkan
lawannya tidak memiliki rumus cepat. Tartagtila meraih berbagai kehormatan
setelah pertandingan itu.</span><span style="font-family: "Kristen ITC"; font-size: 10.5pt; mso-bidi-font-family: "Arial Unicode MS"; mso-fareast-font-family: "Arial Unicode MS";"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial;">
<span style="font-family: 'Kristen ITC'; font-size: 10.5pt;"><span style="color: blue;">Bagaimana seorang anak kecil dapat menghitung
306 x 303 luar kepala? Caranya mudah!<br />
Bagi anak SMP sudah mengenal bahwa<br />
(x+2)(x+3)=<br />
x.x + (2x+3x) + 2.3 =<br />
<br />
Mirip dengan itu caranya:<br />
306 x 303 =<br />
9 (dari 3×3)<br />
27 (dari 6×3 + 3×3)<br />
18 (dari 6×3)<br />
Kita peroleh jawaban 92718.<br />
<br />
Contoh lain<br />
207 x 304 = …<br />
6 (dari 2×3)<br />
29 (dari 7×3 + 2×4)<br />
28 (dari 7×4)<br />
Kita peroleh 62928.</span></span><span style="font-family: "Kristen ITC"; font-size: 12.0pt; mso-bidi-font-family: "Arial Unicode MS"; mso-fareast-font-family: "Arial Unicode MS";"><o:p></o:p></span></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-22401939218951772972011-12-25T03:09:00.001-08:002012-01-15T01:56:15.669-08:00CARA MENGUASAI RUMUS CEPAT MATEMATIKA<br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; color: blue; font-family: 'Microsoft Sans Serif', sans-serif;">Bagaimana
cara belajar matematika yang benar?”<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">“Belajar matematika adalah belajar hidup.
Matematika adalah jalan hidup.”</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Trachtenberg mempertaruhkan jiwanya menentang
Hitler. Trachtenberg, setelah menyelami prinsip-prinsip matematika,
menyimpulkan bahwa prinsip kehidupan adalah keharmonisan. Peperangan yang terus
berkobar, menyulut kebencian tidak sesuai dengan prinsip-prinsip matematika.
Matematika adalah keindahan.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Atas penentangannya ini, Hitler menghadiahi
Trachtenberg hukuman penjara. Bagi Trachtenberg, perjara bukan apa-apa. Di
dalam penjara, dia justru memiliki kesempatan memikirkan matematika tanpa
banyak gangguan. Karena sulit mendapatkan alat tulis-menulis, Trachtenberg
mengembangkan pendekatan matematika yang berbasis mental-imajinasi.</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Seribu tahun sebelum itu, AlKhawaritzmi
mengembangkan disiplin matematika baru: aljabar. AlKharitzmi beruntung hidup
dalam lingkungan agama Islam yang kuat. Ajaran Islam, secara inheren, menuntut
keterampilan matematika tingkat tinggi. Misalnya, Islam menetapkan aturan
pembagian waris yang detil. Pembagian waris sistem Islam melibatkan banyak
variabel matematis. Variabel-variabel yang beragam ini menantang penganut Islam
– termasuk AlKhawaritzmi – untuk mencari pemecahan yang elegan.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Pemecahan terhadap sistem persamaan yang
melibatkan banyak variabel ini membawa ke arah disiplin baru matematika:
aljabar. AlKhawaritzmi menulis buku khusus tentang aljabar yang sangat
fenomenal. Buku yang berjudul Aljabar ini menjadi panutan bagi matematikawan
seluruh dunia. Sehingga nama AlKhawaritzmi menjadi dikenal sebagai Aljabar
AlKhawaritzmi (Algebra Algorithm).<o:p></o:p></span></span></div>
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<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Sistem kalender Islam yang berbasis pada
komariah (bulan, lunar) memberikan tantangan tersendiri. Penetapan awal bulan
menjadi krusial di dalam Islam. Berbeda dengan kalender syamsiah (matahari,
solar). Dalam kalender syamsiah, kita tidak begitu sensitif apa berbedaan
tanggal 1 Juni dengan 2 Juni. Tetapi pada sistem komariah, perbedaan 1 Ramadhan
denga 2 Ramadhan berdampak besar.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Itulah sebabnya, astronomi Islam dapat maju
lebih awal. Astronomi memicu lebih berkembangnya teori trigonometri. Aturan
sinus, cosinus, dan kawan-kawan berkembang pesat di tangan para astronom Islam
waktu itu.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Ajaran agama Islam adalah jalan hidup. Untuk
bisa melaksanakan ajaran Islam diperlukan matematika. Matematika menjadi jalan
hidup.</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Sehebat itukah peran matematika?<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Haruskah kita mengambil matematika sebagai jalan
hidup?</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Tidak selalu! Tidak semua orang perlu mengambil
matematika sebagai jalan hidup. Tidak harus semua orang meniru AlKhawaritzmi
dan Trachtenberg.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="color: blue;"><span style="font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Beberapa orang belajar matematika hanya untuk
kesenangan. Beberapa orang yang lain belajar karena kewajiban. Ada pula yang
belajar matematika agar naik jabatan. Ada juga agar lulus UN, SPMB, UMPTN. Ada
juga untuk menjadi juara.</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Masing-masing tujuan, berimplikasi kepada cara
belajar matematika yang berbeda. Misalnya bila Anda belajar matematika untuk
kepentingan lulus UN, SPMB, UMPTN 2008 akan berbeda dengan belajar untuk
memenangkan olimpiade matematika.</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Matematika UN, SPMB, UMPTN 2008 hanya menerapkan
soal pilihan ganda. Implikasinya Anda hanya dinilai dari jawaban akhir Anda.
Proses Anda menemukan jawaban itu tidak penting. Jadi Anda harus memilih siasat
yang cepat dan tepat.</span></span><span style="font-family: 'Microsoft Sans Serif', sans-serif;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="background: white; mso-background-themecolor: background1;">
<span style="color: blue;"><span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: 'Microsoft Sans Serif', sans-serif;">Gunakan berbagai macam rumus
cepat dalam matematika. Rumus cepat ampuh Anda gunakan untuk UN, SPMB, UMPTN.
Tetapi rumus cepat matematika tidak akan berguna untuk olimpiade atau kuliah
kalkulus kelak di perguruan tinggi. Anda harus sadar itu.</span><span style="font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Contoh rumus cepat matematika yang sering
(hampir selalu) berguna ketika UN, SPMB, UMPTN adalah rumus tentang deret
aritmetika.<o:p></o:p></span></span></span></div>
<div class="MsoNormal" style="background: white; mso-background-themecolor: background1;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Contoh soal:</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Jumlah n suku pertama dari suatu deret adalah Sn
= 3n^2 + n. Maka suku ke-11 dari deret tersebut adalah…</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Tentu ada banyak cara untuk menyelesaikan soal
ini.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="background: white; mso-background-themecolor: background1;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Cara pertama, tentukan dulu rumus Un kemudian
hitung U11. Cara ini cukup panjang. Tetapi bagus Anda coba untuk meningkatkan
keterampilan dan pemahaman konsep deret. Rumus Un dapat kita peroleh dari
selisih Sn – S(n-1) .<o:p></o:p></span></span></div>
<div class="MsoNormal" style="background: white; mso-background-themecolor: background1;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Cara kedua, sedikit lebih cerdik dari cara
pertama. Kita tidak perlu menentukan rumus Un. Karena kita memang tidak ditanya
rumus tersebut. Kita langsung menghitung U11 dengan cara menghitung selisih</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">S11 – S10 = U11</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">[3(11^2) + 11] – [3(10^2) + 10]</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">= 3.121 – 3.100 + 11 – 10</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">= 3.21 + 1</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">= 64<o:p></o:p></span></span></div>
<div class="MsoNormal" style="background: white; mso-background-themecolor: background1;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Cara ketiga, adalah rumus matematika paling
cepat dari kedua rumus di atas. Tetapi sebelum menerapkan cara ketiga, kita
harus memahami konsepnya terlebih dahulu dengan baik.</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Bentuk baku dari n suku pertama deret aritmetika
adalah</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Sn = (b/2)n^2 + k.n</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Un = b(n-1) + a</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">a = S1 = U1<o:p></o:p></span></span></div>
<div class="MsoNormal" style="background: white; mso-background-themecolor: background1;">
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Anda harus pahami konsep di atas dengan baik.
Cobalah untuk beberapa soal yang berbeda-beda. Tanpa pemahaman konsep yang baik,
rumus cepat ini akan berubah menjadi rumus berat.</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Dengan hanya melihat soal (tanpa menghitung di
kertas) bahwa</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Sn = 3n^2 + n</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Kita peroleh</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">b = 6 (dari 3 x 2)</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">a = 4 (dari S1 = 3 + 1)</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">U11 = 6.10 + 4 = 64 (Selesai)</span><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Semua perhitungan di atas dapat kita lakukan
tanpa menggunakan alat tulis. Semua kita lakukan hanya dalam imajinasi kita.
Ulangi beberapa kali. Anda pasti akan menguasainya dengan baik.<o:p></o:p></span></span></div>
<span style="color: blue; font-family: 'Microsoft Sans Serif', sans-serif; font-size: 11pt; line-height: 115%;"><br />
<span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;">Trik untuk menguasai rumus cepat matematika
adalah kuasai pula rumus standarnya – rumus biasanya. Dengan menguasai dua cara
ini Anda akan semakin terampil menggunakan rumus </span></span>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-13119483961000031472011-12-21T21:13:00.001-08:002012-01-15T01:56:48.320-08:00BARISAN DAN DERET<br />
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<i><span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Pengertian<o:p></o:p></span></i></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">1. Barisan
adalah suatu rangkaian bilangan yang tersusun menurut aturan atau pola
tertentu.<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Bentuk umum pada
barisan :<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>1 </sub>, u<sub>2</sub>,u<sub>3,</sub>….
u<sub>n</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>1</sub> =
suku yang pertama<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>2</sub> =
suku yang kedua<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>3</sub> =
suku yang ketiga<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>n</sub> =
suku yang ke-n<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<i><span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">2. Deret<o:p></o:p></span></i></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Bentuk umum pada deret:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">S<sub>n</sub> = u<sub>1</sub> +
u<sub>2</sub> + u<sub>3</sub> + ……. + u<sub>n</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">S<sub>n</sub> =
Jumlah n suku yang pertama<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">B = Beda<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Contoh soal:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Diketahui deret 2 + 4
+ 6 + …..<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Hitunglah jumlah lima
suku yang pertama !<br />
jawab :<br />
b = u<sub>2</sub> - u<sub>1</sub> = 4 - 2 = 2<br />
s<sub>5</sub> = 1<sup>2 </sup>+ 2 + 4 + 6 + 8 = 21<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -18.0pt;">
<i><span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></i><i><span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Barisan
Aritmatika<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpLast" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Bentuk umum:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>1</sub>, U<sub>2</sub>,
U<sub>3</sub>,………. U<sub>n</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Rumus:<br />
beda -> b = U<sub>n</sub> - U<sub>n-1</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">suku ke-n barisan
aritmatika:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>n</sub> =
a+(n-1)b<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>n</sub> =
Suku ke-n<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">a = Suku pertama
= U<sub>1</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">b = beda<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Contoh soal<b>:<o:p></o:p></b></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">1. Diketahui
barisan 6, 9, 12,..<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Tentukan: a.
Beda<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">b. Suku ke 50<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Jawab:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">a. b = U<sub>n</sub> -U<sub>n-1</sub> =9-6
= 3<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">b. S<sub>50 </sub>=
a+(n-1)b<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 6+(50-1) 3<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 6+(49) 3<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 153<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Jadi,<b> </b>suku
ke-50 adalah 153.<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">2. Diketahui barisan aritmatika dengan U = 2
dan U = 14.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Tentukan: a.
Nilai suku pertama dan bedanya b. Suku ke-25<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Deret aritmatika<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Bentuk umum:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>1</sub>,u<sub>2</sub>,u<sub>3</sub>……u<sub>n</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Rumus:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Jumlah n suku pertama:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">S<sub>n</sub> =
n/2 (a + U<sub>n</sub> ) atau S<sub>n</sub> = n/2 {2a + (n - 1)b atau
U<sub>n </sub>= S<sub>n</sub> - S<sub>n - 1</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Contoh soal:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Hitunglah jumlah 50
suku pertama dari deret 2 + 4 + 6 + 8 + …….<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Jawab:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">2 + 4 + 6 + 8 + …… U<sub>50</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">a = 2, b = 2, n = 50<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">S<sub>n</sub> =
n/2 { 2a + (n - 1)b}<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">S<sub>50</sub> =
50/2 {2(2) + (50 - 1)2}<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 25 {4 + (49)2}<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 25 {4 + 98}<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 25 (102)<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 2550<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">2. <i>Barisan Geometri<o:p></o:p></i></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Barisan bilangan U<sub>1</sub>,U<sub>2</sub>,U<sub>3</sub>,……
U<sub>n</sub> disebut dengan barisan geometri, apabila punya yang namanya
rasio (r).<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">r = U<sub>2</sub>/U<sub>1</sub> =
U<sub>3</sub>/U<sub>2</sub> = U<sub>4</sub>/U<sub>3 </sub>= U<sub>n</sub>/U<sub>n-1</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Contoh soal:<o:p></o:p></span></div>
<ol start="1" type="1">
<li class="MsoNormal" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; color: #333333;"><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Tentukan rasio ke 8 dari
barisan 2,4,8,16,…<o:p></o:p></span></li>
</ol>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Jawab:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">a = 2<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">r = 4/2<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 2<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>n</sub> =
ar<sup>n-1</sup><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>10</sub> =
2 . 2<sup>10-1</sup><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 2 . 2<sup>9</sup><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 2 . 512<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 1024<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<i><span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Deret geometri<o:p></o:p></span></i></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Bentuk umum<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">U<sub>1</sub> + U<sub>2</sub> +
U<sub>3</sub> +…… + U<sub>n</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">a + ar + ar<sup>2</sup> +……..
