Rahasia Ilmu Eksakta

Pelurusan Masalah Titik Belok dan Titik Riak

<div dir="ltr" style="text-align: left;" trbidi="on"><br /><div style="text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiN80zglWbyH__AiKCxBZTLVcj9ZNdx-v0xg9DWCX09bbJUvmi3QAIrJGyhh-pkXcz8R25E8RC7JfZG9lm1EJqbYCpQfq25OQqrEgE1jURj46vnwV8LfhYHyyAZx6xgLsaPQ8PgXaVjKU/s1600/lempar+lembing.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="illustrasi titik belok" border="0" height="384" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiN80zglWbyH__AiKCxBZTLVcj9ZNdx-v0xg9DWCX09bbJUvmi3QAIrJGyhh-pkXcz8R25E8RC7JfZG9lm1EJqbYCpQfq25OQqrEgE1jURj46vnwV8LfhYHyyAZx6xgLsaPQ8PgXaVjKU/s640/lempar+lembing.jpg" title="illustrasi titik belok" width="640" /></a></div><div class="MsoNormal" style="line-height: 150%; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman", serif; font-size: 14pt; line-height: 150%;"><br /></span></div><div class="MsoNormal" style="line-height: 150%; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman", serif; font-size: 14pt; line-height: 150%;"><br /></span></div><div class="MsoNormal" style="line-height: 150%; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman", serif; font-size: 14pt; line-height: 150%;">Hal ini sering kali menjadi kesalahan mahasiswa, dari tahun ke tahun. Salah satu kesalahan tersebut terkait dengan konsep</span></div><a name='more'></a> titik belok (<i>inflection point</i>). Beberapa mahasiswa menulis bahwa titik belok dari y = f(x) adalah titik c dengan f ’’(c) = 0. Padahal, dalam kuliah, telah didefinisikan bahwa titik belok dari y = f(x) adalah titik c sedemikian sehingga f kontinu di c dan kecekungan kurva di sebelah kiri c berbeda dengan kecekungan kurva di sebelah kanan c.<span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-fareast-font-family: "Times New Roman"; mso-no-proof: no;"><o:p></o:p></span><br />  <div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;"><br /></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%;">Sebagai contoh, c = 0 merupakan titik belok dari y = f(x) = x</span><sup><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%; mso-ansi-language: EN-US;">3</span></sup><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%;">, karena f kontinu di 0, f cekung ke bawah di sebelah kiri 0 (f ’’(x) = 6x < 0 untuk x < 0), dan f cekung ke atas di sebelah kanan 0 (f ’’(x) = 6x > 0 untuk x > 0). Memang, untuk contoh ini, kita mempunyai f</span><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%; mso-ansi-language: EN-US;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%; mso-ansi-language: EN-US;">”</span><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%;">(0) = 0, tetapi ini bukan merupakan syarat cukup untuk menjadikan c = 0 titik belok.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%;"><br /></span></div><div class="MsoNormal" style="background: white; line-height: 150%; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-fareast-font-family: "Times New Roman"; mso-no-proof: no;">Untuk melihat bahwa secara umum <i>f </i>’’(<i>c</i>) = 0 bukan syarat cukup untuk menjadikan <i>c</i> titik belok, coba lihat contoh lainnya, yaitu <i>y</i> = <i>f</i>(<i>x</i>) = <i>x</i><sup>4</sup>. Di sini, <i>f</i>’(<i>x</i>) = 4<i>x</i><sup>3</sup> dan <i>f </i>’’(<i>x</i>) = 12<i>x</i><sup>2</sup>. Jadi <i>f </i>’’(0) = 0, tetapi <i>f </i>’’(<i>x</i>) > 0 baik untuk <i>x</i> > 0 maupun <i>x</i> < 0. Jadi kurva <i>y</i> = <i>f</i>(<i>x</i>) memiliki kecekungan yang sama di sebelah kiri dan kanan 0. Titik <i>c</i> = 0 dalam hal ini bukan merupakan titik belok.<o:p></o:p></span></div><div class="MsoNormal" style="background: white; line-height: 150%; margin-bottom: 0.0001pt;"><br /></div><div class="MsoNormal" style="background: white; line-height: 150%; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-fareast-font-family: "Times New Roman"; mso-no-proof: no;">Titik <i>c</i> dengan <i>f </i>’’(<i>c</i>) = 0  tetapi  <i>f </i>’’(<i>x</i>) bertanda sama di sebelah kiri dan kanan <i>c</i> disebut <b>titik riak</b> (“<i>undulation point</i>”). Selain pada kurva <i>y</i> = <i>f</i>(<i>x</i>) = <i>x</i><sup>4</sup>, titik <i>c</i> = 0 juga merupakan titik riak pada kurva <i>y</i> = <i>f</i>(<i>x</i>) = <i>x</i><sup>4</sup> + <i>x</i>, yang grafiknya diperlihatkan pada gambar di bawah ini.