+ ar<sup>n-1</sup><o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Rumus jumlah n suku
deret geometri:<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">S<sub>n </sub>= a
(1 - r<sup>n</sup>)/1 - r jika
r < 1<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Dan<o:p></o:p></span></div>
<div class="MsoNormal" style="background: white; line-height: 15.0pt; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">S<sub>n</sub> = a
(r<sup>n</sup> - 1)/r - 1 jika
r > 1<o:p></o:p></span></div>
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<br /></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Contoh soal:<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Hitunglah jumlah 8
suku dari deret 2 + 4 + 8 +…..<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">Jawab:<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">2 + 4 + 8 +….<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">a = 2<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">r = 2 berarti harus
memakai yang r > 1<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">maka:<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">S<sub>n</sub> = a
(r<sup>n</sup> - 1)/r-1<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">S<sub>8 </sub>= 2
( 2<sup>8</sup> - 1)/ 2-1<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 2 (256 - 1)/2-1<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 2 (255)<o:p></o:p></span></div>
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<span style="color: #333333; font-family: 'Times New Roman', serif; font-size: 12pt;">= 510<o:p></o:p></span></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-18351130441016261842011-12-18T07:30:00.000-08:002012-01-15T01:57:00.027-08:00Teori Persamaan Kuadrat<br />
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</h3>
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<span class="Apple-style-span" style="font-family: 'Rock Salt', serif; font-size: small;"><br /></span></h3>
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<span style="font-size: 12pt;">Bentuk Umum :</span><br />
<span style="font-size: 12pt;"><br /></span><br />
<img src="http://latex.codecogs.com/gif.latex?\inline%20\fn_cm%20ax^{2}+bx+c%20=0\,%20;\,%20a\neq%200" /><br />
<span style="font-size: 12pt;"></span><br />
<span style="font-size: 12pt;"><span style="font-size: 12pt;"><br /></span></span><br />
<span style="font-size: 12pt;"><br /></span><br />
<span style="font-size: 12pt;">
Tujuan belajar Persamaan Kuadrat (PK) :<br />
Mencari pembuat nol / akar-akar nya , yang biasa di notasikan dengan :<span class="apple-converted-space"> </span><br />
Cara mencari Akar-akar PK :<br />
1. Rumus ABC</span></div>
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<a href="http://latex.codecogs.com/gif.latex?\fn_cm%20x_{1,2}=\frac{-b\pm\sqrt{b^{2}-4ac}%20}{2a}" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span class="Apple-style-span" style="color: black;"><img border="0" src="http://latex.codecogs.com/gif.latex?\fn_cm%20x_{1,2}=\frac{-b\pm\sqrt{b^{2}-4ac}%20}{2a}" /></span></a></div>
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<span style="font-size: 12pt;"><br /></span></div>
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<span style="font-size: 12pt;"><br /> </span><img src="http://latex.codecogs.com/gif.latex?\fn_cm%20D=Diskriminan\,%20(pembeda)=b^{2}-4ac" /><span class="Apple-style-span" style="font-size: 16px;"> </span></div>
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<span style="font-size: 12pt;">
Jika D > 0 : PK mempunyai 2 akar Real berlainan / berbeda<br />
D = 0 : PK mempunyai 2 akar Real yang
sama / kembar<br />
D<span class="apple-converted-space"> </span><a href="http://www.codecogs.com/eqnedit.php?latex=\fn_cm%20\geqslant" target="_blank"><span style="text-decoration: none;"><img border="0" height="16" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image005.gif" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; position: relative;" title="\fn_cm \geqslant" v:shapes="_x0000_i1029" width="12" /></span></a> 0
: PK mempunyai akar Real<br />
D < 0 : PK mempunyai akar-akar yang
tak Real / Imaginer / Khayal <br />
2. Melengkapi kuadrat sempurna<br />
3. Pemfaktoran<o:p></o:p></span></div>
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<br /></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-32339295438307174712011-12-11T03:59:00.001-08:002012-01-15T01:59:50.065-08:00PERPANGKATAN DAN AKAR BILANGAN<br />
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<b><br /></b></div>
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<b><span style="font-size: 12pt;">
Perpangkatan<br />
<br />
Perpangkatan bilangan adalah perkalian berulang atau berganda bilangan dengan
faktor-faktor bilangan yang sama. Bentuk perpangkatan adalah sebagai berikut..<br />
<br />
a x a x ….x a = aⁿ<br />
<br />
n faktor<br />
<br />
Bentuk umumnya adalah aⁿ, di mana a disebut bilangan pokok atau bilangan dasar,
sedangkan n disebut <a href="http://www.blogger.com/blogger.g?blogID=3177260314790837602" name="more"></a>pangkat atau eksponen.<br />
<br />
Contoh :<br />
<br />
• 2³ (dibaca dua pangkat tiga) = 2 x 2 x 2 =8<br />
<br />
• 5² (dibaca lima pangkat dua0 = 5x 5 = 25<br />
<br />
Perpangkatan bilangan sangat berguna untuk meringkas bentuk perkalian berulang
dalam jumlah besar.<br />
<br />
Selanjutnya kita akan mempelajari babarapa sifat yang berlaku dalam
perpangkatan.<br />
<br />
Terdapat 6 sifat operasi perpanga\katan yaitu :<br />
<br />
(a x b)ⁿ = aⁿ x bⁿ<br />
am x aⁿ = am+n<br />
am : aⁿ = am-n<br />
(a : b)ⁿ = aⁿ : bⁿ<br />
(a)ⁿ = amxn<br />
aⁿ = dengan a 0<br />
<br />
Bukti kebenaran dari sifat-sifat di atas dapat Anda lakukan setalah Anda
mempelajari unit 7 mengenai penalaran induktif dan deduktif. Sementara ini Anda
dapat menggunakan sifat-sifat tersebut untuk menyelesaikan soal-saol mengenai
perpangkatan.<br />
<br />
<br />
<br />
<br />
Pada perpangkatan, bilangan pokok dapat berupa bilangan bulat maupun pecahan,
demikian juga untuk pangkat atau eksponen. Pangkat juga dapat berupa bilangan
nol. Dalam perpangkatan, kedua komponen (bilangan pokok dan pangkat) sama
dengan pentingnya. Namun demikian, perubahan hasil perpangkatan terutama
ditentukan oleh nilai pangkatnya. Oleh karena itu pembedaan nilai pangkat akan
dibahas secara khusus.<br />
<br />
Pangkat dapat barupa bilangan nol, bilangan bulat (positif dan negatif),
bilangan pecahan (rasional) dan bilangan irrasional. Bilangan irrasional tidak
dibahas pada bahan ajar ini. Untuk lebih jelasnya dapat dilihat skema berikut
ini.<br />
<br />
Pangkat Bilangan<br />
<br />
C. Bulat Posetif<br />
<br />
1. Bilangan Bulat<br />
<br />
a. Bulat Negatif<br />
<br />
b. Bulat Nol<br />
<br />
2. Bilangan Pecahan<br />
<br />
b. Pecahan Posetif<br />
<br />
a. Pecahan Negatif<br />
<br />
Bagaimana jika suatu bilangan dipangkatkan dengan nol ? Sembarang bilangan bila
dipangkatkan nol akan maenghasilkan nilai 1, tidak perduli apakah bilangan
pokoknya merupakan bilangan positif atau negative.<br />
<br />
Contoh:<br />
<br />
</span></b><b><span style="font-family: 'Coming Soon', serif; font-size: 12pt;">●</span></b><b><span style="font-size: 12pt;"> 5° = 1<br />
<br />
Seperti yang telah dikemukakan sebelumnya perpangkatan bilangan adalah bentuk
perkalian berulang atau berganda. Berdasarkan skema pangkat bilangan, pangkat
dapat berupa bilangan bulat positif atau negatif. Pangkat bilangan bulat
positif merupakan bentuk parkalian perkalian berulang yang sebenarnya. Nilai
pangkat/ekponen menunjukan banyak perkalian berulang (factor) nilai itu
sendiri.<br />
<br />
Sembarang bilangan bila dipangkatkan 1 akan menghasilkan bilangan itu sendiri.<br />
<br />
Contoh :<br />
<br />
</span></b><b><span style="font-family: 'Coming Soon', serif; font-size: 12pt;">●</span></b><b><span style="font-size: 12pt;"> 21 = 2<br />
<br />
Baik bilangan pokok yang merupakan bilangan bulat maupun pecahan, bila
dipangkatkan dengan 1 maka hasil perpangkatannya bernilai tetap sama yaitu
bilangan itu sendiri.<br />
<br />
Sembarang bilangan bila dipangkatkan 2 akan menghasilkan perkalian berulang 2
kali bilangan itu sendiri. Contoh :<br />
<br />
</span></b><b><span style="font-family: 'Coming Soon', serif; font-size: 12pt;">●</span></b><b><span style="font-size: 12pt;">32 = 3 x 3 = 9<br />
<br />
</span></b><b><span style="font-family: 'Coming Soon', serif; font-size: 12pt;">●</span></b><b><span style="font-size: 12pt;">102 = 10 x 10 = 100<br />
<br />
<br />
Sembarang bilangan bila dipangkatkan 3 akan menghasilkan perkalian berulang 3
kali bilangan itu sendiri.<br />
<br />
Contoh :<br />
<br />
</span></b><b><span style="font-family: 'Coming Soon', serif; font-size: 12pt;">●</span></b><b><span style="font-size: 12pt;"> 43 = 4 x 4 x 4 = 64<br />
<br />
</span></b><b><span style="font-family: 'Coming Soon', serif; font-size: 12pt;">●</span></b><b><span style="font-size: 12pt;"> 103 = 10 x 10 x 10 = 1000<o:p></o:p></span></b></div>
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<br /></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com2tag:blogger.com,1999:blog-3177260314790837602.post-69600187657463611352011-12-11T02:13:00.001-08:002012-01-15T01:57:14.341-08:00CARA MENGHITUNG AKAR KUADRAT<span class="Apple-style-span" style="background-color: white;"><br /></span><br />
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">berbagai macam cara menghitung akar kuadrat.</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">1. Cara coba-coba. Ini adalah cara paling umum untuk menyelesaikan hitungan akar kuadrat. Cara ini sangat cocok bagi anak-anak, kita, yang telah lancar menghitung kuadrat atau perkalian.</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Misal kita akan menghitung akar (kuadrat) dari 64.</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Maka kita coba 5×5 = 25 (terlalu kecil).</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">Coba 9×9 = 81 (terlalu besar).</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">Coba 7×7 = 49 (terlalu kecil).</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">Coba 8×8 = 64 (betul).</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Jadi kita peroleh akar 64 adalah 8.</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">2. Cara faktorisasi. Cara ini cukup menarik dan taktis. Misal, berpakah akar dari 64?</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Maka 64 = 2×32 = 2x2x16 = 4×16</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">Maka</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">akar 64 = akar 4 x akar 16</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">= 2 x 4</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">= 8 (Selesai).</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Cara faktorisasi ini sangat berguna sampai pelajaran matematika tingkat tinggi. Ketika duduk di bangku SMA, kita sering menggunakan cara faktorisasi. Ketika kuliah kalkulus, kita juga sering menggunakan cara faktorisasi.</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Misal, berapa akar dari 72?</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">Maka</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">72 = 9×8 = 9x4x2</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">Jadi akar 72 = 3x2x akar 2</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">= 6akar2 = 6√2.</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">3. Cara pendekatan. Cara ini adalah variasi dan lanjutan dari cara coba-coba. Setelah berlatih beberapa kali, kita akan sangat mahir dengan cara ini. Cara pendekatan ini sangat dahsyat untuk menghitung akar yang nilainya cukup besar.</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Misal, berapakah akar dari 1681?</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Pendekatan paling masuk akal adalah 40×40 = 1600.</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Karena satuan dari 1681 adalah 1 maka satuan dari akarnya tentu 1 atau 9. Dalam hal ini kita memilh 1. (Mengapa?).</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Jadi kita peroleh jawaban 40+1 = 41</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Misal, berapakah akar dari 3364?</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Pendekatan paling masuk akal adalah 50×50 = 2500.</span><br />
<span class="Apple-style-span" style="background-color: white; color: blue;">(sedangkan 60×60 = 3600, terlalu besar).</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;">Karena satuan dari 3364 adalah 4 maka satuan dari akarnya adalah 2 atau 8. Dalam hal ini kita memilih 8. (Mengapa?)</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Georgia, 'Bitstream Charter', serif; font-size: 14px; line-height: 23px; margin-bottom: 1.7em; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<span class="Apple-style-span" style="background-color: white; color: blue;"><span class="Apple-style-span">Jadi kita peroleh jawaban 50+8 = </span>58.</span></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-55142462696414785562011-12-11T01:19:00.001-08:002012-01-15T01:57:26.460-08:00Rumus Bangun Ruang – Matematika<span class="Apple-style-span" style="color: blue;"><br /></span><br />
<h3 id="post-138" style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">
<span class="Apple-style-span" style="font-family: Arial, Verdana, 'BitStream vera Sans', Helvetica, sans-serif;"><span class="Apple-style-span" style="color: blue; font-size: 12px; line-height: 18px;"><br /></span></span></h3>
<div class="postmetadata" style="clear: both; font-family: 'Lucida Grande', 'Lucida Sans Unicode', Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati; font-size: 9px; font-style: italic; list-style-type: none; min-height: 14px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px; text-align: left;">
<span class="Apple-style-span" style="color: blue;"><br /></span></div>
<div class="entry" style="font-family: 'Lucida Grande', 'Lucida Sans Unicode', Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati; font-size: 12px; line-height: 1.4em;">
<h2 style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: url(http://dana160.student.umm.ac.id/wp-content/themes/comment-central/images/star.png); background-origin: initial; background-repeat: no-repeat no-repeat; font-family: Arial, Verdana, 'BitStream vera Sans', Helvetica, sans-serif; font-size: 20px; font-variant: small-caps; font-weight: 700; line-height: 30px; padding-left: 30px; text-decoration: none; width: 400px;">
</h2>
<div>
<span class="Apple-style-span" style="color: blue;">Rumus Kubus</span><br />
<span class="Apple-style-span" style="color: blue;">- Volume : Sisi pertama dikali sisi kedua dikali sisi ketiga (S pangkat 3)</span><br />
<span class="Apple-style-span" style="color: blue;"><img alt="Q" class="alignnone size-full wp-image-139" height="115" src="http://dana160.student.umm.ac.id/files/2010/02/Q.jpeg" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(204, 204, 204); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(204, 204, 204); border-top-style: solid; border-top-width: 1px; max-width: 100%; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="Q" width="119" /></span><br />
<span class="Apple-style-span" style="color: blue;">Rumus Balok</span><br />
<span class="Apple-style-span" style="color: blue;">- Volume : Panjang dikali lebar dikali tinggi (p x l x t)</span><br />
<br />
<span class="Apple-style-span" style="color: blue;">Rumus Bola</span><br />
<span class="Apple-style-span" style="color: blue;">- Volume : phi dikali jari-jari dikali tinggi pangkat tiga kali 4/3 (4/3 x phi x r x t x t x t)</span><br />
<span class="Apple-style-span" style="color: blue;">- Luas : phi dikali jari-jari kuadrat dikali empat (4 x phi x r x r)</span><br />
<a href="http://dana160.student.umm.ac.id/files/2010/02/BALOK.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span class="Apple-style-span" style="color: blue;"><img alt="BALOK" border="0" class="alignnone size-full wp-image-140" height="66" src="http://dana160.student.umm.ac.id/files/2010/02/BALOK.jpeg" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(204, 204, 204); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(204, 204, 204); border-top-style: solid; border-top-width: 1px; max-width: 100%; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="BALOK" width="101" /></span></a><span class="Apple-style-span" style="color: blue;"><img alt="BOLA" class="alignnone size-full wp-image-142" height="99" src="http://dana160.student.umm.ac.id/files/2010/02/BOLA1.jpeg" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(204, 204, 204); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(204, 204, 204); border-top-style: solid; border-top-width: 1px; max-width: 100%; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="BOLA" width="101" /></span><br />
<span class="Apple-style-span" style="color: blue;">Rumus Limas Segi Empat</span><br />
<span class="Apple-style-span" style="color: blue;">- Volume : Panjang dikali lebar dikali tinggi dibagi tiga (p x l x t x 1/3)</span><br />
<span class="Apple-style-span" style="color: blue;">- Luas : ((p + l) t) + (p x l)</span><br />
<span class="Apple-style-span" style="color: blue;"><img alt="LIMAS" class="alignnone size-full wp-image-143" height="110" src="http://dana160.student.umm.ac.id/files/2010/02/LIMAS.jpeg" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(204, 204, 204); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(204, 204, 204); border-top-style: solid; border-top-width: 1px; max-width: 100%; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="LIMAS" width="94" /></span><br />
<span class="Apple-style-span" style="color: blue;">Rumus Tabung</span><br />
<span class="Apple-style-span" style="color: blue;">- Volume : phi dikali jari-jari dikali jari-jari dikali tinggi (phi x r2 x t)</span><br />
<span class="Apple-style-span" style="color: blue;">- Luas : (phi x r x 2) x (t x r)</span><br />
<span class="Apple-style-span" style="color: blue;"><img alt="TABUNG" class="alignnone size-full wp-image-144" height="104" src="http://dana160.student.umm.ac.id/files/2010/02/TABUNG.jpeg" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(204, 204, 204); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(204, 204, 204); border-top-style: solid; border-top-width: 1px; max-width: 100%; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="TABUNG" width="104" /></span><br />
<span class="Apple-style-span" style="color: blue;">Rumus Kerucut</span><br />
<span class="Apple-style-span" style="color: blue;">- Volume : phi dikali jari-jari dikali jari-jari dikali tinggi dibagi tiga (phi x r2 x t x 1/3)</span><br />
<span class="Apple-style-span" style="color: blue;">- Luas : (phi x r) x (S x r)</span><br />
<span class="Apple-style-span" style="color: blue;">- S : Sisi miring kerucut dari alas ke puncak (bukan tingi)</span><br />
<span class="Apple-style-span" style="color: blue;"><img alt="KERUCUT" class="alignnone size-full wp-image-146" height="107" src="http://dana160.student.umm.ac.id/files/2010/02/KERUCUT.jpeg" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(204, 204, 204); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(204, 204, 204); border-top-style: solid; border-top-width: 1px; max-width: 100%; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="KERUCUT" width="87" /></span><br />
<span class="Apple-style-span" style="color: blue;">Rumus Prisma Segitiga Siku-siku</span><br />
<span class="Apple-style-span" style="color: blue;">- Volume : alas segitiga kali tinggi segitiga kali tinggi prisma bagi dua (as x ts x tp x</span><br />
<span class="Apple-style-span" style="color: blue;"><img alt="PRISMA" class="alignnone size-full wp-image-145" height="112" src="http://dana160.student.umm.ac.id/files/2010/02/PRISMA.jpeg" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(204, 204, 204); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(204, 204, 204); border-top-style: solid; border-top-width: 1px; max-width: 100%; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="PRISMA" width="114" /></span></div>
</div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-31840868751222399482011-12-11T00:50:00.001-08:002012-01-15T01:57:43.472-08:00RUMUS - RUMUS TRIGONOMETRI<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<h3 class="post-title entry-title" style="background-attachment: initial; background-clip: initial; background-image: url(http://www1.blogblog.com/dots/bg_post_title_left.gif); background-origin: initial; background-position: 0% 0.25em; background-repeat: no-repeat no-repeat; font-family: Verdana, Arial, sans-serif; font-size: 14px; font-weight: bold; font: normal normal normal 100%/normal Georgia, serif; line-height: 1.4em; margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0.25em; padding-bottom: 1px; padding-left: 45px; padding-right: 0px; padding-top: 0px;">
<span class="Apple-style-span" style="color: #eeeeee; font-size: 11px; font-weight: normal; line-height: 17px;"><span class="Apple-style-span" style="background-color: initial;">. </span><span class="Apple-style-span" style="background-color: black;">Bentuk Umum</span></span></h3>
<div class="post-body entry-content" id="post-body-199976464321110182" style="font-family: Verdana, Arial, sans-serif; font-size: 11px; line-height: 1.6em; margin-bottom: 0.75em; margin-left: 0px; margin-right: 0px; margin-top: 0px;">
<div style="text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvhVTqT9JAe9v6m0lPgI3OrREfqDzK2DC4b5tUp8hrz-fKlDEYORlCBxZbq_0JFZXiyWyqnkMvbV82kbeE7dgOXHCHcSIy0tyNEvYVkInlyT_MtoLtwbBN1Ub9zNimuxfhSAJ5gOMDyvfS/s1600-h/trigono1.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350038406474003058" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvhVTqT9JAe9v6m0lPgI3OrREfqDzK2DC4b5tUp8hrz-fKlDEYORlCBxZbq_0JFZXiyWyqnkMvbV82kbeE7dgOXHCHcSIy0tyNEvYVkInlyT_MtoLtwbBN1Ub9zNimuxfhSAJ5gOMDyvfS/s320/trigono1.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 316px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 207px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">B. Sudut-Sudut Istimewa</span></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBN_SvYdxGNh7DoSAduX8qxkOzcCyPhBdCFx3z_6wpUmluFP6yXeg9sl_rn2DSnXsvyG5gxsWnte0ckcGrhSn_iZuf_dK8Bnc89_xd05wHgQqtGUnamfqOC0SRRxeNA1Ux00xxW8XAWWHQ/s1600-h/trigono2.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350038976247044114" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBN_SvYdxGNh7DoSAduX8qxkOzcCyPhBdCFx3z_6wpUmluFP6yXeg9sl_rn2DSnXsvyG5gxsWnte0ckcGrhSn_iZuf_dK8Bnc89_xd05wHgQqtGUnamfqOC0SRRxeNA1Ux00xxW8XAWWHQ/s320/trigono2.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 127px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 320px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">C. Hubungan Sudut Berelasi antara Sin, Cos dan Tangen</span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnqNcH7KcZK4o0bAh3QxJuu9F3iXfXVGFLJJtH7XpTs1V5RIoSzAzDwx33lJaWpb7tpebXdHJwWzRX_nHJOdzyhneTz0VJgD_z8Szn3-4_80o72CvVC6FwPEhyphenhyphenDYjg8OMaDwWvBINp_hUw/s1600-h/trigono3.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350039410607075186" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnqNcH7KcZK4o0bAh3QxJuu9F3iXfXVGFLJJtH7XpTs1V5RIoSzAzDwx33lJaWpb7tpebXdHJwWzRX_nHJOdzyhneTz0VJgD_z8Szn3-4_80o72CvVC6FwPEhyphenhyphenDYjg8OMaDwWvBINp_hUw/s320/trigono3.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 470px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 220px;" /></span></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgq1lImU59LkYb77BWmTIhMhVQxMtyapKVNnlAOd6uqRmohuYTBOXsMleGlD2Psh2RXQkPlPT3STPNM1oVMUA69AEoKiWOMBNSVIaScsSPJH-UwJVVMmAs60dxAmSjiUGmNr7K7_r9nw2EW/s1600-h/trigono4.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350040141194546962" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgq1lImU59LkYb77BWmTIhMhVQxMtyapKVNnlAOd6uqRmohuYTBOXsMleGlD2Psh2RXQkPlPT3STPNM1oVMUA69AEoKiWOMBNSVIaScsSPJH-UwJVVMmAs60dxAmSjiUGmNr7K7_r9nw2EW/s320/trigono4.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 319px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 232px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">D. Rumus-rumus Trigonometri</span><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">1. Aturan sinus</span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdLqFBkLDqMGH3cy47IYBlJQHjNc4toxswtUDjBqEnHnB2r0PkvhnDbL65Ej4jpyYceLxh9mbegAhOkHFcj7Go1haAWFBI4T0oD1Hrt2hBv3zyTvcHjM3Ek_eZKK2P6reVRjYG009YyAsW/s1600-h/trigono5.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350044905095176914" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdLqFBkLDqMGH3cy47IYBlJQHjNc4toxswtUDjBqEnHnB2r0PkvhnDbL65Ej4jpyYceLxh9mbegAhOkHFcj7Go1haAWFBI4T0oD1Hrt2hBv3zyTvcHjM3Ek_eZKK2P6reVRjYG009YyAsW/s320/trigono5.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 61px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 170px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">2. Aturan Cosinus</span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJfZtzjkLjnkvs2QgU-ePVsglSte1Wt_gloimlK37Wv_2PSckrpRx7kgPUOmn2uDaA10z8uZT0cZs7BXLxTsmUdrrsq5xPjkFp34UY4izU11IueP-r9vmcMWYE8Rp6vAgwSB4qg3ZdgH63/s1600-h/trigono6.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350045160167956850" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJfZtzjkLjnkvs2QgU-ePVsglSte1Wt_gloimlK37Wv_2PSckrpRx7kgPUOmn2uDaA10z8uZT0cZs7BXLxTsmUdrrsq5xPjkFp34UY4izU11IueP-r9vmcMWYE8Rp6vAgwSB4qg3ZdgH63/s320/trigono6.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 102px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 200px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">3. Luas Segitiga ABC</span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRgs0TO7VWsDGrUJI_JTkG8Ezh5R-PygMIk5r4HYEcQVDMMnusrz9_WolXBpzCABJ0aQNcW3yiZaVRTT2kb7PYuSNHe-ygUCHcDdJYdUoI-eIJUEHnq4sFb52zsE9HodzZIuPcUdecCvQy/s1600-h/trigono7.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350045503751554370" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRgs0TO7VWsDGrUJI_JTkG8Ezh5R-PygMIk5r4HYEcQVDMMnusrz9_WolXBpzCABJ0aQNcW3yiZaVRTT2kb7PYuSNHe-ygUCHcDdJYdUoI-eIJUEHnq4sFb52zsE9HodzZIuPcUdecCvQy/s320/trigono7.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 151px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 128px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">4. Jumlah dan Selish Dua Sudut</span><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMmOvfddFfUUIYLpgdEe68mlEMrvALBPgDc-hvQP2G1Lv2b7vZKyLcFcJAptTtmshR3863wnHmXl75yUyUqDdnSQ4VE5JPCcajnKlMc-lelzlvIhfgmWKuU5-uGfWzaebUsUaT2xRiUP7t/s1600-h/trigono8.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350045802364013090" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMmOvfddFfUUIYLpgdEe68mlEMrvALBPgDc-hvQP2G1Lv2b7vZKyLcFcJAptTtmshR3863wnHmXl75yUyUqDdnSQ4VE5JPCcajnKlMc-lelzlvIhfgmWKuU5-uGfWzaebUsUaT2xRiUP7t/s320/trigono8.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 214px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 305px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">5. Sudut 2A (Sudut Kembar)</span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivKlmCYrx5OIeRXuHbpdq84hNtAkFJwUahpna0Lz1JMqSnipB8oCgMKvlzSDQNNh02EiZf89XCS_fCHLv_UdMWlSUgN4YY4ME2mOn8YH-bPBXQ_rqpaCvFtoYA7WamkALEweYrpttKaXlo/s1600-h/trigono9.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350046138079382786" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivKlmCYrx5OIeRXuHbpdq84hNtAkFJwUahpna0Lz1JMqSnipB8oCgMKvlzSDQNNh02EiZf89XCS_fCHLv_UdMWlSUgN4YY4ME2mOn8YH-bPBXQ_rqpaCvFtoYA7WamkALEweYrpttKaXlo/s320/trigono9.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 207px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 207px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">6. Hasil Kali Dua Fungsi Trigonometri</span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDRGbyf0SGKxf44jEsziTFzEqyStOXB48m-GwO2xaM_3xlCF7RJvQflDHGeJa5v-tsuz485CCvle7C0jbDH4017spw5sG6FTNzZk2a8G1gP5a12Y3sTucm25Kl9I0_ZjVmti2egk8i4nl-/s1600-h/trigono10.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350046434290359714" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDRGbyf0SGKxf44jEsziTFzEqyStOXB48m-GwO2xaM_3xlCF7RJvQflDHGeJa5v-tsuz485CCvle7C0jbDH4017spw5sG6FTNzZk2a8G1gP5a12Y3sTucm25Kl9I0_ZjVmti2egk8i4nl-/s320/trigono10.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 142px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 298px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><span style="font-weight: bold;"><br />7. </span>Jumlah Selisih Dua Fungsi Trigonometri</span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvGIwwuYSSNhyII_TrxLWm2-pAwLv34Mv5zgPkWpxOLdlfcQSR1sNu1xgGaxRgysK_aL8maiZmhdoIK7x3NnfoJ6ni_dXnzE9aS_74tOv5nTWqxHKCy21URDnRKoefva7yAde3FpF4RsPs/s1600-h/trigono11.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350046856055658898" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvGIwwuYSSNhyII_TrxLWm2-pAwLv34Mv5zgPkWpxOLdlfcQSR1sNu1xgGaxRgysK_aL8maiZmhdoIK7x3NnfoJ6ni_dXnzE9aS_74tOv5nTWqxHKCy21URDnRKoefva7yAde3FpF4RsPs/s320/trigono11.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 187px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 320px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">8. Persamaan Trigonometri</span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfOpAjNJbmsuFDe4x83alcfkr3-we1OVzxOxtgQMJYMJFg-T7W-zSVJ8K0semxc6D0FZuvytGjVQKzOkezJh_T3eN20Ihzhkzukf6QOChVPLtDXjtO0rQdYiIUf9UJZDY3eN4vdStwHrMC/s1600-h/trigono12.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350047298123118354" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfOpAjNJbmsuFDe4x83alcfkr3-we1OVzxOxtgQMJYMJFg-T7W-zSVJ8K0semxc6D0FZuvytGjVQKzOkezJh_T3eN20Ihzhkzukf6QOChVPLtDXjtO0rQdYiIUf9UJZDY3eN4vdStwHrMC/s320/trigono12.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 306px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 222px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">9. Bentuk <span style="font-style: italic;">a Cos x + b Sin x</span></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZiTisyRdLd3DFuCG77-es6vvqTD9L_TEBz9APrhJCFNQg596vk589RvTccv20kpAaJUE2ldMJ7VptzBI7xNGu6W4VTfEdhwXa_U5lA-UkkP5G4SWlP0jHx1swC4mxvQzXVN6Vn7Zs3c1M/s1600-h/trigono13.jpg"><span class="Apple-style-span" style="color: #eeeeee;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350047626910133458" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZiTisyRdLd3DFuCG77-es6vvqTD9L_TEBz9APrhJCFNQg596vk589RvTccv20kpAaJUE2ldMJ7VptzBI7xNGu6W4VTfEdhwXa_U5lA-UkkP5G4SWlP0jHx1swC4mxvQzXVN6Vn7Zs3c1M/s320/trigono13.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 102px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 316px;" /></span></a><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">10. Bentuk <span style="font-style: italic;">a Cos x + b Sin x = c</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPqYeubQFK7MsoTala_Yk0vfxQEKfcwLP2XpMA0CdAezSMkhDA0AkJyE0FjpknDvfkQudghM0wxpwhMS__ot0w7ovzzIQUTaChzI8UuKkHZzXZyt1Qi0APafb0U5ERj-VVxinXFNkxz_L-/s1600-h/trigono15.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350048028837339634" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPqYeubQFK7MsoTala_Yk0vfxQEKfcwLP2XpMA0CdAezSMkhDA0AkJyE0FjpknDvfkQudghM0wxpwhMS__ot0w7ovzzIQUTaChzI8UuKkHZzXZyt1Qi0APafb0U5ERj-VVxinXFNkxz_L-/s320/trigono15.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 176px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 138px;" /></a></span><br />
<span class="Apple-style-span" style="color: #eeeeee;"><br /></span><br />
<span class="Apple-style-span" style="color: #eeeeee;">11. Nilai Maksimum dan Minimum Fungsi <span style="font-style: italic;">f(x) =</span><span style="font-style: italic;">a Cos x + b Sin x</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBtUSFR3SVhisO0_q26GkVtNn_D4mGK6DfKpLMtJH_ZmFFP_29ma4a-WgwWBQWjoAXls4SCGjfBxB1zN6jRKXcUKK8Z_1iz5PSfs9Z_OI5GWvx8WwsdqlN4-J9bnpshM0QLPWlxWe346D3/s1600-h/trigono16.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5350048490314734082" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBtUSFR3SVhisO0_q26GkVtNn_D4mGK6DfKpLMtJH_ZmFFP_29ma4a-WgwWBQWjoAXls4SCGjfBxB1zN6jRKXcUKK8Z_1iz5PSfs9Z_OI5GWvx8WwsdqlN4-J9bnpshM0QLPWlxWe346D3/s320/trigono16.jpg" style="border-bottom-color: rgb(153, 187, 153); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(153, 187, 153); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(153, 187, 153); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(153, 187, 153); border-top-style: solid; border-top-width: 1px; cursor: pointer; height: 175px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 4px; padding-left: 4px; padding-right: 4px; padding-top: 4px; width: 425px;" /></a></span></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-22170992851649700862011-12-11T00:33:00.001-08:002012-01-15T01:58:24.404-08:00Rumus Phytagoras<span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><a href="http://www.sisilain.net/2010/10/rumus-phytagoras.html" style="text-decoration: none;">Rumus Phytagoras</a></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"> </span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;">adalah rumus yang sering di pakai dalam pelajaran matematika di sekolah. Kadang kita di buat bingung dengan</span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"> </span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><b>rumus pitagoras matematika</b></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;">, bagaimana cara membuktikan kebenarannya? Kurang lebih uraian tentang rumus</span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><a href="http://www.sisilain.net/2010/10/rumus-phytagoras.html" style="text-decoration: none;">phytagoras</a></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"> </span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;">seperti di bawah ini.</span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;">Rumus asli phytagoras</span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><br />
<div class="separator" style="clear: both; font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px; text-align: center;">
<a href="http://www.sisilain.net/2010/10/rumus-phytagoras.html" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-decoration: none;"><span class="Apple-style-span" style="color: black;"><img border="0" src="http://2.bp.blogspot.com/_srNI1ByHI_U/TMMKvkaKTbI/AAAAAAAAAxU/DIj-i_W4eP8/s1600/phytagoras.JPG" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(236, 236, 236); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(236, 236, 236); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(236, 236, 236); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(236, 236, 236); border-top-style: solid; border-top-width: 1px; border-width: initial; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px; position: relative;" /></span></a></div>
<span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;">Membuktikan kebenarannya, di mulai dengan membuat gambar sebuah persegi besar, kemudian gambarlah sebuah persegi kecil di dalam persegi besar tersebut, seperti gambar berikut:</span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><br />
<div class="separator" style="clear: both; font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px; text-align: center;">
<a href="http://www.sisilain.net/2010/10/rumus-phytagoras.html" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-decoration: none;"><span class="Apple-style-span" style="color: black;"><img border="0" src="http://2.bp.blogspot.com/_srNI1ByHI_U/TMMLmE73hOI/AAAAAAAAAxY/6I0fmj0ZgP8/s1600/rumus_phytagoras.JPG" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(236, 236, 236); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(236, 236, 236); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(236, 236, 236); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(236, 236, 236); border-top-style: solid; border-top-width: 1px; border-width: initial; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px; position: relative;" /></span></a></div>
<span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-size: 13px;"><span style="font-size: 13px;">Perhitungannya :<br />Luas persegi besar = Luas persegi kecil + 4 Luas segitiga</span> </span></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-size: 13px;">( b + a ) . ( b + a ) = c . c + 4 . 1/2 b.a </span></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-size: 13px;"></span></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><br /></span><br />
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b<span style="font-size: 12px;"><b><sup>2</sup></b></span><span style="font-size: 12px;"><b><sup></sup></b></span><span style="font-size: 12px;"><b><sup></sup></b></span><span style="font-size: 15px;"> + 2 b.a</span> + a<span style="font-size: 12px;"><b><sup>2</sup></b></span> = c<span style="font-size: 11px;"><span style="font-size: 10px;"><b><sup>2</sup></b></span> </span>+ 2 b.a<br />
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b<span style="font-size: 12px;"><b><sup>2</sup></b></span> + a<span style="font-size: 12px;"><b><sup>2</sup></b></span> = c<span style="font-size: 12px;"><b><sup>2</sup></b></span> + 2 b.a - 2 b.a<br />
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b<span style="font-size: 12px;"><b><sup>2</sup></b></span> + a<span style="font-size: 12px;"><b><sup>2</sup></b></span> = c<span style="font-size: 12px;"><b><sup>2</sup></b></span></div>
<span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-weight: bold;"></span></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 18px;">Berdasarkan rumus tersebut terbukti bahwa sisi miring sebuah segitiga siku - siku adalah akar dari jumlah kuadrat sisi - sisi yang lain.</span>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-10301491842168793822011-12-11T00:14:00.001-08:002012-01-15T01:58:44.560-08:00MATRIKS<span class="Apple-style-span" style="color: #cccccc;"><br /></span><br />
<span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><b>MATRIKS SATUAN</b></span><br />
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">adalah suatu matriks bujur sangkar, yang </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><i><b>semua elemen diagonal utamanya adalah 1</b></i>, </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">sedangkan </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">elemen lainya adalah 0.</span></span><br />
<span style="font-family: 'Bookman Old Style'; font-size: small;"><span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">Notasi : I (Identitas)</span></span><br />
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<tr><td height="25" rowspan="2" width="7%"><span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: 'Bookman Old Style'; font-size: small;"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">I<sub>2</sub></span></span><span style="font-family: 'Bookman Old Style'; font-size: small;"><span style="font-family: Symbol; font-size: x-small;"> =</span></span></span></td><td height="25" rowspan="2" width="14%"><span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: Symbol;">é</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> 1 0 </span><span style="font-family: Symbol; font-size: x-small;"><img height="8" src="http://bebas.ui.ac.id/v12/sponsor/Sponsor-Pendamping/Praweda/image/putih%203x3.gif" width="1" />ù</span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span><span style="font-family: Symbol; font-size: x-small;">ë</span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> 0 1 </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: Symbol;"><img height="8" src="http://bebas.ui.ac.id/v12/sponsor/Sponsor-Pendamping/Praweda/image/putih%203x3.gif" width="1" />û</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"></span></span></td><td rowspan="2" width="9%"><span style="font-family: 'Bookman Old Style'; font-size: small;"><span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">I<sub>3</sub> =</span></span></td><td height="25" rowspan="2" width="70%"><span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: Symbol;">é</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> 1 0 1</span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> </span><span style="font-family: Symbol; font-size: x-small;">ù</span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span><span style="font-family: 'Bookman Old Style'; font-size: small;"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">ê</span></span></span><span style="font-family: 'Bookman Old Style'; font-size: small;"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> 0 1 0 </span></span><span style="font-family: 'Bookman Old Style'; font-size: small;"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">ú</span></span></span><span style="font-family: Symbol; font-size: x-small;"><br />ë</span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> 0 0 1 </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: Symbol;">û</span></span></span></td></tr>
<tr></tr>
</tbody></table>
<span class="Apple-style-span" style="color: #cccccc;"><br /></span><br />
<b><span style="font-family: 'Bookman Old Style'; font-size: small;"><span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">Sifat AI = IA = A</span></span></b><br />
<span class="Apple-style-span" style="color: #cccccc;"><br /></span><br />
<span style="font-family: 'Bookman Old Style'; font-size: small;"><span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><b>MATRIKS INVERS</b></span></span><br />
<span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">Jika A dan B adalah matriks bujur sangkar dengan ordo yang sama dan<b>AB = BA = 1</b>, maka B dikatakan invers dari A (ditulis A<sup>-1</sup>) dan A dikatakan invers dari B (ditulis B<sup>-1</sup>).</span><br />
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">Jika A = </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">é</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> a b </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">ù</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> , maka A-1 =<u> 1 </u> = </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">é</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> d -b </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">ù</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><br />Jika A = </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">ë</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> c d </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">û</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> , maka A-1 = ad - bc ttt </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">ë</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> -c a </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">û</span></span></span><br />
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<ul>
<li><span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">Bilangan (ad-bc) disebut determinan dari matriks A</span></li>