<o:p></o:p></span></div><div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0.0001pt;"><br /></div><div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: 0.0001pt;"><span style="color: #333333; font-family: "Lucida Sans Unicode","sans-serif"; font-size: 11.5pt; mso-ansi-language: EN-US; mso-fareast-font-family: "Times New Roman";"></span><span style="color: #333333; font-family: "Lucida Sans Unicode","sans-serif"; font-size: 11.5pt; mso-ansi-language: EN-US; mso-fareast-font-family: "Times New Roman"; mso-no-proof: no;"><o:p></o:p></span></div><div class="MsoNormal" style="background: white; line-height: 150%; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman", serif; font-size: 14pt; line-height: 150%;"> <table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir4aARKlKHngbgcr07t8_ghcvObGPKvgUBvwZCzUeff5u1XxrSa6AWPn-k7UJUORebqJGJsqr54ZVGvJb5M8ou6JYQaUPoye9ps0g57r_gIBdN91WvPo93ednWShatkL_Zo3PdVoB7JTA/s1600/kurva+titik+belok+dan+riak.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="titik riak dan titik belok" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir4aARKlKHngbgcr07t8_ghcvObGPKvgUBvwZCzUeff5u1XxrSa6AWPn-k7UJUORebqJGJsqr54ZVGvJb5M8ou6JYQaUPoye9ps0g57r_gIBdN91WvPo93ednWShatkL_Zo3PdVoB7JTA/s1600/kurva+titik+belok+dan+riak.jpg" title="titik riak dan titik belok" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><br /></td></tr></tbody></table></span></div><div class="MsoNormal" style="background: white; line-height: 150%; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman", serif; font-size: 14pt; line-height: 150%;">Masih terkait dengan kurva <i>y</i> = <i>f</i>(<i>x</i>) = <i>x</i><sup>4</sup> dan <i>y</i> = <i>f</i>(<i>x</i>) = <i>x</i><sup>4</sup> + <i>x</i>, bila kita hitung turunan ketiganya, kita peroleh <i>f </i>’’’(<i>x</i>) = 24<i>x</i>, sehingga <i>f </i>’’’(0) = 0. Jadi tidak mengherankan bila kecekungan kurva <i>y</i> = <i>f</i>(<i>x</i>) tidak berbeda di sekitar 0.<o:p></o:p></span></div><div class="MsoNormal" style="background: white; line-height: 150%; margin-bottom: 0.0001pt;"><br /></div><div class="MsoNormal" style="background: white; line-height: 150%; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman", serif; font-size: 14pt; line-height: 150%;">Secara umum, jika <i>f </i>’’(<i>c</i>) = 0 dan <i>f </i>’’’(<i>c</i>) ≠ 0, maka <i>c</i> merupakan titik belok (sebagaimana yang terjadi pada <i>y</i> = <i>f</i>(<i>x</i>) = <i>x</i><sup>3</sup>). Tetapi, sekalipun <i>f</i> mempunyai turunan kedua di <i>c</i> dan sekitarnya, tidak ada jaminan bahwa <i>f</i> mempunyai turunan ketiga di c. Dalam hal ini, kita harus kembali ke definisi, yaitu memeriksa kecekungan di sebelah kiri dan kanan <i>c</i>.<o:p></o:p></span></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img alt="illustrasi titik riak dan belok" height="281" src="https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQWkoPSe0CAcNGQbP7ldQXRJnUy_dA4PZw3jlzVvlhemC9guAhi" style="background-color: transparent; margin-left: auto; margin-right: auto;" title="illustrasi titik riak dan belok" width="640" /></td></tr><tr><td class="tr-caption" style="text-align: center;">illustrasi titik riak dan belok</td></tr></tbody></table><div class="MsoNormal" style="background: white; line-height: 150%; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman", serif; font-size: 14pt;">Bila </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">f </i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">’’(</span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">c</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">) = 0 bukan merupakan syarat cukup, apakah ia merupakan </span><b style="font-family: "Times New Roman", serif; font-size: 14pt;"><i><u>syarat perlu</u></i></b><span style="font-family: "Times New Roman", serif; font-size: 14pt;">? Jawabannya tidak juga. Sebagai contoh, </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">y</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;"> = </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">f</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">(</span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">x</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">) = </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">x</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">|</span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">x</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">| kontinu dan mempunyai turunan pertama di 0, yaitu </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">f </i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">’(0) = 0, tetapi tidak mempunyai turunan kedua di 0. Meskipun demikian, </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">f </i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">’’(</span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">x</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">) < 0 untuk </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">x</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;"> < 0 dan </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">f </i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">’’(</span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">x</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">) > 0 untuk </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">x</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;"> > 0, sehingga </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">c</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;"> = 0 merupakan titik belok karena kurva </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">y</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;"> = </span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">f</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">(</span><i style="font-family: "Times New Roman", serif; font-size: 14pt;">x</i><span style="font-family: "Times New Roman", serif; font-size: 14pt;">) cekung ke bawah di sebelah kiri 0 dan cekung ke atas di sebelah kanan 0.</span></div><div class="MsoNormal" style="background: white; line-height: 150%; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman", serif; font-size: 14pt; line-height: 150%;"><br /></span></div><div class="MsoNormal"><span style="font-family: "Times New Roman", serif; font-size: 14pt; line-height: 115%;">Jadi, jangan terpaku pada satu referensi saja. Lebih baik kaji lebih teliti dan temukan bahwa tidak setiap pembahasan di buku itu selalu benar. Tingkatkan rasa ingin tahu anda supaya terjadi hal yang sama dengan pembahasan titik belok dan titik riak ini.</span></div></div></div>

Hal ini sering kali menjadi kesalahan mahasiswa, dari tahun ke tahun. Salah satu kesalahan tersebut terkait dengan konsep titik belok (inflection point). Beberapa mahasiswa menulis bahwa titik belok d...

30Jan2017

Penerapan Ilmu Aljabar Dalam Kehidupan Sehari-hari

January 23, 2017 aljabar , ilmu , kehidupan , Matematika , pnerapan , sehari-hari , sekolah

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" 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gzRTLVt6UJEFVISpGNi4sgELiuACR44+aEzbvRmP5loWk3/N7/C6vYiLcuyzvmlnUHcJjV6gkE3yqrLy2vjVa9SyN0Yg3W51wRi/9pLz1KkikMTumYztdaHVJAKuHBOwpe1TvJ+cuYP7zvMGk09sF5ICeCannjeGjemZru3qanJlx1uM0QRsMWcCAVuYOYPuU0tX7is9nNS7uxyv9gQXHtSrteRCWiUfyxztR0mNdjVG+E7H+EIfXICtzsmZj54CXEkep8+CikBXOO/fd+9nHfLwtbrtg9oP8HNqsrKyrJSHLhry044jDTKkRot/Fp4zd4/L49ijQQPzTDXlW2ReGVoXKRQavO/AuY4AZ4EmP+RiQ+EtPIjyA0mcJ1rZiYWWM4Is6WuKewcrayAoAZ6A2tsKaouH2VVRhb15MqNEtD+K1q/IpRsqUcU70gIKTec5SOH+dK+hmNVhJx7/2k+ukGMw+8TVYWTPBn7Pe9IcoBoXqTNGoVP0o5OXMEVIAhplZXwvrSo/FzUICWdDjQAr1HNTp/P25xl1zXr8P7AkR1y3iQhtI1lhrauOZ7dmIFbCfCSiw9gYE3xtSBcDuI7+99HS3juXtQrwRQ+jlChaPB1uMMXrSeutwAfKcLWWFlZjRsdJ6JKyFkploFl6zMN+BFCwXBGycW7ni6PEKmEPNsSOLJC2xiyEVhsDgoZhIQSkbiyMHF05mScZQGqo7ja9ft+tjWnD+hQn7g6Px/SWs92trefa59Xq0N7T1y7zPeocEJ6N+40VpeVV9+AGKRElEGnYiXN2ojKbLaYCZvfs9DksiPp2rNRjYsjhELMtih/Zmjr2z0QDofbw62Ikup0ENtp5+8hRuOawhGeZe2ZGP/DxJ4PGNQWQZ4csboheKK8trLyypUbl2/cOHH12o0rl6+3JHuLcZJVWlkNnOuqkxLSyGa2kXRrR9hmruKlXqlOuRYPkq8j0SYSRFKgynIkm7r6fQqQGndULlRCliAQKBH3EVjh9IHUNXHyaV3AY7dLFpXsYIWY9uJyZGl5abyb2FJRdDcwfvAe/JwC9iHlLUCUq//oVEptiDObdZRttDdqrqpPgKOCCQ+1Lq3laZBNGOfIkanMxTaWeNV2hhgcHfgUSOVgPxo/8gTPsg4chWxcxSH3Uq7Nq728PdGPqo03ueNIa0FT4EKAZcFnlZU3Ajq50YUc5io5q3QMRAmAZiZUctCeOdKLV6rCs76CrNypinNkuj/TkfQN98Y9gKQNB3YhiRj4QSOHyP+ewSzrACSpT5Mo7F0qrtW1joLVtfAN7Rbw9PzgBd/hBpvcXgscuQK+cPmqk5HSkSCi6+spHe2E91X1Fg48JgXaU/FOyrO+JoFeZ8NrjRCo2Nm+TLWhOP1RhElhPEAgUk7AonP1v/+S7fSHHyoZnXZesiSPqHkoVFoNNhmfj0kkn7iFiLUIEa2Wr5JfCehUUkYd9rYJq8wuikROC6iLcxgYhOAjAml9mB+vp6glUyE5D03qOpTlI/0csmOVeHk3Cj/B7d6tpaRCgpDTNo5z6XQImZZhSE3oMmZSLeWVFcCrymqLimq3t2CDBKcPC7CoorSo9nIoykhVOn9HjTdiriKcBgg2sMwMyEiFTPNSjM1qalpnT64K8hcMTUh3ZtH/TlIvtZoa8mvcEQGvN8Pc2Nis2kVLISgICaFURVpNy9CsmvbJsgS20iLAxvdqgDsCyaos4llW5YlPQqRKSrWNQtx32+qrjBBqEAAyOxjaKvHNg96ETkdP68rzfjmFdsjxfRPSaBZHno0AvzFHWjuatco416QPbdqyqeuw32GjaVrJxKIXc7n9lHj2fppoO/E2yRdXq4v4kQvsJ1uqT4QcjBHyDq0HlF83oKqqYkgbb4gCVqn15EvAX1YZwDrWOVKjZyn+vgXMcNZii1eiNMq2oEvK601AHt7EVxhmhzs7/ajdJFma+YE0W2/ExxIqKsF7YNVVg/MABcJKKy2qvvHVkI6SEgZSa+KDRzNgMiPK1d4K2OQ6bkBRx/sSknO51tmvETh5tQmUWaGt7zBbz79aMsirIT5gVxJNlBq29PX1TZ3NXYJasEgTW4GB1ZZubwFlleJRiyJQIbAseHttHpG0XChg2oIdcbPuQPVVKogAph4CDBFZ/8sXjmCn4uCc62zHgZMkctcRZjs7WQOeSDU4sK/BXDMtH+875FkWGXYkV/CoT21iDAjH7u1FuAlVVnT5k70Ohne4DuRJLliJVmdjbdSkr9cAiGxoVKvDEVzOMit3rJZQGzLyqQ2X7Uj44t1uLWOGZR1fbQRvkkkf2p+DhaSLr/8qnmQqa+G72MBJWuBDPKlw/VoAIEgBmYFD2vmOJDaFGzmcDkdPvicGlmihbCoMzUy6GN0i968xryLV0bBkXCWoa9NiAXiH1Q6tnODzH6kuzWrHnMvnoTXtf+antYrKWvAkCV/vKYKItv0yQhyQbiFh5NoCHrU2GE7+oQZtmxVBRPVaCUy2zDzrMiKlQ5l916BVp3wlZcogJcVeQh7tylZbyqXMDltdlEouJZTpPHrYBDRzGWx1rSHg+rX8bCtvk8kxoJYrJ+ZDnIF2oXZvfl0wGF6Y+Nrptbvf2Jlfcy4qrOeB1ZtpRDHOzExbZtGhnrddiF3BwZid2E0IBLb+JaDhynJf1+yh3VGS4g4t/NCW/l5Te+9ybtL3kBWMElMszKtaEnOEPOequPxHLfLbwe/71B1ZLxD+dGd4jlIapHIVA97f4MxqsxEo7LEHDTRaHpuGYgXYkyjVWSWSRfCwcWoXvM2WLqRmVC/1LFdEqPHOz1/mSRWw4vKKynj/kK+L15Z/elV7rgn7j5ysps6EEOt0OjjKqNJlj0ApWyUSu9WoZJc3Sr3DqXMxNK2b3bQctgTArrQXYNh28+bN+oh72TBQ51ZfLuUnmQBedTXuaZeXYrMsB1Ly6ScQscNLlWdNapJWyeVKILBZXkNG9UokpoicYZYnmDIhh3gZnh3r27JlBXzp39/9lz9xzE1BYHlnqZCoR//j7rLEVGsydsfDd1n5ZW1P/1I1LYWkdXdU50SkJVs7GtIkkQAJdK3YEZbVC2wsQg6Hv3P3Uu4kF8yxw2gU/efNV5ctk4I0tWtvVPKTQC18HpAYdq3ms4LK36EB71K/WeNzA7FcfP/6iAewcVLnqnqLGjM4LSfrVM/NHe4a27SS+hLgtId0H9+MPdSxPO/Kr5H4/3w5NQIKGivFJTsw0tLqisrRT05Y3b4lzFISWsjYZBp+wBZ/aLbaJZJ2m3S1qapMb5aTYJoOMrL7cFdX3yrgdUX+0/LwTRa1adGSL31cfOHQjRNXrtTiMBCfI+RHeME2rweuVF+f73wopz9pRgtl/yoDY3PpHBQOBpZOiUQyScnX1O7WmA0up4vhdA52CpbfCt7lMPUweBPLww/XK9GyhtkgCWpdpMuJ/ngZkgCcmILLrMQMrPqquqyosvbKY62exbpv9qfWUxXVHzwX0DKUA7f4jT2AzUordWttnBK0zslRjI2cA++yXFzo2019PP7wzYc//vjmzT/5lw4FDfbhiMqskWnMQgqNVldvvxubJ6w14GFF8+fAxRQVVVz787CnI9M0mwMpN2jWtXrsHZ4erY3ikFTDhCEEqEGRayaZMj0BOT2OCzG2f3ZsCy85llsXcmr/9PBNMGTDww/vb85v7vA2LZolwC1SJE9OoWssjseuVMZtshaT5+vq/4Cg0ILLC9cQanWn1SYagraUWhg0CitMYje1WjkXYqLgJk0OlW59Gwk0FgPHOkma5qLOWVh9Y3192fC2DDsY9uObBFIy6OOb+5t9USYWa1vk0BXnIunRScP4r1SX8qkA9iknPklMTFZWXnWo6FhbMGmazcG0KQS9kETt4BslEk9PSId2YzepkzuWmopaGV49YUMOG+fiXLrI3PCh2Sz7HOtnGYf5YYHTyPzk4YdRQwcFjoxZhK0DZQZeDYMqixIV16LS0Akc9XCCcMVJQ1pAJkdJG1ozd3BqLLZQGKOz9zrVAfjgnMvI3sruFk2VlGGR00HSlANpp7J7OyzlMN/8T8SiP92kWxV2Sl+lt2X7FEUrlfVH6x1XeSvE0e6K/zo/xFVaXv1HF+QZ8mQruK59UZ6tIbTIhFVnd/eCgQ5YGQbd4j4Cmd6iAnwuTp2dk9ucDCsFP2n4+KYF2fO9P6KlhCG72dHUtsiXCdC17ZUVfFdq9JMKXFquqIa0xwi5CIPi3mTnQCyHC9So1LzqeLEP+Emlg13EWdYKz+VSSWl1VpcAWSiH6y/gI8FTzvUq8r0xo0Wuau3IDMPuBconS4yo6pH2j5d5EnbdfwMyVWCX1aWjuBstjcRn2xRuR868U2axBt1JcBLPKEct5pprFLNTSUh1h7O6BBFNvZPTsST1rb+ow7BKvD+yGGkl0rY3paObkqf+jMXJ0/kqBgFX++R6RUXLFXV8l0dl0adWJaSqVD/fvlOY2pbcokWjc/YF1UVtlMNhuIWpXhmlExA0ylBb1yEkz5PJEUk6MM/Glthko2gdZ2/uVQcX0NX0LFA+Mz4KQyZANkukwxu2Xr18vf9EWQUmKmVln5BYbVG+/lLnji7DNwhre8ouJe5glLLhsvp6pyjrnbRQqJvNNEilFF4tAIdwlsW3p5sefemUdbc3v6Y5bF0gGT0LnUCZuSqvnkEqjYwO59d1DKhHtY/NfzJ69cSNGyecBlAbwwcAhXv53bmWyDmMKo7Q7vbrbAzLrlhdyC0yxoFrCekdkC1dSQetqTJXWbR8nUrR3NTQEGcnHfPqRBBWnE2n6jKVk8MvicqNv9Wh1aqHzndPHb4Y7PezDo60uutqavLr5v2cYJnd3jK6G0CFraiHN077uQBLcohb12ENFkQTUldGANgyvLCK8qoii5PLBntAG5/HytAbx0o1PER+1NfrbLdujssQYDx79mJnf0+vx+PuBGPgBPVLqEJjg8TU/jaDokFTfNn1tjrXh02j4wQCw1zGahtLmxTQkK25MhyfPYh6wTO8YZBppLyNgRuwJcY9eWw17jckk5szZGiou3vgYnfPeS3yB/fb5Dl3s2tiAMl+kWYFNArHwQURvR5/IjM45UIBl+kku2wLjt329lJ5tzeMzjV5YhoVQvBzBOKStypTYptsQl7J2c25xcr1d/hMA4GIarE69FFYafZ5GhICIjpgl9jf6CfXt8/RjCiCUGX2G/v6U4tIpkK5py74xeYNa4Oo3kxL8/RKpEzZGD7xI18xcK4u3J0b2lDUGAWCo/B50OJ6cr0a1pknasDjVmZXILw3sl5HQuoEAqHtUMYoZdfCP2jULjfBA+iCeFgqz6JDafZlQc3wHW2z4rGh3Ni6XXKWz3bdaFHNFV7tBWx5ehKtO7zhDr/QqM2kW12x5LcNSw2ULIgd6WGlKdNeWj2ye1H/XndNs/Xi1Plc2GYZI9uEy3i5Yrhldxq2PNl6IxvugggIIbM7g5FsOpTMLQitffk+DsjOHs7lSncKembKffHVC9qwr86p1fYPX7zYfX5oaHOaCo8FKdVkQ76vN2c9hJjH2CIJbOsWmQHJBYQxksWShxP/JGFdqY+DxYvYdMpX73KGAxfuuoCcwQ6fRzvPMRTpcASCwYsXZ7u7h3jppAytDR3BSE6qKG8H12ji1lxQyBIIbUK8jStDa1u64ic+yKRoNdAA3NuRlIesAqc5oL5w112vXvinn2gl+V5PGEUoWklTFMWQHOeKYHGSVLC9bQkXwRdLTC5qvc3GuGhYjifnWYPLs/FUnlCvbJBx8fW20ZYqjaberIwGTBcRQLvrgX+6664LIQ+exfO07w7tPxWJxWIkoDQoDSrG4UKupUzOOAAmOaBF5C1lNwanihAKlVlduT5+azdea6tDlo8LlANBVueYDKCwd/RVDC0uF5CnQZFfU6Ooa/BJPHZP7+Qk3lLiYNEy3W1Dq2fUr2NuLXEzOynI8gW6rPb+mIPftr2yh8wQRXOH1+d7SI1+8sBdd6WBQ0G3R+L1+nby/FNR1wxiH3UsM7WlBCO+1UNOZDTLNzadWQOHs3ijYP2p5QYvlhSf+tV/uuuuDHBT3WeH+/vR2z1u90MSuxfv/fIg2zJJi/42HJtk4WfOhbbd2XOiQrxNKLweaPmKdnRXprx6OMlFuru7d3de7O8ftXs9PYEoReghdsk05vrbfwKUxokdCaHKCgCbxlAVhL3wskPWS0tD64VMbA+oM6P30NAU8tTUNUtMPaGYymLUQU6wnrHCZcXgNOKeI21dtE9ApmECyzc3lhHPq1mKuxDMIl5DkMbj07zAgSI0+a3Xg9ytefvFYuZDm0AYyfIkm3YbNeQyBfKVpFn9QLbisgjzGzpGzfPvpoHJr//bL5W/oJH0tpqljHLw01sqNJaFbc7CtK4werGsBC5kKy6QRZQ5YxSIcl1H0PXaT1977vmf0zrURgmXSlXXLlWIxhMneHtfNinhgus2SCymR7OwPYAyV9xsTMU25O90o189/8vvvvz0y39js7mbwigaU5pvDzybDo/sECpndiOnH63QA15JfPsfyFbcoXRoxy4yysmdvp654z/42U9fe/GXP/i6jhrALVS7249iRNUt46vCWwWEQgFzKMsix7Q9twYtvy6wCJt2qjsh588PnQ/QVMDz9kvffvG1Z55++bkXX/thlJ7nvXKNz+tB1pj8FtWngrCNy/PZAWBL11q0lpNuKtqzF9wDVs7mwqJzOVjgWxSD2F8d/xlo7fvfee6nz7/moNpSqwCc56hTR90C4dLrGH7qjvZnt/YP59ywnVs87R05/GmN6SdZ2O56lSOEeNAURCCVMk7nz5977dvPPfP03/X3/6+nn/nhKeZURt2iQeIOItuSdbAVhMBpGwQA1+EsaCtOp6XfgjrW1vrQ4p+378/GdoElGYaCi6Zpg0GpQ9/5wc+ee/GHjiilO/2z1158iYlkdYdqGjpMrW0x+TrinhXL1nEAABWmSURBVMYR308l78/2JLPtNam/7g73mnrtizfaJOUc+dRTUi4absoyzaZs2gWesvXcwLnwGz09ra2tQaf/pf/54vP/44yTMdLo755/5rm/tcVyJYq+h1qdtjWvPakT76eSqmyoa2wMd/STCPsScy51knBn5Jv015mvk+r2JYpBXu03dmzdseMb32rL3E+TA9td/d6afEW+QqHYuXNnQ+8Z8CGn/0FnMLj8PX/z8ovPfMdGvpHzn6jzulFEvqZegIzjVEqG1DmdbD/I8KHkRMaWsbf5BaRwI+a79x/E/737LpOV7DTHxzFqTNx9W3fct/W+rQLUnrHsmhc5yrsytrs1qb/99N/7bUbK2uO1cy8f/9nfkmRv7tcvX9HgQfsZ4eqVVwX01KnjKJWUkEpVKqXNxVoPzWIF7saepKZjwPnEwfvvv//J+3lRqTNWul1rgnwzvyHwDcAG/933NW20Nf0nfK2LsD2