<li><span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">Matriks A mempunyai invers jika <b>Determinan A ¹ 0</b> dan disebut matriks <b><i>non singular</i></b>.<br /><br /><b>Jika determinan A = 0</b> maka A disebut matriks <b><i>singular</i></b>.</span></li>
</ul>
<span class="Apple-style-span" style="color: #cccccc;"><br /></span><br />
<span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><b>Sifat A . A<sup>-1</sup> = A<sup>-1</sup> . A = I</b></span><br />
<span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><b><i>Perluasan</i></b></span><br />
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">A . B = I </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;"> ®</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> A = B<sup>-1</sup> B = A<sup>-1</sup><br />A . B = C </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">®</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> A = C .<sup> B-1</sup> B = A<sup>-1 </sup>. C</span></span><br />
<span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><b><i>Sifat-Sifat</i></b></span><br />
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">1. (A<sup>t</sup>)<sup>t</sup> = A<br />2. (A + B)<sup>t</sup> = A<sup>t</sup> + B<sup>t</sup><br />3. (A . B)<sup>t</sup> = B<sup>t</sup> . A<sup>t</sup><br />4. (A<sup>-t</sup>)<sup>-t</sup> = A<br />5. (A . B)<sup>-1</sup> = B<sup>-1 </sup>. A<sup>-1</sup><br />6. A . B = C </span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: symbol;">®</span></span><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"> |A| . |B| = |C|</span></span><br />
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<span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"></span><br />
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<span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">ax + by = p ditulis<br />
cx + dy = q<br />
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A X B<br />
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</span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a b</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">x</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.gif" v:shapes="_x0000_i1025" width="1" />ù</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">=</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"> é</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">p</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">c d</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">y</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">=</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"> ë</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"><o:p></o:p></span></span></div>
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<span style="color: #cccccc; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;"><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">AX = B</span></b><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">, maka</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">X = A<sup>-1</sup></span></b><b><sup><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span></sup></b><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">. B</span></b><span style="font-family: Verdana, sans-serif; font-size: 12pt;"><o:p></o:p></span></span></div>
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<ol start="1" type="1"><span style="color: black; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">
<li class="MsoNormal" style="line-height: normal; margin-bottom: 12pt;"><span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Cara Matriks<br />
<br />
</span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">x</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.gif" v:shapes="_x0000_i1026" width="1" />ù</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">=</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><u><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> 1 </span></u><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">=</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">d -b</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">p</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">y</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> ad -
bc </span><span style="font-family: Symbol; font-size: 10pt;"><img height="2" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image002.gif" v:shapes="_x0000_i1027" width="2" />ë</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">-c a</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br style="mso-special-character: line-break;" />
<br style="mso-special-character: line-break;" />
<o:p></o:p></span></span></li>
<li class="MsoNormal" style="line-height: normal; margin-bottom: 12pt;"><span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Cara Determinan</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">= =<o:p></o:p></span></span></li>
</span></ol>
<span style="color: black; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-small;">
<table border="0" cellpadding="0" class="MsoNormalTable" style="margin-left: 2.25pt; mso-cellspacing: 1.5pt; mso-yfti-tbllook: 1184; width: 117.46%;">
<tbody>
<tr style="mso-row-margin-left: 5.58%; mso-row-margin-right: 9.84%; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="5%"><div class="MsoNormal">
<span class="Apple-style-span" style="color: #cccccc;"><br /></span></div>
</td>
<td rowspan="3" style="padding: .75pt .75pt .75pt .75pt; width: 6.7%;" width="6%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">x =</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 13.14%;" valign="bottom" width="13%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Dx</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 10.68%;" valign="bottom" width="10%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Symbol; font-size: 10pt;">ê</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">p b</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ú</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ê</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">q d</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ú</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 18.06%;" valign="bottom" width="18%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Dy</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 33.82%;" valign="bottom" width="33%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Symbol; font-size: 10pt;">ê</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a p</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ú<u><br />
</u>ê</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">c q</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ú</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="9%"><div class="MsoNormal">
<span class="Apple-style-span" style="color: #cccccc;"><br /></span></div>
</td>
</tr>
<tr style="mso-row-margin-left: 5.58%; mso-row-margin-right: 9.84%; mso-yfti-irow: 1;">
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="5%"><div class="MsoNormal">
<span class="Apple-style-span" style="color: #cccccc;"><br /></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 13.14%;" width="13%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: 'Courier New'; font-size: 10pt;">—————</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">=</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 10.68%;" width="10%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: 'Courier New'; font-size: 10pt;">——————</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 18.06%;" width="18%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">; y =</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: 'Courier New'; font-size: 10pt;">————</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">=</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 33.82%;" width="33%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: 'Courier New'; font-size: 10pt;">——————</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="9%"><div class="MsoNormal">
<span class="Apple-style-span" style="color: #cccccc;"><br /></span></div>
</td>
</tr>
<tr style="mso-row-margin-left: 5.58%; mso-row-margin-right: 9.84%; mso-yfti-irow: 2;">
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="5%"><div class="MsoNormal">
<span class="Apple-style-span" style="color: #cccccc;"><br /></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 13.14%;" valign="top" width="13%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">D</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 10.68%;" valign="top" width="10%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Symbol; font-size: 10pt;">ê</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a b</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ú</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ê</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">c d</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ú</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 18.06%;" valign="top" width="18%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">D</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 33.82%;" valign="top" width="33%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span class="Apple-style-span" style="color: #cccccc;"><span style="font-family: Symbol; font-size: 10pt;">ê</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a b</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ú<br />
ê</span><span style="font-family: Symbol; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">c d</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img height="2" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image002.gif" v:shapes="_x0000_i1028" width="2" />ú</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></span></div>
</td>
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="9%"><div class="MsoNormal">
<span class="Apple-style-span" style="color: #cccccc;"><br /></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td colspan="7" style="padding: 0in 0in 0in 0in; width: 99.46%;" valign="top" width="99%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="mso-cellspacing: 0in; mso-padding-alt: 6.75pt 6.75pt 6.75pt 6.75pt; mso-yfti-tbllook: 1184; width: 100.0%;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background: #CCCCCC; padding: 6.75pt 6.75pt 6.75pt 6.75pt; width: 307.5pt;" width="410"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<b><span style="font-family: Arial, sans-serif; font-size: 12pt;">Transformasi Geometri </span></b><b><span style="font-family: Arial, sans-serif; font-size: 10pt;"><br />
</span></b><span style="font-family: Arial, sans-serif; font-size: 7.5pt;"><a href="http://bebas.ui.ac.id/v12/sponsor/Sponsor-Pendamping/Praweda/Matematika/Matematika%202.htm">Matematika Kelas 2</a></span><span style="font-family: Arial, sans-serif; font-size: 7.5pt;"> </span><span style="font-family: Arial, sans-serif; font-size: 7.5pt;">> Matriks</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: black; padding: 6.75pt 6.75pt 6.75pt 6.75pt; width: 37.5pt;" width="50"></td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td colspan="2" style="background: white; padding: 6.75pt 6.75pt 6.75pt 6.75pt;"></td>
</tr>
<tr style="mso-yfti-irow: 2; mso-yfti-lastrow: yes;">
<td colspan="2" style="background: white; padding: 6.75pt 6.75pt 6.75pt 6.75pt;"><div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<b><i><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">Transformasi adalah
suatu perpindaban/perubaban.</span></i></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<ol start="1" type="1">
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list .5in;"><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">TRANSLASI
(Pergeseran sejajar)</span></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><o:p></o:p></span></li>
</ol>
<table border="1" cellpadding="0" class="MsoNormalTable" style="margin-left: .5in; mso-cellspacing: 1.5pt; mso-yfti-tbllook: 1184; width: 90.0%;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background: white; padding: .75pt .75pt .75pt .75pt; width: 17.0%;" width="17%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Matriks</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; padding: .75pt .75pt .75pt .75pt; width: 33.0%;" width="33%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Perubahan</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; padding: .75pt .75pt .75pt .75pt; width: 50.0%;" width="50%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Perubahan</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 41.25pt; mso-yfti-irow: 1;">
<td style="height: 41.25pt; padding: .75pt .75pt .75pt .75pt; width: 17.0%;" width="17%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">b<img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.gif" v:shapes="_x0000_i1029" width="3" /></span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="height: 41.25pt; padding: .75pt .75pt .75pt .75pt; width: 33.0%;" width="33%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x+a, y+b)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="height: 41.25pt; padding: .75pt .75pt .75pt .75pt; width: 50.0%;" width="50%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,y) = 0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x-a, y-b) = 0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 59.25pt; mso-yfti-irow: 2; mso-yfti-lastrow: yes;">
<td colspan="3" style="height: 59.25pt; padding: .75pt .75pt .75pt .75pt;"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">Ket :</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
x' = x + a</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">x = x' - a<br />
y' = y + b</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">y = y' -b</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<ol start="2" type="1">
<li class="MsoNormal" style="color: black; line-height: normal; mso-list: l0 level1 lfo2; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><i><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Sifat:</span></i><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><o:p></o:p></span></li>
<ul type="circle">
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level2 lfo2; mso-margin-top-alt: auto; tab-stops: list 1.0in;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Dua
buah translasi berturut-turut</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">diteruskan
dengan</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.gif" v:shapes="_x0000_i1030" width="3" /></span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">b</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
dapat</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">digantikan
dengan </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">c</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">translasi</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">tunggal</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a
+</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">c</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="2" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image002.gif" v:shapes="_x0000_i1031" width="2" />ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
<img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.gif" v:shapes="_x0000_i1032" width="3" /></span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">d</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> <img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image004.gif" v:shapes="_x0000_i1033" width="4" /></span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">b
+ d</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> <o:p></o:p></span></li>
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level2 lfo2; mso-margin-top-alt: auto; tab-stops: list 1.0in;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Pada
suatu translasi setiap bangunnya tidak berubah.<br style="mso-special-character: line-break;" />
<br style="mso-special-character: line-break;" />
<o:p></o:p></span></li>
</ul>
<li class="MsoNormal" style="color: black; line-height: normal; mso-list: l0 level1 lfo2; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">REFLEKSI
(Pencerminan terhadap garis)</span></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><o:p></o:p></span></li>
</ol>
<table border="1" cellpadding="0" class="MsoNormalTable" style="margin-left: .5in; mso-cellspacing: 1.5pt; mso-yfti-tbllook: 1184; width: 90.0%;">
<tbody>
<tr style="height: 42.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background: white; height: 42.0pt; padding: .75pt .75pt .75pt .75pt; width: 26.0%;" width="26%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Pencerminan terhadap</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; height: 42.0pt; padding: .75pt .75pt .75pt .75pt; width: 15.0%;" width="15%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Matriks</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; height: 42.0pt; padding: .75pt .75pt .75pt .75pt; width: 32.0%;" width="32%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Perubahan Titik</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; height: 42.0pt; padding: .75pt .75pt .75pt .75pt; width: 27.0%;" width="27%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Perubahan fungsi</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="padding: .75pt .75pt .75pt .75pt; width: 26.0%;" width="26%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">sumbu-x</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 15.0%;" valign="top" width="15%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">1</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: white; font-family: Verdana, sans-serif; font-size: 10pt;">-</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">0 -1</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.gif" v:shapes="_x0000_i1034" width="1" />û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 32.0%;" width="32%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,-y)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 27.0%;" width="27%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,y) = 0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,-y) = 0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="padding: .75pt .75pt .75pt .75pt; width: 26.0%;" width="26%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">sumbu -y</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 15.0%;" width="15%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">-1 0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: white; font-family: Verdana, sans-serif; font-size: 10pt;">-</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">0 1</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 32.0%;" width="32%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(-x,y)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 27.0%;" width="27%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,y) = 0</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(-x,y) = 0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 24.75pt; mso-yfti-irow: 3;">
<td style="height: 24.75pt; padding: .75pt .75pt .75pt .75pt; width: 26.0%;" width="26%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">garis y = x</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="height: 24.75pt; padding: .75pt .75pt .75pt .75pt; width: 15.0%;" width="15%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">1</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">1 0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="2" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image002.gif" v:shapes="_x0000_i1035" width="2" />û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="height: 24.75pt; padding: .75pt .75pt .75pt .75pt; width: 32.0%;" width="32%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(y,x)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="height: 24.75pt; padding: .75pt .75pt .75pt .75pt; width: 27.0%;" width="27%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,y) = 0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(y,x) = 0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td style="padding: .75pt .75pt .75pt .75pt; width: 26.0%;" width="26%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">garis y = -x</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 15.0%;" valign="top" width="15%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: white; font-family: Verdana, sans-serif; font-size: 10pt;">-</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: white; font-family: Verdana, sans-serif; font-size: 10pt;">-</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">1</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë -</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">1 -0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 32.0%;" width="32%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(-y,-x)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 27.0%;" width="27%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,y) = 0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(-y,-x)= 0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<ol start="4" type="1">
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level1 lfo2; mso-margin-top-alt: auto; tab-stops: list .5in;"><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
<br />
</span></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Ket.