aoft2K9IpVRHMKiW6Z5772WmOeXvprEPR7G5Fq85UZUISsSRlFMR3wwmFUrmS4SJzhw7jYqTCgxxPY0wHMT74/8nTGUmBxxpBvRKf/dRTO3i17fgbhkLpHYMc2J7NwNbcO+8ire349QBsx5/54RmmddmMqqGjN7Rq29SYDZwTcfHhc34nCyGVM0irhjgjQeiVg08efEL6zdM/Om18F8A9kV5a9iLjfT/+pjUI77DSdmz9htZIBtPdSQ5sWQVcRfNAYsxXonv5B699/4xteWy4Am1HbasvM8gIxoE4JR8MCKmKivrdTQo8hgTQAM8kWK2NZCfhk4Nkb+qfbkBfu2/Hjq1bv6H6zVZQGqy4H3GGzLJ6jvW2ZMqE9fby9yeZyZUTD4X3XADRq/WbMr2Uw8ZpUFKu/a0e3tspwugMrLODKuSKxRilyhV49/77vzufujf3S09hdcX/x3r7MTJwmTm6d5GfvNC+1GZuieuZ5157bo6ZXA095zd5xqSr9ZsAj3Q41YHeJkVN4sZAbQfvf9eBJt2mUTUp18XgM2tSMVhtW7cm0IH6tt5HOVRZg2wdKDuDe3TJ8VLJ+y8///LT/0ixSzdUMuE1e+ajJLFqv2lJ24u4Mxw68y44EOXFBvw1r58xBF65/34mebxMTS/65n38MuP9CCBk1Nl7fiFfaXv1wgNYLly48Kg2e0Npxs+yP33xtedOUdFlOyoZUtNkCiJqdbZpjr6x4AY7rGdI8P0H2fiByfmeiFz3/YP3v6JNDfh3IO57vDni1Qbonvoek73rr87bGm4P7m0LBXt6TfbWc7nOXUli0wK2H/wjrVtp/jQDXUNTeLdtVdDOpa2WMMlR2PMntzo3WA025v4nn9i/cPd1vWrmX3iV7cC+BAASOtSRUTpShDvwFmhFTQ2A8oSXO00i9PTPfvDLM1Rk2f1M2dgUzaYQWhlaVTR9n71CTXOnMR9JOe12hrHdf/AJV/rr2tFu/Zi3S6w3XoNfa3s73agU7jR+6E2dcIK3Rvt2KtJR1AW//eLLr3yHWfY4jQxR+Ly9QFXkKzd5NLHWdO+7s01JnsYxm0u+2G4bx0AUP+1O//vN6H/v2BH3lPzC27H1N7F0h6Jwp/14s5MfvPB1PBQOvx0KjIZ7H7J7k3DrAsqXP/zOs4xtdScZNHR4wshKWVaTnOtjmUfi7GxTUSSEgCct6jCPucYd9T8NWF9JP69W4XY9tSPlLHlW+WMuGkp76T1p/FCh9uZ7e52Bi11jgyMvDL6weWxo9mzn2x7eWdUNqFmHy8VGV8BWo6hrsofnoxGbfJVpnYzJKvvstCoNAewnDwp1o/Ymr8SO/EqAdtCcfoJmE/pGwknyesMffE2r4tpT2GpM6cetnTV5rN3H3il+pFHMyy7RrpLBLVMhfv7Gq41SUppFvUtiU9Q1e+3uYOhUTEWsvpouy45M+TUBSs7SPI18lw4BpXYp3+WZ5cE0Jl/T+ygfA3bs+M3XfhOPdj/W2gTRhYy9xpNuwia0+1hxwS5RiZi/CkQlxaJiccE76rcl8Go097RF9s91e3Ottxpfk93U3oP8EZqo16zi0PiUaOjFIwimiJBCloM8Rz5Y/2Q8FcBv2IVEx9v2L1vjzCSmRRHpv8AH33JIlWm8qsaTdtxaQ/BQSWGhqBgAlYgKSkTi1DWm5Re71549KIx7Wk0dvaPq/ZEYLV1P60PlXzwY34xoqcvxypPxDCCewvEXtUAter7FmyJmyQaKDT36f378PTUtcKVZVbqfrDFpL4rFBYUFcBU2FoqLeWBiuES73unMXmYKbIESTziITsUMUss62yAyY3wsvqYuXRp6o3K5LhB7ggfEI3vlR/j9whmaDdbvbY17f4aTGtsk3qDjIidQpid5OL4lpQMNdY4k0IgfaSwWNYqKAWGxuLBYLB5UL4Cra4BlFR7oCUQjjMCs16x/QEHGoAGJqT0QdGr3nzp16tE2Kxa1OoRcUiHtQmeYV175rlzFnEF+9C4mmCjltnv2f4zX29anEE0wQFjqTIiRR95IWzCKhTpEQ3BsxD+IseHFJhI3Fu/aFbdJ/IXGLVYPvKA+b0dvj3X/Swytuh3PLJHRDhejlAotZrNZr9dXmZNCOHUqQmpgSAcbYDmSolXs09i1tKUcpc+DGKBdW7/hNMbnWOtMal0wPUym6c19qKRkajNGUyISlRzbPDQ0WAL+srAwfom2qAfaUWgOL6uqtTiL5cHJZLm1Xs8hjpYLpQL+P6NKStKA7UlXGvFobrfSTz11xiYkEw7Em3lsU11rciU3aTeLSrrON4IvaRzpDrKRWNR5cQhsFNYdXOAvu5Gr/lYMcG2iISgdpHUMHppwIKSizmC3wmSUayQ9j8accmWKmmW6hAZtQsmKN7oLCsWbh8XFosKR4QgjJQgpo0Xo/Ah4FXFhgbhQ/AJC694FsB6R6S1ShgOBaIeUtB/Hgm+OZtx+nd1vpSO5DzHMb0hWcH3aQVhWg9qSxuLi8xH+RB8bjppzh0bgK6JCWHfFfch5a9PW65UqhBgjwl7zePae4Z1upF6iEtCU3IUp6SwEuxvpBITH+lVCASF3OeWwrjTkbgAnKiwWFRSXDCPyNvdNVyfycJiTO3Am/sqiE0IVTUslyx2J0k5NGFZaQcGu2aHGgqEI3vTvSgxp6WPdEN9E2CwL+rS35SzeNQv5Xx6X1PVNcCZPOFbYApcmpgRtVqhH4OaLxV3nRcXn8aE2ttRwmgUda9zFx4LGY52resLcbRZZvcPriQgZDnOT76x+liaU8JrN2kG8pkSbp4pFuylCSKedUGLwjxQDbriKzzLMhi85s+EMMrkdAjqCOco3gVTVrarHr0iSOe8h4MTgCwc7S0qGlYRcl7btVzN3DJgYJmO7xmJA0DfUKvV0UHvpV48i1mh0PAG065XWnb6e0dWMnfi0CdrsnRoBZyEWjzhHMDYqY4ul4awIUoJCiOmbI3J6Q5+8ovE/e2nbvfvu/QWw5wBmJmb0hv/ZR89md6RyiCSZyHqnSvB6K3jEOlg8TAvYjB1XlmGIDGIM/YU5o/Q2nMi+ehHuvwTItt37JrIJAt8FzqxC1tcvXfrFRdOK3UdTMswDtgJskyXomGiKUWbqxoJK4norLPYrCXoDn44qY97koV36BdJJXdSTT5Do9X337oMvPBt0L+8xa9rtKWxxmyw5dKxxy5wr8+AHS2dSbyXDNGFkN+7hJJozPJR9b/kRohnSiH59aRs2UXjzd2+2LTuj15xkXFhvYl43/ZtFI1Mo8xmhxLA4oTfAJhDoNu7xYhrbm9v27dv26+Ckc4CjEXprG8a1jcf3unbZ8yM6+pMOp3k4hU28qw9lbN6UUUNicRybaJYCbIuH6T8zUaJn3/x1dDLcb7KrA89uA2uEC0Pb9vdOdmAZd6kIp1i1z8/HN3Hh4SFRYcFsRoTWWwdLktimIK5z6zzBaj1iRjqSpBi1u8ON3ty3LWGQ2/Zd+nmQopfTW4M6tRwVPZt5bKKxbki2R7rUC+OseuZsSXES22GI6+RqiuC3S0iWNpBOz3/1PPrP9/IGydvk6/sdKkKVc/dRQlemNOLp6YZcBsLAEGCDBK7PmniapMwSQ4OipN5Khg0CIcmscD+3U/Qcam11D7S9tS2Oi79e99vkhNCImnLPBOU3q9UDkvi3ahq8vZ3WEkhBC0V93fi9uGRw1u+gjEbagbpGRCKcnmK6OdJmIAhuA9cbRIFeiTvw60v77o07EZBLb/JnHKq4QJPXk3PJ+TzexJ4/nyfYeb5vEzgTsSiuN6y6Xe9s7pudHds8KBYXFDQW8tUv4CVSoWBDsenVnvb+t/YtaG3bpV8HKaFQSEeDXg9C7lzYkuJ9IzS8uQSXSMDudu2KY4N0DZCIS4oLikW4pvAIH98ai6dIQiBwbeQjJo3g+Pfduy8F7dKb/S4VQRjJkLujPWKpjyzZe1JIAtrzg+AecZ0OgnNh4wK2ROFVLN4lFjfu4r99TIufmbHcE2Vut5gnwYekrHHbtrecZ/DBjbRj+CETwo8YMVuX6Jl5e61jI8V8LasgfhV0dSfqymnYGksa4X/wJd0uISFUoQ3LcjTGwLOXFnzIvkun/AyeSqQCaLTHET8C05Jzd4TCo50dAUDxQhbvLApFuzeXpCpbhfgCFT6CS5XwCpyP4nMv6fWeGbdmkemsb6V0Btp7Xe0yEFKammx78603U08Ak1oXE8ud4UODJQvF1YSff6GwMIW0gK9vFYLiikWguLE5JT48jNuwEKBHzyYpVnylkVJCavOjNyHtufef/YmtwTJVKDsnqOsNjoj4smpBor4aN8uSxb2OXY2i4l2iIaTE0zvGDXyOnznw67iHvHffvtedZwyEnHIg/+vYQvfd+1Yg+XRQJmsAWBE+O8gz/+IMmxQXixpTXyhMXAWPNDYWD6n52WKCvN1bBJYRDYeAK/PIfhG0CYSGiN+NfpUgy2+hZAVAE8t8pIVnGAhkmsZSeit8pDHNuYAHFePmwGBXG82f1Kq6DQ/UWrVYUEfoFwDkX3+NOINAwLSFm+yP/isfEfZts6YeDpZXdSp9BrghsFmUtMb428Y4mkaI2rsWIIsLRYObh86f74+oBPEDdm9xj+KaJOLJbx549tJb6IwKfIi11dPcq237V95r3vvWmbQthWb1QwuRQDKM3WGBCF/xbuIjjQWiwkbRSMmIWFSY9CzwvZLNKOoiDXiSjBAQzMYFAHwafxNwwzAKguNXccjTJEExSwBICiQErwcoJm1LoWChr1yn5ml/QbqfFJeMgIo6rcNnIQw0LvSEX5jipETiOE8lki9zL7db4p3EunBUKqWiwaaOc0iugYzuzUuX/vlNREq5tFqcjEZJZinZPZiBTVzSWLJ5qtOv1mpNTXbt2WMivqHIX7sG/RQR15rBuZFP4NXHEs/kmI9EWz0dbit/2JnegSYnJzlazmQkmRomUdaqmxoSpWJYMb/MBmfnGIMrPi+mmEdDYKEJvRWL+tRyDA2i9gqHFd5esaBECtbR7pF4kC2+C1hmRAa5VE6zzsz9anptvBfu9Y8Up+tt166SqahKQPoTVeZwVDsi5pk/vsQlhxkhuBHb+o6BWK/IqNR4iM8UjKSmTfUOF21jEZM9wGhW8+ebeKbEGdgaS85GVEIm9WyAc0amW7Rgr6KxiEAgVCLBhlaUq5KDMnX2xyLp/7TFRjLyHHVEM96cuvPtY418hz4RwAoxUySohcGUMFGFBhvjgRtiQfE7USPeo7ZxdUksxvb41h9JO1Jl2otGk3vVmxHEjN0jqeEYHAAaB4dpQr4QIhTtRJ5uSFSQ5JOiF9QGASFnN/Qx5bL4A7k72tWrP4HCYvVIdov5qZEkNtF5sDnbQmVFESTyDFPieB6Aszkx3oItd2zgc4Uxl/Tl13h79tNrsRaLNXi+JB1bYfFhSqhqW8gUsN7q0Uhqve0SdZGCDa254oDVW9fUu9hjrCAEOi9Ot8nCEatKwCBFBjaNdXABW+NQDMI3uYF1SfB64YEok/Mkn2UlNpSoGxTEScngnFweTZsRVUwCtrnBlE0WP3IsIpAS6zhjct0iYxCi17O+I5tFxWkxQPTOSwLlxbQ6piLAYxPzvgQ8SkHjO3MqAUHd2pEQaxINWl/EkfUfa0zL2ArFg6ekZPpUpGLSkqdpGyxIxoDCwnfwI13oDczcZJb1/VsydCxDb+J3rIZI+rY2xaQZr7fGhdS1ZChCCA3sxga49YhMm4Vt10WGTZ+Eqpusz6vqHBEVJvgkppQvCQnlXwG27PUmLt40p02vFTU46vMsu4tLUr6kWNxNEoK/Br1hP5nJS0oOa9MrmM0AIjZUIlqopYycpQmhcgPX27rFkBW7RcXHtOmbkJp1Gr32WGMqxykuLlEbCILeQD+5brGgDD4J1yOb1WnVlGaXOTZVIlqwycbNEamAWOmo+S+E6F+CIJCYHEzUgkTHnO2pCNfkjJxN1Uv42D1lEwqlG9kLXrfIqKz8DWvxhbMBO/+k8ZrmXtQ9slAvwQOVVlhu8o3scaxf6q3nC4vT8gB8/wUlWw4FJ8+Fw62dU5sz+jgloqGIlBBsdP62XpGjY424a5NRMC95ZPDY5r5jm98BhWbUXkcOUfg52xvW47g10ZAXIYUpLkhNWvPwcB9xl6hYlLmvo1g0FsUPibLpPu+7XqXoGVw0SNa5CosTlzjjKuQdTuMxNS6XG9l1PBTz8xEN0z+Y6GKnLnFhivljg+ULYOLiY8P4JA6hciMryrcoGhsaaczRx1nQIh7KaCw41s9J+adIcX8dy40XDQ1mWZDyk+ld4Ph6e6QRgsSYlcFPWsX7mj7vG16LaLj+zeJGfvQ/bo3YLOPtKv6Dxl2ike45GhskWOSan9L9+YpGqZ4aFDWmrLBRnNFsbCzZHIio+IbiBlfLb4vU2/znRwBFI47k4kcaxdjr72rc1ShuLB45dnaO4p+PbiQR/Ve02JKiscT83YO7GhtLYHk9gkGJ4c2u4pHBobNtpAGfvSFlnOzqt9d/oURmtjnPbi4RJaVkZGTw/FSA1TFS/sGHBofzVk7O/7zFTCHtWXxC7/nuqc6Lw21zMcYgF/Jn8IE5Mn89cS2XaBiEUDQWoyiKVipVctAY/2hcgnKyazgl54speh1qDUYjFH6QMVYX/xRSFcM6N7Tj9hmJOdrbJDENaCM22oiHf+QqikMuw9pr1l9EIZAkH58RGsK7mTkXixB3G/aTfkGESEwx1HkfMiGb8NYPKfwiiTK1Px73A75coqGQ78uKDc+fNH1ZsUFiEO8Lfxmx5eljQf4RNFMb2tneING73sAHFrRv5NTWhkm9Fm/RaVd93vfxmYg5alLkh7+c2PIsanv+uS8ptjwB6uj9smLLk6K/tsLP6kUmRV9aveXJzF+CrO2O3JE7ckfuyB25I3fk/zP5f/5OTOIngvcXAAAAAElFTkSuQmCC" style="cursor: move;" title="allmipa" /></a>Jika kita mendengar kata Aljabar pasti Identik dengan Matematika. Berbicara tentang Matematika tak akan pernah terlepas dari<br /><a name='more'></a> kehidupan. Karena hampir dalam setiap aktivitas sehari-hari pasti menggunakan Matematika. Mulai dari bangun tidur hingga menjelang tidur lagi. Oleh karena itu, Matematika menjadi salah satu pelajaran terpenting yang harus dikuasai oleh setiap orang yang ingin meraih sukses dalam kehidupannya. Dalam keahlian bermatematika kita dituntut untuk dapat menyelesaikan masalah dengan benar, sekaligus kita diberi kebebasan untuk menjawab dengan berbagai cara asalkan jawabannya benar dan dengan cara yang benar. Disini kita diminta untuk jujur dalam menyelesaikan masalah yang ada dengan cara yang benar dan teliti. Karena jika kita menjawab soal matematika dengan tidak jujur, maka hasilnya? Dapat diprediksi sendiri kan.. Nah, dalam belajar Matematika juga dapat belajar tentang nilai kejujuran…</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px; text-align: justify;"><img alt="pembelajaran di kelas" height="398" src="https://saripedia.files.wordpress.com/2013/11/kartun-ilustrasi-pendidikan-belajar-mengajar-320x199.jpg?w=320" title="pembelajaran di kelas" width="640" /><br />Membahas mengenai manfaat Aljabar dalam kehidupan sehari-hari, mengingatkan kita yang mungkin sebagai guru atau orang tua saat ada pertanyaan yang terlontar dari anak dengan wajah polosnya. “Apa manfaat Aljabar dalam kehidupan kita sehari-hari?” Mereka belum tahu betapa pentingnya Aljabar yang merupakan dasar dari segala ilmu Matematika. Mungkin saat belajar Matematika di Sekolah Dasar kelas 1 atau 2 kita akan diberi soal seperti ini, “2 + Berapa? = 5”, bukankah itu serupa dengan “2 + x = 5, berapakah nilai x?” Setelah kita hitung maka akan menemukan jawabannya, yaitu 3. Selanjutnya, manfaat belajar Aljabar untuk kehidupan kita sehari-hari akan dikupas sebagai berikut.</div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;"><br /></div></div><ol style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; list-style-position: outside; margin: 0px 0px 1.25em 20px; padding: 0px;"><li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px; text-align: justify;"><strong style="box-sizing: border-box; line-height: inherit;"><u style="box-sizing: border-box;">Penerapan Aljabar bagi siswa</u></strong></li></ol><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Tentu saja, manfaat Aljabar bagi para pelajar adalah agar nilai ulangan Matematika tidak jatuh saat diberi soal Aljabar. Selain itu, manfaat Aljabar yang sering diterapkan siswa adalah untuk memanajemen uang saku yang diberikan orang tua tiap minggu. Contoh penerapan aljabar dalam hal ini sebagai berikut:</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px; text-align: justify;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img alt="Jajan di kantin sekolah" height="429" src="https://mialkhoiriyahmelikan.files.wordpress.com/2015/11/kantin.jpg?w=1400" style="margin-left: auto; margin-right: auto;" title="Jajan di kantin sekolah" width="640" /></td></tr><tr><td class="tr-caption" style="text-align: center;">Jajan di kantin sekolah</td></tr></tbody></table>Misalnya, uang saku kita sebesar Rp 70.000,00 setiap minggu. Karena setiap hari Selasa dan Rabu ada pelajaran tambahan, serta hari Jumat ada kegiatan ekstra kurikuler pada pukul 14.20 WIB sedangkan setelah pulang sekolah kita tidak pulang dahulu (langsung lanjut belajar tambahan) maka dibutuhkan uang makan + uang jajan sebesar Rp 10.000,00. Nah, kita kebingungan menentukan uang saku setiap hari selain Selasa, Rabu, dan Jum’at selama satu minggu jika dalam satu minggu itu kita ingin menabung uang sebesar Rp 25.000,00. Dengan bantuan aljabar kita dapat menentukan uang saku kita per hari.</div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;"><i><u>Cara menyelesaikan menggunakan Aljabar:</u></i></div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Kita anggap uang saku kita per hari (selain Selasa, Rabu, dan Jumat karena sudah ada jatahnya, yaitu Rp 10.000,00) dengan x. Maka,</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Rp 70.000 = (uang saku 1 minggu)</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Rp 25.000 = (uang tabungan selama 1 minggu)</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">70.000 – 25.000 = (3 X 10.000) + 1(6x -3x)</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Rp 45.000 = Rp 30.000 + 1(3x)</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Rp 45.000 = Rp 30.000 + 3x</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Rp 45.000 – Rp 30.000 = 3x</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Rp 15.000 = 3x</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">x = Rp 15.000/3</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">x = Rp 5.000</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">{Mengapa (3 X 10.000)? 3 berasal dari Hari Selasa, Rabu, dan Jumat dalam satu Minggu. Berarti kan ada 3 hari}</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px; text-align: justify;">{Mengapa 1(6x – 3x)? 1 berasal dari 1 minggu sedangkan 6x – 3x berasal dari 6 hari dalam satu Minggu kecuali Minggu karena libur, dikurangi 3 hari (Selasa, Rabu, dan Jumat karena telah dijatah)}</div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Jadi, uang saku per hari yang kita gunakan selain Selasa, Rabu, dan Jumat (sekali lagi karena telah dijatah) dan selain Minggu (karena libur) maksimal sebesar Rp 5.000,00. Tidak boleh lebih tetapi boleh kurang </div></div><ol start="2" style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; list-style-position: outside; margin: 0px 0px 1.25em 20px; padding: 0px;"><li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px; text-align: justify;"><strong style="box-sizing: border-box; line-height: inherit;"><u style="box-sizing: border-box;">Penerapan Aljabar bagi Ibu Rumah Tangga</u></strong></li></ol><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Kemudian manfaat aplikasi Aljabar bagi Ibu Rumah Tangga adalah untuk memanajemen uang gaji, uang saku anak, uang sekolah anak, dll. Contoh memanajemen uang bagi Ibu Rumah Tangga adalah sebagai berikut:</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px; text-align: justify;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img alt="Ibu memberikan uang saku kepada anaknya" height="426" src="http://pinkkorset.com/wp-content/uploads/2016/05/uang-saku-anak-780x520_c.jpg" style="margin-left: auto; margin-right: auto;" title="Ibu memberikan uang saku kepada anaknya" width="640" /></td></tr><tr><td class="tr-caption" style="text-align: center;">Ibu memberikan uang saku kepada anaknya</td></tr></tbody></table>Seorang Ibu setiap bulan mendapat gaji sebesar Rp 2.000.000,00. Ia diberi uang tambahan dari suaminya sebesar Rp 4.000.000,00 per bulan. Dibutuhkan Rp 1.000.000,00 untuk uang belanja per bulan. Uang kesehatan Rp 500.000,00 dan uang sekolah total dari ke-2 anaknya sebesar Rp 3.000.000,00. Sang Ibu bingung, <span style="box-sizing: border-box; line-height: inherit;">berapa uang saku</span> <span style="box-sizing: border-box; line-height: inherit;">perorangan</span> yang harus ia berikan