: Ciri khas suatu matriks Refleksi adalah</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><b><i><span style="font-family: Verdana, sans-serif; font-size: 10pt;">determinannya
= -1</span></i></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
<br />
<br />
<b><i>SIFAT-SIFAT</i></b><o:p></o:p></span></li>
</ol>
<ol start="4" type="1">
<ol start="1" type="a">
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level2 lfo3; mso-margin-top-alt: auto;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Dua
refleksi berturut-turut terhadap sebuah garis merupakan suatu</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><b><i><span style="font-family: Verdana, sans-serif; font-size: 10pt;">identitas</span></i></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">,</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">artinya
yang direfleksikan tidak berpindah.</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><o:p></o:p></span></li>
<li class="MsoNormal" style="color: black; line-height: normal; mso-list: l0 level2 lfo3; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Pengerjaan
dua refleksi terhadap</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><b><i><span style="font-family: Verdana, sans-serif; font-size: 10pt;">dua
sumbu yang sejajar</span></i></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">, menghasilkan translasi
(pergeseran) dengan sifat:<o:p></o:p></span></li>
<ul type="square">
<li class="MsoNormal" style="color: black; line-height: normal; mso-list: l0 level3 lfo3; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 1.5in;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Jarak bangun asli dengan
bangun hasil sama dengan dua kali jarak kedua sumbu pencerminan.<o:p></o:p></span></li>
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level3 lfo3; mso-margin-top-alt: auto; tab-stops: list 1.5in;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Arah translasi tegak lurus
pada kedua sumbu sejajar, dari sumbu pertama ke sumbu kedua.
Refleksi terhadap dua sumbu sejajar bersifat</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">tidak
komutatip.<o:p></o:p></span></li>
</ul>
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level2 lfo3; mso-margin-top-alt: auto;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Pengerjaaan
dua refleksi terhadap</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">dua
sumbu yang saling tegak lurus,</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">menghasilkaan
rotasi (pemutaran)</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">setengah
lingkaran terhadap titik potong dari kedua sumbu pencerminan.</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Refleksi
terhadap dua sumbu yang saling tegak lures bersifat</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">komutatif.<o:p></o:p></span></li>
<li class="MsoNormal" style="color: black; line-height: normal; mso-list: l0 level2 lfo3; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Pengerjaan
dua refleksi berurutan terhadap</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">dua
sumbu yang berpotongan</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">akan
menghasilkan rotasi (perputaran) yang bersifat:<o:p></o:p></span></li>
<ul type="square">
<li class="MsoNormal" style="color: black; line-height: normal; mso-list: l0 level3 lfo3; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 1.5in;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Titik potong kedua sumbu
pencerminan merupakan pusat perputaran.<o:p></o:p></span></li>
<li class="MsoNormal" style="color: black; line-height: normal; mso-list: l0 level3 lfo3; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 1.5in;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Besar sudut perputaran sama
dengan</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">dua
kali sudut antara kedua sumbu pencerminan.<o:p></o:p></span></li>
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level3 lfo3; mso-margin-top-alt: auto; tab-stops: list 1.5in;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Arah perputaran sama dengan arah
dari sumbu pertama ke sumbu kedua.</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br style="mso-special-character: line-break;" />
<br style="mso-special-character: line-break;" />
<o:p></o:p></span></li>
</ul>
</ol>
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level1 lfo3; mso-margin-top-alt: auto; tab-stops: list .5in;"><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">ROTASI
(Perputaran dengan pusat 0)</span></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><o:p></o:p></span></li>
</ol>
<table border="1" cellpadding="0" class="MsoNormalTable" style="margin-left: .5in; mso-cellspacing: 1.5pt; mso-yfti-tbllook: 1184; width: 90.0%;">
<tbody>
<tr style="height: 24.75pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background: white; height: 24.75pt; padding: .75pt .75pt .75pt .75pt; width: 13.0%;" width="13%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">rotasi</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; height: 24.75pt; padding: .75pt .75pt .75pt .75pt; width: 23.0%;" width="23%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">matriks</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; height: 24.75pt; padding: .75pt .75pt .75pt .75pt; width: 27.0%;" width="27%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">perubahan titik</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; height: 24.75pt; padding: .75pt .75pt .75pt .75pt; width: 37.0%;" width="37%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">perubahan fungsi</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="padding: .75pt .75pt .75pt .75pt; width: 13.0%;" width="13%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">½</span></b><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span></b><b><span style="font-family: Symbol; font-size: 10pt;">p</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 23.0%;" width="23%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">0 -1</span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">1</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: white; font-family: Verdana, sans-serif; font-size: 10pt;">-</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 27.0%;" width="27%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(-y,x)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 37.0%;" width="37%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,y) = 0</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(y,-x) = 0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="padding: .75pt .75pt .75pt .75pt; width: 13.0%;" width="13%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Symbol; font-size: 10pt;">p</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 23.0%;" valign="top" width="23%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">-1 0</span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">1 -1</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 27.0%;" width="27%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(-x,-y)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 37.0%;" width="37%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,y) = 0</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(-x,-y) = 0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="padding: .75pt .75pt .75pt .75pt; width: 13.0%;" width="13%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">3/2</span></b><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span></b><b><span style="font-family: Symbol; font-size: 10pt;">p</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 23.0%;" width="23%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">0 <span style="color: white;">-</span>1</span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">-1 0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 27.0%;" width="27%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(y,-x)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 37.0%;" width="37%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,y) = 0</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(-y,x) = 0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td style="padding: .75pt .75pt .75pt .75pt; width: 13.0%;" width="13%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Symbol; font-size: 10pt;">q</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt; width: 23.0%;" valign="top" width="23%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">cos</span><span style="font-family: Symbol; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">-sin</span><span style="font-family: Symbol; font-size: 10pt;">q ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">sin</span><span style="font-family: Symbol; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> cos</span><span style="font-family: Symbol; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td colspan="2" style="padding: .75pt .75pt .75pt .75pt;"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x cos</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">- y sinq, x sin</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">+ y cos</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">)<br />
F(x,y) = 0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x cos</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">+ y sin</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">, -x sin</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">+ y cos</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">q</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">) = 0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<ol start="6" type="1">
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level1 lfo3; mso-margin-top-alt: auto; tab-stops: list .5in;"><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Ket.:
Ciri khas suatu matriks Rotasi adalah</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><b><i><span style="font-family: Verdana, sans-serif; font-size: 10pt;">determinannya
= 1</span></i></b><span style="font-family: 'Bookman Old Style', serif; font-size: 12pt;"><br />
</span><span style="font-family: Verdana, sans-serif; font-size: 12pt;"><br />
</span><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">SIFAT-SIFAT</span></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><o:p></o:p></span></li>
<ol start="0" type="a">
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level2 lfo3; mso-margin-top-alt: auto;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Dua
rotasi bertumt-turut mempakan rotasi lagi dengan sudut putar</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: white; font-family: Verdana, sans-serif; font-size: 10pt;">d</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">sama
dengan jumlah kedua sudut putar semula.<o:p></o:p></span></li>
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level2 lfo3; mso-margin-top-alt: auto;"><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Pada
suatu rotasi, setiap bangun tidak berubah bentuknya.<br />
<br />
<i>Catatan:</i></span><i><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span></i><i><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span></i><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
Pada transformasi pergeseran (translasi), pencerminan (refleksi) dan
perputaran (rotasi), tampak bahwa bentuk bayangan sama dan sebangun
(kongruen) dengan bentuk aslinya. Transformasi jenis ini disebut</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">transformasi
isometri.</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br style="mso-special-character: line-break;" />
<br style="mso-special-character: line-break;" />
<o:p></o:p></span></li>
</ol>
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level1 lfo3; mso-margin-top-alt: auto; tab-stops: list .5in;"><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">DILATASI
(Perbesaran terhadap pusat 0)</span></b><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><o:p></o:p></span></li>
</ol>
<table border="1" cellpadding="0" class="MsoNormalTable" style="margin-left: .5in; mso-cellspacing: 1.5pt; mso-yfti-tbllook: 1184; width: 90.0%;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background: white; padding: .75pt .75pt .75pt .75pt; width: 14.0%;" width="14%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Dilatasi</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; padding: .75pt .75pt .75pt .75pt; width: 19.0%;" width="19%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Matriks</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; padding: .75pt .75pt .75pt .75pt; width: 33.0%;" width="33%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Perubahan titik</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: white; padding: .75pt .75pt .75pt .75pt; width: 34.0%;" width="34%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Perubahan fungsi</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="height: .5in; mso-yfti-irow: 1; mso-yfti-lastrow: yes;">
<td style="height: .5in; padding: .75pt .75pt .75pt .75pt; width: 14.0%;" width="14%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(0,k)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="height: .5in; padding: .75pt .75pt .75pt .75pt; width: 19.0%;" width="19%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">k 0</span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">0 k</span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="height: .5in; padding: .75pt .75pt .75pt .75pt; width: 33.0%;" width="33%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(kx,ky)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="height: .5in; padding: .75pt .75pt .75pt .75pt; width: 34.0%;" width="34%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,y)=0</span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x/k,y/k)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<ol start="8" type="1">
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level1 lfo3; mso-margin-top-alt: auto; tab-stops: list .5in;"><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span></b><i><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Ket.:</span></i><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
<br />
(0, k) merupakan perbesaran atau pengecilan dengan tergantung dari
nilai k.<br />
<br />
Jika A' adalah peta dari A, maka untuk:<br />
a. k > 1</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">A' terletak
pada perpanjangan OA<br />
b. 0 < k < 1</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">A' terletak
di antara O dan A<br />
c. k > 0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">A' terletak
pada perpanjangan AO<br style="mso-special-character: line-break;" />
<br style="mso-special-character: line-break;" />
<o:p></o:p></span></li>
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: 12.0pt; mso-list: l0 level1 lfo3; mso-margin-top-alt: auto; tab-stops: list .5in;"><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">TRANSFORMASI
LINIER<br />
</span></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
Ditentukan oleh matriks</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a b</span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">c d</span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
<br />
</span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">x'</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.gif" v:shapes="_x0000_i1036" width="3" />ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">=</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a b</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">x</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.gif" v:shapes="_x0000_i1037" width="1" />ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">y'</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> <img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image004.gif" v:shapes="_x0000_i1038" width="4" /></span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">c d</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">y</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
<br />
<br />
</span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">x</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.gif" v:shapes="_x0000_i1039" width="1" />ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">=</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><u><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> 1 </span></u><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.gif" v:shapes="_x0000_i1040" width="1" />é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a -b</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">x'</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.gif" v:shapes="_x0000_i1041" width="1" />ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">y</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> ad
- bc</span><span style="font-family: Symbol; font-size: 10pt;">
ë -</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">c
d</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Symbol; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">y'</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><o:p></o:p></span></li>
</ol>
<table border="1" cellpadding="0" class="MsoNormalTable" style="margin-left: .5in; mso-cellspacing: 1.5pt; mso-yfti-tbllook: 1184; width: 90.0%;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="padding: .75pt .75pt .75pt .75pt;"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">Perubahan Titik</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Perubahan Fungsi</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1; mso-yfti-lastrow: yes;">
<td style="padding: .75pt .75pt .75pt .75pt;"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">(x,y)</span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">(ax+by, cx+dy)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-family: Verdana, sans-serif; font-size: 10pt;">F(x,y)=0</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">®</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">dx - by , -cx + ay</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">ad - bc ad - bc</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="2" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image002.gif" v:shapes="_x0000_i1042" width="2" />û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<ol start="10" type="1">
<li class="MsoNormal" style="color: black; line-height: normal; mso-list: l0 level1 lfo3; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><b><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span></b><span style="font-family: Verdana, sans-serif; font-size: 10pt;">Prinsipnya
adalah mencari matriks invers dari matriks transformasi yang
diketahui.<o:p></o:p></span></li>
</ol>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<br /></div>
</td>
</tr>
</tbody></table>
</td>
</tr>
<tr style="mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td colspan="7" style="padding: 0in 0in 0in 0in; width: 99.46%;" valign="top" width="99%"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="mso-cellspacing: 0in; mso-padding-alt: 6.75pt 6.75pt 6.75pt 6.75pt; mso-yfti-tbllook: 1184; width: 100.0%;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background: #CCCCCC; padding: 6.75pt 6.75pt 6.75pt 6.75pt; width: 307.5pt;" width="410"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<b><span style="font-family: Arial, sans-serif; font-size: 12pt;">Komposisi Transfromasi dan
Transformasi Invers</span></b><b><span style="font-family: Arial, sans-serif; font-size: 10pt;"><br />
</span></b><span style="font-family: Arial, sans-serif; font-size: 7.5pt;"><a href="http://bebas.ui.ac.id/v12/sponsor/Sponsor-Pendamping/Praweda/Matematika/Matematika%202.htm">Matematika Kelas 2</a></span><span style="font-family: Arial, sans-serif; font-size: 7.5pt;"> </span><span style="font-family: Arial, sans-serif; font-size: 7.5pt;">> Matriks</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
</td>
<td style="background: black; padding: 6.75pt 6.75pt 6.75pt 6.75pt; width: 37.5pt;" width="50"></td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td colspan="2" style="background: white; padding: 6.75pt 6.75pt 6.75pt 6.75pt;"></td>
</tr>
<tr style="mso-yfti-irow: 2; mso-yfti-lastrow: yes;">
<td colspan="2" style="background: white; padding: 6.75pt 6.75pt 6.75pt 6.75pt;"><div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<b><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">KOMPOSISI TRANSFORMASI</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">Jika A =</span><span style="font-family: Symbol; font-size: 10pt;">
é</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">a b</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">adalah T<sub>1</sub></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">dan B</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">=</span><span style="font-family: 'Times New Roman', serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">e f</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">adalah
T</span><sub><span style="font-family: Verdana, sans-serif; font-size: 10pt;">2</span></sub><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"><br />
</span><span style="color: white; font-family: Verdana, sans-serif; font-size: 10pt;">ttt </span><span style="font-family: Symbol; font-size: 10pt;"> <img border="0" height="2" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image002.gif" v:shapes="_x0000_i1043" width="2" />ë</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">c d</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: white; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;"> ë</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">g h<img border="0" height="2" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image002.gif" v:shapes="_x0000_i1044" width="2" /></span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
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<span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"><br />
maka T<sub>2</sub></span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">° T<sub>1</sub></span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">= BA =</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">e f</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù</span><span style="font-family: 'Times New Roman', serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">é</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 10pt;">a b</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">ù<br />
</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"> <img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.gif" v:shapes="_x0000_i1045" width="3" /></span><span style="font-family: Symbol; font-size: 10pt;"><img border="0" height="2" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image002.gif" v:shapes="_x0000_i1046" width="2" />ë</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">g h<img border="0" height="2" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image002.gif" v:shapes="_x0000_i1047" width="2" /></span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: Verdana, sans-serif; font-size: 10pt;"><img border="0" height="8" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.gif" v:shapes="_x0000_i1048" width="3" /></span><span style="font-family: Symbol; font-size: 10pt;">ë</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">c d</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="font-family: Symbol; font-size: 10pt;">û</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="color: black; font-family: Symbol; font-size: 10pt;">®</span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">menyatakan
transformasi T<sub>1</sub></span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">dilanjutkan
dengan T<sub>2</sub></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><br />
</span><b><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">TRANSFORMASI INVERS</span></b><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">Jika suatu transformasi diwakili oleh matriks M, memetakan
titik P ke P1, maka transformasi ini memetakan P1 ke P, diwakili oleh
matriks M<sup>-1</sup>(yaitu jika M<sup>-1</sup></span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;"> </span><span style="color: black; font-family: Verdana, sans-serif; font-size: 10pt;">ada).</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
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<td style="border: none;" width="159"></td>
<td style="border: none;" width="295"></td>
<td style="border: none;" width="103"></td>
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<br /></div>
</span>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-45502195368344128672011-12-09T08:27:00.001-08:002011-12-09T08:27:51.931-08:00RUMUS-RUMUS PECAHAN<!--[if gte mso 9]><xml>
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<br />
<div align="center" class="MsoNormal" style="mso-layout-grid-align: none; text-align: center; text-autospace: none;">
<b style="mso-bidi-font-weight: normal;"><span style="color: #231f20;"><br /></span></b></div>
<div class="MsoNormal" style="mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">1. Pecahan
merupakan bilangan yang menggambarkan bagian dari keseluruhan.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">2. Pecahan
senilai adalah pecahan-pecahan yang bernilai sama.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">3. Pecahan
senilai diperoleh dengan cara mengalikan atau membagi pembilang dan penyebutnya
dengan bilangan yang sama.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">4. Suatu
dapat disederhanakan dengan cara membagi pembilang dan penyebut pecahan
tersebut dengan faktor persekutuan terbesarnya.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">5. Jika
penyebut kedua pecahan berbeda, untuk membandingkan pecahan tersebut, nyatakan
menjadi pecahan yang senilai, kemudian bandingkan pembilangnya.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">6. Pada garis
bilangan, pecahan yang lebih besar berada di sebelah kanan, sedangkan pecahan
yang lebih kecil berada di sebelah kiri.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">7. Di antara
dua pecahan yang berbeda selalu dapat ditemukan pecahan yang nilainya di antara
dua pecahan tersebut. </span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">8. Untuk
mengubah bentuk pecahan ke bentuk persen dapat dilakukan dengan cara mengalikan
pecahan tersebut dengan 100%.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">9. Untuk
menentukan hasil penjumlahan atau pengurangan dua pecahan, samakan penyebut
kedua pecahan tersebut, yaitu dengan cara mencari KPK dari
penyebut-penyebutnya, kemudian baru dijumlahkan atau dikurangkan pembilangnya.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">10. Untuk
menentukan hasil perkalian dua pecahan dilakukan dengan cara mengalikan
pembilang dengan pembilang dan penyebut dengan penyebut.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">11. Invers
perkalian dari pecahan </span><i><span style="font-size: 11pt;">p/q
</span></i><span style="font-size: 11pt;">adalah </span><i><span style="font-size: 11pt;">q/p</span></i></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">12. Suatu
bilangan jika dikalikan dengan invers perkaliannya hasilnya sama dengan 1.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">13.
Penjumlahan dan pengurangan pecahan desimal dilakukan pada masing-masing nilai
tempat dengan cara bersusun. Urutkan angka-angka ratusan, puluhan, satuan,
persepuluhan, perseratusan dan seterusnya dalam satu kolom.</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">14. Hasil
kali bilangan desimal dengan bilangan desimal diperoleh dengan cara mengalikan
bilangan tersebut seperti mengalikan bilangan bulat. Banyak desimal hasil kali
bilangan-bilangan</span></div>
<div class="MsoNormal" style="color: #eeeeee; text-align: justify;">
<span style="font-size: 11pt;">desimal
diperoleh dengan menjumlahkan banyak tempat desimal dari pengali-pengalinya.</span></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-3516766888998645852011-12-09T08:24:00.001-08:002012-01-15T01:59:35.173-08:00RUMUS-RUMUS BILANGAN BULAT<br />
<div align="center" class="MsoNormal" style="mso-layout-grid-align: none; text-align: center; text-autospace: none;">
<b style="mso-bidi-font-weight: normal;"><span style="color: #231f20;"><br /></span></b></div>
<div class="MsoNormal" style="color: white; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="color: white; text-align: justify;">
<span style="font-size: 11pt;">1. Bilangan
bulat terdiri dari bilangan bulat negatif, nol, dan bilangan bulat positif.</span></div>
<div class="MsoNormal" style="color: white; text-align: justify;">
<span style="font-size: 11pt;">2.
Sifat-sifat penjumlahan pada bilangan bulat:</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">a. Sifat tertutup</span></div>
<div class="MsoNormal" style="color: white; margin-left: 1in; text-align: justify;">
<span style="font-size: 11pt;">Untuk setiap bilangan bulat <i>a </i>dan <i>b</i>, berlaku <i>a </i>+
<i>b </i>= <i>c </i>dengan <i>c </i>juga bilangan bulat.</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">b. Sifat komutatif</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;"> Untuk setiap
bilangan bulat <i>a </i>dan <i>b</i>, selalu berlaku <i>a </i>+ <i>b </i>= <i>b
</i>+ <i>a</i>.</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">c. Sifat asosiatif</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;"> Untuk setiap
bilangan bulat <i>a</i>, <i>b</i>, dan <i>c </i>selalu berlaku (<i>a </i>+ <i>b</i>)
+ <i>c </i>= <i>a </i>+ (<i>b </i>+ <i>c</i>).</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">d. Mempunyai unsur identitas</span></div>
<div class="MsoNormal" style="color: white; margin-left: 1in; text-align: justify;">
<span style="font-size: 11pt;">Untuk sebarang bilangan bulat <i>a</i>, selalu berlaku <i>a </i>+
0 = 0 + <i>a</i>. Bilangan nol (0) merupakan unsur identitas pada penjumlahan.</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">e. Mempunyai invers</span></div>
<div class="MsoNormal" style="color: white; margin-left: 1in; text-align: justify;">
<span style="font-size: 11pt;">Untuk setiap bilangan bulat <i>a</i>, selalu berlaku <i>a </i>+
(–<i>a</i>) = (–<i>a</i>) + <i>a </i>= 0. Invers dari <i>a </i>adalah –<i>a</i>,
sedangkan invers dari –<i>a </i>adalah <i>a</i>.</span></div>
<div class="MsoNormal" style="color: white; text-align: justify;">
<span style="font-size: 11pt;">3. Jika <i>a </i>dan
<i>b </i>bilangan bulat maka berlaku <i>a </i>– <i>b </i>= <i>a </i>+ (–<i>b</i>).</span></div>
<div class="MsoNormal" style="color: white; text-align: justify;">
<span style="font-size: 11pt;">4. Operasi
pengurangan pada bilangan bulat berlaku sifat tertutup.</span></div>
<div class="MsoNormal" style="color: white; text-align: justify;">
<span style="font-size: 11pt;">5. Jika <i>p </i>dan
<i>q </i>bilangan bulat maka</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">a. <i>p
x</i></span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><i><span style="font-size: 11pt;">q </span></i><span style="font-size: 11pt;">= <i>pq;</i></span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">b. (–<i>p</i>)
x <i>q </i>= –(<i>p x</i></span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><i><span style="font-size: 11pt;">q</span></i><span style="font-size: 11pt;">)
= –<i>pq;</i></span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">c. <i>p
x </i>(–<i>q</i>) = –(<i>p x </i></span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><i><span style="font-size: 11pt;">q</span></i><span style="font-size: 11pt;">) = –<i>pq;</i></span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">d. (–<i>p</i>)
x</span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><span style="font-size: 11pt;">(–<i>q</i>)
= <i>p x </i></span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><i><span style="font-size: 11pt;">q </span></i><span style="font-size: 11pt;">= <i>pq.</i></span></div>
<div class="MsoNormal" style="color: white; text-align: justify;">
<span style="font-size: 11pt;">6. Untuk
setiap <i>p</i>, <i>q</i>, dan <i>r </i>bilangan bulat berlaku sifat</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">a.
tertutup terhadap operasi perkalian;</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">b.
komutatif: <i>p x q </i>= <i>q x p</i>;</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">c.
asosiatif: (<i>p x q</i>) x <i>r </i>= <i>p x </i>(<i>q x </i></span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><i><span style="font-size: 11pt;">r</span></i><span style="font-size: 11pt;">);</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">d.
distributif perkalian terhadap penjumlahan: <i>p x (q </i>+ <i>r</i>) = (<i>p x
q</i>) + (<i>p x </i></span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><i><span style="font-size: 11pt;">r</span></i><span style="font-size: 11pt;">);</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">e.
distributif perkalian terhadap pengurangan: <i>p x</i></span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><span style="font-size: 11pt;">(<i>q </i>– <i>r</i>)
= (<i>p x q</i>) – (<i>p x</i></span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><i><span style="font-size: 11pt;">r</span></i><span style="font-size: 11pt;">).</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">
<span style="font-size: 11pt;">7. Unsur identitas pada perkalian adalah 1, sehingga untuk
setiap bilangan bulat <i>p </i>berlaku <i>p x </i>1 = 1 x <i>p </i>= <i>p</i>.</span></div>
<div class="MsoNormal" style="color: white; text-align: justify;">
<span style="font-size: 11pt;">8. Pembagian
merupakan operasi kebalikan dari perkalian.</span></div>
<div class="MsoNormal" style="color: white; text-align: justify;">
<span style="font-size: 11pt;">9. Pada
operasi pembagian bilangan bulat tidak bersifat tertutup.</span></div>
<div class="MsoNormal" style="color: white; text-align: justify;">
<span style="font-size: 11pt;">10. Apabila
dalam suatu operasi hitung campuran bilangan bulat tidak terdapat tanda kurung,
pengerjaannya berdasarkan sifat-sifat operasi hitung berikut.</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">a.
Operasi penjumlahan (+) dan pengurangan (–) <i>sama kuat</i>, artinya operasi
yang terletak di sebelah kiri dikerjakan terlebih dahulu.</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">b.
Operasi perkalian ( </span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><span style="font-size: 11pt;">) dan pembagian (:) <i>sama kuat</i>,
artinya operasi yang terletak di sebelah kiri dikerjakan terlebih dahulu.</span></div>
<div class="MsoNormal" style="color: white; margin-left: 0.5in; text-align: justify;">
<span style="font-size: 11pt;">c.
Operasi perkalian ( </span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><span style="font-size: 11pt;">) dan pembagian (:) <i>lebih kuat </i>daripada
operasi penjumlahan (+) dan pengurangan (–), artinya operasi perkalian (</span><span style="font-family: Symbol; font-size: 10.5pt;"> </span><span style="font-size: 11pt;">)
dan pembagian (:) dikerjakan terlebih dahulu daripada operasi penjumlahan (+)
dan pengurangan (–).</span></div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-34857624835415455862011-12-09T08:06:00.001-08:002012-01-15T01:59:13.478-08:00Operasi Aljabar (Materi SMP Kelas VIII semester 1<br />
<div class="pd-rating sd-content" id="pd_rating_holder_691672_post_17" style="display: inline-block;">
<span style="float: left;"></span></div>
<div style="text-align: left;">
Soal Terbimbing Untuk Pemahaman :<br />
1. Sederhanakan bentuk-bentuk berikut :</div>
<div style="padding-left: 30px; text-align: left;">
a.7x + 3x</div>
<div style="padding-left: 30px; text-align: left;">
b.5a + 3b + a – 5b</div>
<div style="padding-left: 30px; text-align: left;">
c. (-3y<sup>2</sup> + 2y – 4) + (2y<sup>2</sup> – 3y + 5)</div>
<div style="padding-left: 30px; text-align: left;">
d. (2p<sup>3</sup> + p – 5) – (2p<sup>2</sup> + 3p – 4)</div>
<div style="text-align: left;">
Penyelesaian :<br />
a. 7x + 3x = ( .7. + .3. )x = ….<br />
b. 5a + 3b + a – 5b = … + … + … + … = ( … + … )a + ( … – … )b = … ….<span id="more-17"></span><br />
c. (-3y<sup>2</sup> + 2y – 4) + (2y<sup>2</sup> – 3y + 5) = … …. … … … …</div>
<div style="padding-left: 210px; text-align: left;">
= ( … ….)y<sup>2</sup> + ( … …)y + ( … …)<br />
= … …. …</div>
<div style="padding-left: 30px; text-align: left;">
d. (2p<sup>3</sup> + p – 5) – (2p<sup>2</sup> + 3p – 4) = … …. … … … …</div>
<div style="padding-left: 240px; text-align: left;">
= … …. ( … …)p + ( … …)</div>
<div style="padding-left: 240px; text-align: left;">
= … …. … …</div>
<div style="text-align: left;">
2. Tentukan hasil perkalian berikut :</div>
<div style="padding-left: 30px; text-align: left;">
a. 5a x 2b</div>
<div style="padding-left: 30px; text-align: left;">
b. -3p x 4p</div>
<div style="padding-left: 30px; text-align: left;">
c. <a href="http://s879.photobucket.com/albums/ab354/masjoker/?action=view&current=OPRSALJB2.jpg" target="_blank"><img alt="2" border="0" src="http://i879.photobucket.com/albums/ab354/masjoker/OPRSALJB2.jpg" /></a></div>
<div style="padding-left: 30px; text-align: left;">
d. 6ab<sup>2</sup> x -2a<sup>3</sup>b x 4b<sup>2</sup></div>
<div style="text-align: left;">
<a href="http://www.addtoany.com/share_save"><br /></a></div>
<div style="text-align: left;">
Penyelesaian :</div>
a. 5a x 2b = 5 x a x 2 x b = 5 x 2 x a x b = ….<br />
b. -3p x 4p = … x … x … x … = … x … x … x … = ….<br />
c. <a href="http://s879.photobucket.com/albums/ab354/masjoker/?action=view&current=OPRSALJB2.jpg" target="_blank"><img alt="2" border="0" src="http://i879.photobucket.com/albums/ab354/masjoker/OPRSALJB2.jpg" /></a> = … x … x … x … x … x …<br />
<div style="padding-left: 150px;">
= … x … x … x … x … x … = …….</div>
d. 6ab<sup>2</sup> x -2a<sup>3</sup>b x 4b<sup>2</sup> = … x … x … x … x … x … x … x …<br />
<div style="padding-left: 150px;">
= … x … x … x … x … x … x … x …</div>
<div style="padding-left: 150px;">
= …. x … x ….</div>
<div style="padding-left: 150px;">
= ……</div>
3. Jabarkan kemudian sederhanakan :<br />
<div style="padding-left: 30px;">
a. 3(2p – 3r)</div>
<div style="padding-left: 30px;">
b. 2(p – q) + 3p(p+q)</div>
<div style="padding-left: 30px;">
c. 3a(a – b) – 5(a<sup>2</sup> – 2a + b)</div>
4. Jabarkan dan sederhanakan :<br />
<div style="padding-left: 30px;">
a. (x – 3)(x + 1)</div>
<div style="padding-left: 30px;">
b. (2s + t)(3s – 5t)</div>
<div style="padding-left: 30px;">
c. (a<sup>2</sup> + a)(3a + 2)</div>
5. Jabarkan dan sederhanakan :<br />
<div style="padding-left: 30px;">
a. (2a + 1)<sup>2</sup></div>
<div style="padding-left: 30px;">
b. (10b – 2)<sup>2</sup></div>
<div style="padding-left: 30px;">
c. (-3n – 2m)<sup>2</sup></div>
Penyelesaian :<br />
3. a. 3(2p – 3r) = 3x<sup>2</sup>p +3x(-3r) = …. ….<br />
<div style="padding-left: 30px;">
b. <a href="http://s879.photobucket.com/albums/ab354/masjoker/?action=view&current=OPRSALJB5.jpg" target="_blank"><img alt="5" border="0" height="43" src="http://i879.photobucket.com/albums/ab354/masjoker/OPRSALJB5.jpg" width="102" /></a> = … … … … = … … … … = … …</div>
<div style="padding-left: 30px;">
c. (-3n – 2m)<sup>2</sup> = … … …. …. …. = … …. …. …. …..</div>
= …. ….. ….. <span style="background-color: lime; color: red;"> </span><br />
4. a. (x – 3)(x + 1) = … … … … … = … … …<br />
<div style="padding-left: 30px;">
b. (2s + t)(3s – 5t) = … … … … … = … … …</div>
<div style="padding-left: 30px;">
c. (a<sup>2</sup> + a)(3a + 2) = … … … … … = … … …</div>
5. a. (2a + 1)<sup>2</sup> = (2a + 1)(2a + 1) = … + … + … + … = … + … + …<br />
<div style="padding-left: 30px;">
b. (10b – 2)<sup>2</sup> = (10b – 2)(10b – 2) = … + … + … + …</div>
<div style="padding-left: 270px;">
= … + … + …</div>
c. (-3n – 2m)<sup>2</sup> = (-3n – 2m)(-3n – 2m) = … + … + … + …<br />
<div style="padding-left: 270px;">
= … + … + …</div>
Soal Latihan 1 :<br />
1. Sederhanakan :<br />
<div style="padding-left: 30px;">
a. a(a – b) – b (b – c) – c(c – a)</div>
<div style="padding-left: 30px;">
b. p<sup>2</sup> + p – 3 – p(p – 2) + 2p(3p + 1)</div>
2. Jabarkanlah :<br />
<div style="padding-left: 30px;">
a. (2x + 3)(3x – 2)</div>
<div style="padding-left: 30px;">
b. (2x<sup>2</sup> – 5)(3x<sup>2</sup> – x +2)</div>
3. Jabarkanlah :<br />
<div style="padding-left: 30px;">
a. (3x + 2)<sup>2</sup></div>
<div style="padding-left: 30px;">
b. (4p – ½)<sup>2</sup></div>
4. Jabarkan kemudian sederhanakan :<br />
<div style="padding-left: 30px;">
a. 2(x + 2)<sup>2</sup> – (x + 1)<sup>2</sup></div>
<div style="padding-left: 30px;">
b. -3ab(2a<sup>2</sup> + 4ab – 5b<sup>2</sup>)</div>
5. (3x + 2y)<sup>2</sup> – (2x – 5y)<sup>2</sup><br />
2. Pembagian pada bentuk aljabar Selesaikan pembagian berikut :<br />
<div style="padding-left: 30px;">
a. 12ab : 3a</div>
<div style="padding-left: 30px;">
b. 16x<sup>2</sup>y<sup>3</sup> : 12x<sup>3</sup>y</div>
<div style="padding-left: 30px;">
c. <a href="http://s879.photobucket.com/albums/ab354/masjoker/?action=view&current=OPRSALJB6-1.jpg" target="_blank"><img alt="Photobucket" border="0" src="http://i879.photobucket.com/albums/ab354/masjoker/OPRSALJB6-1.jpg" /></a></div>
Penyelesaian :<br />
a. 12ab : 3a = (12 : 3) x (a : a) x b = ….. x …. x ….. = ……………….<br />
b. 16x<sup>2</sup>y<sup>3</sup> : 12x<sup>3</sup>y =( …. : .…) x ( .… : .…) x ( .… : .…)<br />
<div style="padding-left: 120px;">
= ……. x ……… x ……… = …………..</div>
c. <a href="http://s879.photobucket.com/albums/ab354/masjoker/?action=view&current=OPRSALJB6-1.jpg" target="_blank"><img alt="Photobucket" border="0" src="http://i879.photobucket.com/albums/ab354/masjoker/OPRSALJB6-1.jpg" /></a> = ) : ……… = ( …. : ….) x ( …. : …. ) = …… x …… = ………..<br />
<div style="text-align: justify;">
Menentukan Faktor-faktor Bentuk Aljabar
Memfaktorkan suatu bentuk aljabar artinya adalah mengubah bentuk
penjumlahan/pengurangan suku-suku menjadi bentuk perkalian dari
factor-faktornya. Perkalian bentuk aljabar terdiri dari 5 macam, yaitu :</div>
<div style="text-align: justify;">
1. Bentuk aljabar yang memiliki factor persekutuan, contoh : Faktorkanlah</div>
<div style="padding-left: 30px; text-align: justify;">
bentuk :</div>
<div style="padding-left: 30px; text-align: justify;">
a. 12x<sup>3</sup> + 8x<sup>2</sup> – 6x</div>
<div style="padding-left: 30px; text-align: justify;">
b. 10a<sup>2</sup>b – 15a<sup>3</sup>b<sup>2</sup> + 20a<sup>2</sup>b<sup>2</sup></div>
<div style="text-align: justify;">
Penyelesaian :</div>
<div style="padding-left: 30px; text-align: justify;">
a. 12x<sup>3</sup> + 8x<sup>2</sup> – 6x = 2.6.x.x.x + 2.4.x.x – 2.3.x</div>
<div style="padding-left: 60px; text-align: justify;">
= 2x(6x<sup>2</sup> + 4x – 3)</div>
<div style="padding-left: 30px; text-align: justify;">
b. 10a<sup>2</sup>b – 15a<sup>3</sup>b<sup>2</sup> + 20a<sup>2</sup>b<sup>2</sup> = 5.2.a.a.b – 5.3.a.a.a.b.b + 5.a.a.b.b</div>
<div style="padding-left: 210px; text-align: justify;">
= 5a<sup>2</sup>b (2 – 3ab + b)</div>
<div style="text-align: justify;">
2. Pemfaktoran bentuk a<sup>2</sup> ± 2ab + b<sup>2</sup></div>
<div style="padding-left: 30px; text-align: justify;">
Rumus : <strong>a<sup>2</sup> + 2ab + b<sup>2</sup> = (a + b)<sup>2</sup></strong> <strong>a<sup>2</sup> – 2ab + b<sup>2</sup> = (a – b)<sup>2</sup></strong></div>
<div style="padding-left: 30px; text-align: justify;">
contoh : Faktorkanlah :</div>
<div style="padding-left: 30px; text-align: justify;">
a. 16x<sup>4</sup> + 56x<sup>2</sup>y<sup>2</sup> + 49y<sup>4</sup></div>
<div style="padding-left: 30px; text-align: justify;">
b. 36a<sup>2</sup> – 60ab + 25b<sup>2</sup></div>
<div style="text-align: justify;">
Penyelesaian</div>
<div style="padding-left: 30px; text-align: justify;">
a. 16x<sup>4</sup> + 56x<sup>2</sup>y<sup>2</sup> + 49y<sup>2</sup> = (4x<sup>2</sup>)<sup>2</sup> + 2.(4x<sup>2</sup>).(7y<sup>2</sup>) + (7y<sup>2</sup>)<sup>2</sup></div>
<div style="padding-left: 180px; text-align: justify;">
= ( … + …)(… + …)</div>
<div style="padding-left: 30px; text-align: justify;">
b. 36a<sup>2</sup> – 60ab + 25b<sup>2</sup> = ( … )<sup>2</sup> – 2.( … ).( … ) + ( … )<sup>2</sup></div>
<div style="padding-left: 180px; text-align: justify;">
= ( … + …)(… + …)</div>
<div style="text-align: justify;">
3. Pemfaktoran bentuk selisih dua kuadrat</div>
<div style="padding-left: 30px; text-align: justify;">
Rumus : <strong>a<sup>2</sup> – b<sup>2</sup> = (a + b)(a – b)</strong></div>
<div style="padding-left: 30px; text-align: justify;">
Contoh soal : Faktorkanlah :</div>
<div style="padding-left: 30px; text-align: justify;">
a. y<sup>2</sup> – 144</div>
<div style="padding-left: 30px; text-align: justify;">
b. 9x<sup>2</sup> – 64</div>
<div style="padding-left: 30px; text-align: justify;">
c. 3a<sup>2</sup> – 48</div>
<div style="text-align: justify;">
Penyelesaian :</div>
<div style="padding-left: 30px; text-align: justify;">
a. y<sup>2</sup> – 144 = (y)<sup>2</sup> – (12)<sup>2</sup> = (y + 12)(y – 12)</div>
<div style="padding-left: 30px; text-align: justify;">
b. 9x<sup>2</sup> – 64 = (3x)<sup>2</sup> – (8)<sup>2</sup> = ( … + … )( … – … )</div>
<div style="padding-left: 30px; text-align: justify;">
c. 3a<sup>2</sup> – 48 = 3(a<sup>2</sup> – 16) = 3{( … )<sup>2</sup> – ( … )<sup>2</sup>)</div>
<div style="padding-left: 180px; text-align: justify;">
= 3( … + … )( … – … )</div>
<div style="text-align: justify;">
4. Pemfaktoran bentuk : x<sup>2</sup> + bx + c , dimana b dan c bilangan real</div>
<div style="padding-left: 30px; text-align: justify;">
Rumus : <strong>x<sup>2</sup> + bx + c = (x + p)(x + q) dimana b = p + q dan c = p x q</strong></div>
<div style="text-align: justify;">
Contoh soal :</div>
<div style="text-align: justify;">
Faktorkanlah :</div>
<div style="padding-left: 30px; text-align: justify;">
a. m<sup>2</sup> – 15m + 14</div>
<div style="padding-left: 30px; text-align: justify;">
b. x<sup>2</sup> + 16x – 36</div>
<div style="padding-left: 30px; text-align: justify;">
c. X<sup>2</sup> – 5xy – 24y<sup>2</sup></div>
<div style="text-align: justify;">
Penyelesaian :</div>
<div style="padding-left: 30px; text-align: justify;">
a. m<sup>2</sup> – 15m + 14 = (m – 1)(m – 14)</div>
<div style="padding-left: 30px; text-align: justify;">
b. x<sup>2</sup> + 16x – 36 = (x + …)(x – …)</div>
<div style="padding-left: 30px; text-align: justify;">
c. x<sup>2</sup> – 5xy – 24y<sup>2</sup> = (x + …)(x – …)</div>
<div style="text-align: justify;">
5. Pemfaktoran bentuk : ax<sup>2</sup> + bx + c dimana a,b, dan c bilangan real & a ≠ 1</div>
<div style="text-align: justify;">
Cara penyelesaian : terlebih dahulu “ bx “ diuraikan menjadi dua suku dengan aturan : ax<sup>2</sup> + bx + c = ax<sup>2</sup>
+ rx + sx + c, dimana r dan s adalah dua bilangan dengan syarat jika
dikali hasilnya = a x c dan jika dijumlah = b. r x s = a x c dan r + s =
b</div>
<div style="text-align: justify;">
Contoh soal :</div>
<div style="text-align: justify;">
Faktorkanlah :</div>
<div style="padding-left: 30px; text-align: justify;">
a. 5x<sup>2</sup> + 13x + 6</div>
<div style="padding-left: 30px; text-align: justify;">
b. 10p<sup>2</sup> – 7p – 12</div>
<div style="padding-left: 30px; text-align: justify;">
c. 8x<sup>2</sup> – 26xy + 15y<sup>2</sup></div>
<div style="text-align: justify;">
Penyelesaian :</div>
<div style="padding-left: 30px; text-align: justify;">
a. 5x<sup>2</sup> + 13x + 6 = 5x<sup>2</sup> + 10x + 3x + 6</div>
<div style="padding-left: 150px; text-align: justify;">
= 5x(x + 2) + 3(x + 2)</div>
<div style="padding-left: 150px; text-align: justify;">
= (x + 2)(5x +3)</div>
<div style="padding-left: 30px; text-align: justify;">
b. 10p<sup>2</sup> – 7p – 12 = 10p<sup>2</sup> + …. – …. – 12</div>
<div style="padding-left: 150px; text-align: justify;">
= … ( … + … ) – … ( … + … )</div>
<div style="padding-left: 150px; text-align: justify;">
= ( …. + …. )( …. – …. )</div>
<div style="padding-left: 30px; text-align: justify;">
c. 8x<sup>2</sup> – 26xy + 15y<sup>2</sup> = 8x<sup>2</sup> – …. – …. + 15y<sup>2</sup></div>
<div style="padding-left: 180px; text-align: justify;">
= … ( … – … ) – … ( … – … )</div>
<div style="padding-left: 180px; text-align: justify;">
= ( …. – …. )( …. – …. )</div>
<div style="text-align: justify;">
Soal Latihan 2 :</div>
<div style="text-align: justify;">
Faktorkanlah selengkapnya :</div>
<div style="text-align: justify;">
1. 8p<sup>2</sup>q – 12pq<sup>2</sup></div>
<div style="text-align: justify;">
2. 3abc + 6ab – 9bc</div>
<div style="text-align: justify;">
3. y<sup>4</sup> – 16</div>
<div style="text-align: justify;">
4. 2x<sup>4</sup> – 32</div>
<div style="text-align: justify;">
5. p<sup>4</sup> – (2p – q)<sup>2</sup></div>
<div style="text-align: justify;">
6. n<sup>2</sup> – 14n + 24</div>
<div style="text-align: justify;">
7. x<sup>2</sup> – 5px + 6p<sup>2</sup></div>
<div style="text-align: justify;">
8. 2x<sup>2</sup> + 7x + 6</div>
<div style="text-align: justify;">
9. 6y<sup>2</sup> – y – 2</div>
<div style="text-align: justify;">
10. 2x<sup>2</sup> – 5px + 3p</div>
<div style="text-align: justify;">
LATIHAN ULANGAN BAB 1</div>
<div style="text-align: justify;">
Pilihlah salah satu jawaban yang paling tepat!</div>
<div style="text-align: justify;">
1. Bentuk paling sederhana dari 5x + 3y – 2 – x + y + 2 adalah …</div>
<div style="padding-left: 30px; text-align: justify;">
a. 4x + 3y c. 4x + 3y – 4</div>
<div style="padding-left: 30px; text-align: justify;">
b. 4x + 4y d. 4x + 4y – 4</div>
<div style="text-align: justify;">
2. Jumlah dari 2p + 3q – 4 dan p – 3q + 2 adalah ..</div>
<div style="padding-left: 30px; text-align: justify;">
a. 2p – 2 c. 2p – 6</div>
<div style="padding-left: 30px; text-align: justify;">
b. 3p – 2 d. 3p – 6</div>
<div style="text-align: justify;">
3. Hasil pengurangan 6a<sup>2</sup> – 12a dari 7a<sup>2</sup> + 2a adalah …</div>
<div style="padding-left: 30px; text-align: justify;">
a. –a<sup>2</sup> – 14a c. a<sup>2</sup> – 10a</div>
<div style="padding-left: 30px; text-align: justify;">
b. –a<sup>2</sup> – 10a d. a<sup>2</sup> + 14a</div>
<div style="text-align: justify;">
4. Hasil dari (p – 3q)(2p – 5q) adalah …</div>
<div style="padding-left: 30px; text-align: justify;">
a. 2p<sup>2</sup> – 11pq – 15q<sup>2</sup></div>
<div style="padding-left: 30px; text-align: justify;">
b. 2p<sup>2</sup> + 11pq – 15q<sup>2</sup></div>
<div style="padding-left: 30px; text-align: justify;">
c. 2p<sup>2</sup> – pq – 15q<sup>2</sup></div>
<div style="padding-left: 30px; text-align: justify;">
d. 2p<sup>2</sup> + pq – 15q<sup>2</sup></div>
<div style="text-align: justify;">
5. (3x + 2y)(9x<sup>2</sup> – 6xy + 4y<sup>2</sup>) = …</div>
<div style="padding-left: 30px; text-align: justify;">
a. 27x<sup>3</sup> + 8y<sup>3</sup> .</div>
<div style="padding-left: 30px; text-align: justify;">
b. 27x<sup>3</sup> – 8y<sup>3</sup> .</div>
<div style="padding-left: 30px; text-align: justify;">
c. 27x<sup>3</sup> + 24xy<sup>2</sup> – 8y<sup>3</sup> .</div>
<div style="padding-left: 30px; text-align: justify;">
d. 27x<sup>3</sup> – 36x<sup>2</sup>y – 8y<sup>3</sup> .</div>
<div style="text-align: justify;">
6. Hasil dari (4p – 5q)<sup>2</sup> adalah …</div>
<div style="padding-left: 30px; text-align: justify;">
a. 16p<sup>2</sup> – 20pq + 25q<sup>2</sup></div>
<div style="padding-left: 30px; text-align: justify;">
b. 16p<sup>2</sup> – 20pq – 25q<sup>2</sup></div>
<div style="padding-left: 30px; text-align: justify;">
c. 16p<sup>2</sup> – 40pq + 25q<sup>2</sup></div>
<div style="padding-left: 30px; text-align: justify;">
d. 16p<sup>2</sup> – 40pq – 25q<sup>2</sup></div>
<div style="text-align: justify;">
7. Hasil dari (–2a – )<sup>2</sup> adalah …</div>
<div style="padding-left: 30px; text-align: justify;">
a. 4a<sup>2</sup> – 4 + 1/a2 c. 4a<sup>2</sup> + 4 + 1/a2</div>
<div style="padding-left: 30px; text-align: justify;">
b. 4a<sup>2</sup> –4a + 1/a2 d. 4a<sup>2</sup> – 4a + 1/a2</div>
<div style="text-align: justify;">
8. (2a + 3)<sup>2</sup> – (a – 4)<sup>2</sup> = …</div>
<div style="padding-left: 30px; text-align: justify;">
a. 3a<sup>2</sup> – 7 c. 3a<sup>2</sup> + 4a + 25</div>
<div style="padding-left: 30px; text-align: justify;">
b. 3a<sup>2</sup> + 25 d. 3a<sup>2</sup> + 20a – 7</div>
<div style="text-align: justify;">
9. Pemfaktoran dari 6x<sup>2</sup>y – 8xy<sup>2</sup> adalah …</div>
<div style="padding-left: 30px; text-align: justify;">
a. 2xy(3x – 4xy) c. 2xy(3x – 4y)</div>
<div style="padding-left: 30px; text-align: justify;">
b. 2xy(3x – 6xy) d. 2xy(3x – 6y)</div>
<div style="text-align: justify;">
10. Pemfaktoran dari p(x + y) – q(x + y) adalah …</div>
<div style="padding-left: 30px; text-align: justify;">
a. (x + y)(p + q) c. (x – y)(p + q)</div>
<div style="padding-left: 30px; text-align: justify;">
b. (x + y)(p – q) d. (x – y)(p – q)</div>Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0tag:blogger.com,1999:blog-3177260314790837602.post-65301879968744901562011-12-09T07:29:00.001-08:002012-01-15T01:58:58.869-08:00BENTUK ALJABAR<br />
<b>A. Pengertian Bentuk Aljabar</b><br />
<br />
1. x, 2y, x+3y , 3p+5q, a2 + b + 3 disebut bentuk aljabar<br />
<br />
2. a x2 + bx + c = 0 ; a,b,c,x dan 0 adalah lambang-lambang aljabar<br />
a dan b disebut koefisien ; c disebut konstanta<br />
x2 dan x disebut variabel<br />
<br />
3. 2 x2 ; 2 disebut koefisien dan x2 disebut variabel<br />
5q ; 5 disebut koefisien dan q disebut variabel<br />
<br />
4. 2x dan 3x merupakan dua suku sejenis<br />
<br />
5 x2 dan 7 x merupakan dua suku tidak sejenis<br />
<br />
Unsur-unsur suku sejenis dapat dikumpulkan menjadi satu .<br />
Pada penjumlahan dan pengurangan suku sejenis berlaku hukum distributive<br />
A(B ± C) = AB ± AC<br />
<br />
<i>contoh:</i><br />
1. 4b + 5b = (4+5) b= 9b<br />
2. 3 (2p + 3q) = 6p+ 9q<br />
3. 2 x2 - 4x - x2 + 2x = 2 x2 - x2 - 4x + 2x = x2 (2-1) + x(-4+2) = x2 + x(-2)<br />
= x2 - 2x<br />
<br />
<b>B. Operasi Pada Bentuk Aljabar</b><br />
<i>1. Penjumlahan</i><br />
<br />
ax + bx = (a+b)x<br />
ax + b + cx + d = (a+c)x + (b+d)<br />
contoh:<br />
1. 7x + 3x = ?<br />
2. -2 x2 - 3 x2= ?<br />
3. 2 x2 -3 + x2 - 4 = ?<br />
<br />
Diperbolehkan memperbanyak dengan mencantumkan sumbernya<br />
Jawab :<br />
1. 7x + 3x = (7+3)x = 10x<br />
2. -2 x2 - 3 x2= (-2-3) x2 = -5 x2<br />
3. 2 x2 -3 + x2 - 4 = (2+1) x2 + (-3-4) = 3 x2 - 7<br />
<br />
<i>2. Pengurangan</i><br />
<br />
ax - bx = (a-b)x<br />
ax - b - cx - d = (a - c)x - (b+d)<br />
contoh :<br />
1. 7x – 3x = ?<br />
2. 5x – 8 – 2x – 1 = ?<br />
jawab :<br />
1. 7x – 3x = (7-3)x = 4x<br />
2. 5x – 8 – 2x – 1 = (5-2)x – (8+1) = 3x - 9<br />
<br />
<i>3. Perkalian</i><br />
<br />
<i>a. Perkalian konstanta dengan bentuk aljabar</i><br />
<br />
a(bx+cy) = abx + acy<br />
contoh :<br />
1. 5 (2x+4y) = 10x + 20y<br />
2. -3(3x-2y) = -9x + 6y<br />
<br />
<i>b. Perkalian bentuk aljabar dengan bentuk aljabar</i><br />
<br />
ax(bx+cy) = ab x2 + acxy<br />
ay(bx+cy) = abxy + ac y 2<br />
(x+a) (x+b) = x2+ bx + ax +ab<br />
contoh :<br />
1. 3x(2x+3y) = 6 x2 + 6xy<br />
2. (3x+y) (x-2y) = 3 x . x + (3x . -2y) + y. x + (y . -2y) = 3 x2+ (-6xy)+xy+(-2 y2 )<br />
= 3 x2 - 2 y 2 - 5xy<br />
Diperbolehkan memperbanyak dengan mencantumkan sumbernya<br />
<br />
<i>3. Pembagian</i><br />
<br />
contoh :<br />
1. (8x+4):4 =<br />
4<br />
8x + 4 =<br />
4<br />
1 (8x + 4) = 2x + 1<br />
2. 12 a2 : 3a =<br />
a<br />
a<br />
3<br />
12 2<br />
=<br />
a<br />
a a<br />
3<br />
12 . = 4a<br />
<br />
4. Pangkat Bentuk Aljabar<br />
<br />
contoh :<br />
1. (3x)2 = 3x . 3x = 9 x2<br />
2. (2x – 3y )2 = 2x . 2x + 2. 2x . -3y + (−3y)2<br />
= 4 x2+ (-12xy) + 9 y2<br />
= 4 x2+ 9 y2 - 12xy<br />
<br />
<i>5. Faktorisasi Bentuk Aljabar</i><br />
<br />
ax2 + bx + c = 0<br />
gunakan rumus abc(rumus kuadrat) :<br />
x1,2 =<br />
a<br />
b b ac<br />
2<br />
− ± 2 − 4<br />
Dengan syarat determinannya (D) harus ≥ 0<br />
Dimana D = b2 − 4ac<br />
Faktorisasi:<br />
ax2 + bx + c = (x ± 1 x ) . (x ± 2 x )<br />
<br />
Diperbolehkan memperbanyak dengan mencantumkan sumbernya<br />
contoh soal :<br />
3x2 – 5x + 2 =<br />
a = 3 ; b = -5 ; c =2<br />
D = b2 − 4ac<br />
= (−5)2 - 4.3.2 = 25 – 24 =1 berarti bisa dicari<br />
x1,2 =<br />
a<br />
b b ac<br />
2<br />
− ± 2 − 4 =<br />
2.3<br />
5 ( 5) 2 2 4.3.2 ± − −<br />
=<br />
2.3<br />
5 ± 25 − 4.3.2<br />
=<br />
6<br />
5 ± 25 − 24.<br />
1 x =<br />
6<br />
5 + 25 − 24.<br />
=<br />
6<br />
5 +1<br />
= 1<br />
2 x =<br />
6<br />
5 − 25 − 24.<br />
=<br />
6<br />
5 −1<br />
=<br />
6<br />
4 =<br />
3<br />
2<br />
Sehingga factor di atas sbb ;<br />
3 x2 – 5x + 2 = (x-1) (3x-2)<br />
Catatan :<br />
Kalau didapatkan 1 x atau 2 x bernilai positif maka di dalam persamaan menjadi x - 1 x<br />
atau x - 2 x<br />
Kalau didapatkan 1 x atau 2 x bernilai negatif maka di dalam persamaan menjadi x + 1 x<br />
atau x + 2 x<br />
Kalau didapatkan 1 x atau 2 x berbentuk pecahan maka di dalam persamaan sbb :<br />
contoh di atas didapatkan 2 x =<br />
3<br />
2<br />
3 2 x =2 3 2 x - 2 = 0 ; di dalam persamaan menjadi 3x – 2<br />
C. Menyederhanakan Pecahan Bentuk Aljabar<br />
Cara untuk menyederhanakan pecahan bentuk aljabar yaitu dengan menyederhanakan<br />
pembilang dan penyebut sesederhana mungkin sehingga pembilang dan penyebut tidak<br />
mempunyai faktor-faktor persekutuan lagi.<br />
Diperbolehkan memperbanyak dengan mencantumkan sumbernya<br />
<br />
Contoh ;<br />
Sederhanakan pecahan bentuk aljabar berikut ;<br />
2 3<br />
2 9 9<br />
2<br />
2<br />
+ −<br />
+ +<br />
x x<br />
x x =<br />
Jawab :<br />
sederhanakan pembilang dan penyebutnya .<br />
bisa tidak ya….<br />
Kita cari D (determinannya) terlebih dahulu.<br />
D = b2 − 4ac D pembilang = 92 - 4.2.9 = 81 – 72 = 9 ok<br />
D penyebut = 22 - 4.1.(-3) = 4 +12 = 16 ok<br />
sederhanakan pembilang dan penyebut dengan menggunakan rumus abc<br />
x1,2 =<br />
a<br />
b b ac<br />
2<br />
− ± 2 − 4<br />
Pembilang x1,2 =<br />
2.2<br />
− 9 ± 92 − 4.2.9.<br />
=<br />
4<br />
− 9 ± 9.<br />
=<br />
4<br />
− 9 ± 3<br />
1 x =<br />
4<br />
− 9 + 3<br />
=<br />
4<br />
− 6<br />
=<br />
2<br />
− 3<br />
x =<br />
2<br />
− 3<br />
x +<br />
2<br />
3 = 0 2x+3 = 0<br />
2 x =<br />
4<br />
− 9 − 3<br />
=<br />
4<br />
−12<br />
= -3 x = -3 x +3 = 0<br />
<br />
bentuk peyederhanaannya menjadi : 2x2 + 9x + 9 = (2x+3)(x+3)<br />
Penyebut x1,2 =<br />
2.1<br />
− 2 ± 22 − 4.1.(−3)<br />
=<br />
2<br />
− 2 ± 16.<br />
=<br />
2<br />
− 2 ± 4<br />
1 x =<br />
2<br />
− 2 + 4<br />
=<br />
2<br />
2 = 1 x = 1 x - 1 = 0<br />
2 x =<br />
2<br />
− 2 − 4<br />
=<br />
2<br />
− 6<br />
= -3 x = -3 x +3 = 0<br />
<br />
Diperbolehkan memperbanyak dengan mencantumkan sumbernya<br />
bentuk peyederhanaannya menjadi : x2 + 2x − 3 = (x-1)(x+3)<br />
Sehingga :<br />
2 3<br />
2 9 9<br />
2<br />
2<br />
+ −<br />
+ +<br />
x x<br />
x x =<br />
(x -1)(x 3)<br />
(2x 3)(x 3)<br />
+<br />
+ +<br />
=<br />
( 1)<br />
(2 3)<br />
−<br />
+<br />
x<br />
x<br />
<b>D. Penjumlahan dan Pengurangan Pecahan Bentuk Aljabar</b><br />
<br />
Dalam penjumlahan dan pengurangan pecahan bentuk aljabar penyebut kedua pecahan<br />
harus disamakan terlebih dahulu<br />
Contoh :<br />
( 1)<br />
1<br />
x −<br />
+<br />
( 3)<br />
1<br />
x +<br />
=<br />
(x -1)(x 3)<br />
( 3)<br />
+<br />
x + +<br />
(x -1)(x 3)<br />
( 1)<br />
+<br />
x −<br />
=<br />
(x -1)(x 3)<br />
( 3) ( 1)<br />
+<br />
x + + x −<br />
=<br />
(x -1)(x 3)<br />
2 2<br />
+<br />
x +<br />
Catatan:<br />
(x -1)(x 3)<br />
( 3)<br />
+<br />
x + =<br />
( 1)<br />
1<br />
x −<br />
;<br />
(x -1)(x 3)<br />
( 1)<br />
+<br />
x − =<br />
( 3)Anonymoushttp://www.blogger.com/profile/16828801433299585627noreply@blogger.com0