untuk kedua anaknya tiap minggu tetapi uang per bulannya harus masih tersisa Rp 1.000.000,00 untuk ditabung. Jika Ibu itu pintar Aljabar maka Ibu itu dapat menentukan uang saku tersebut secara tepat, tapi jika tidak? </div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;"><u>Cara mengerjakan menggunakan Aljabar:</u></div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Kita anggap uang saku setiap anak per minggu sebagai x</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">(2.000.000 + 4.000.000) – 1.000.000 = 1.000.000 + 500.000 + 3.000.000 + (4 X 2x)</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">6.000.000 – 1.000.000 = 4.500.000 + (8x)</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">5.000.000 = 4.500.000 + 8x</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">5.000.000 – 4.500.000 = 8x</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">500.000 = 8x</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">x = 500.000/8</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">x = 62.500</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">{Mengapa (4 X 2x) karena 1 bulan = 4 minggu dan 2x itu adalah uang saku 2 orang anak}.</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Jadi, uang saku setiap anak dalam waktu seminggu adalah Rp 62.500,00. Dengan matematika dan sistem Aljabar, cukup simple kan?</div></div><ol start="3" style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; list-style-position: outside; margin: 0px 0px 1.25em 20px; padding: 0px;"><li style="box-sizing: border-box; direction: ltr; margin: 0px; padding: 0px; text-align: justify;"><strong style="box-sizing: border-box; line-height: inherit;"><u style="box-sizing: border-box;">Penerapan Aljabar bagi para Pedagang.</u></strong></li></ol><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px; text-align: justify;">Aljabar dapat membantu pedagang untuk menghitung besar kecil keuntungan atau kerugian yang dapat diperolehnya, dan dapat menentukan besar modal yang dibutuhkan. Contoh penerapan Aljabar dalam kehidupan pedagang adalah sebagai berikut:</div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px; text-align: justify;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img alt="Pedagang Pempek" height="492" 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" style="margin-left: auto; margin-right: auto;" title="Pedagang Pempek" width="640" /></td></tr><tr><td class="tr-caption" style="text-align: center;">Pedagang Pempek</td></tr></tbody></table>Seorang pedagang pempek membeli 5 kg ikan giling dengan harga Rp 60.000,00. Dengan 5 kg ikan giling tersebut dapat dibuat menjadi 10 buah pempek kapal selam. Pedagang itu ingin laba tiap pempek tersebut sebesar Rp 2.000,00. Maka berapa harga jualnya? Jika pedagang itu pandai Matematika, pasti akan mudah mengetahuinya, sebaliknya, jika tidak, apa yang akan terjadi? </div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;"><u>Cara mengerjakan menggunakan sistem Aljabar:</u></div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Kita anggap harga jual pempek itu sebagai x.</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Maka diperoleh:</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">x = (60.000/10) + 2.000</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">x = 6.000 + 2.000</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">x = 8.000</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;">Jadi, harga jual yang bisa diterapkan agar laba satu pempek Rp 2.000 adalah sebesar Rp 8.000,00. Dengan Matematika dan aplikasi Aljabar, sangat sederhana kan?</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Ternyata sobat allmipa, selama kita menjalani kehidupan ini tanpa kita sadari selalu menggunakan ilmu matematika terutama aljabar ini. Dengan aljabar segala permasalahan terkait manajemen uang akan teratasi. Jadi jangan abaikan penerapan aljabar dalam kehidupan sehari-hari.</div></div><div style="background-color: white; box-sizing: border-box; direction: ltr; font-family: lato, helvetica, arial, sans-serif; font-size: 16px; line-height: 1.6; margin-bottom: 1.25em; padding: 0px;"><div style="text-align: justify;"><br /></div></div></div>

Jika kita mendengar kata Aljabar pasti Identik dengan Matematika. Berbicara tentang Matematika tak akan pernah terlepas dari kehidupan. Karena hampir dalam setiap aktivitas sehari-hari pasti menggunak...

23Jan2017

Tripel Pecahan Satuan Dasar Yang Wajib Diketahui

January 21, 2017 dasar , Faktor , Prima , pythagoras , satuan , tripel

<div dir="ltr" style="text-align: left;" trbidi="on"><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img alt="pythagoras set" src="https://yos3prens.files.wordpress.com/2012/04/compass.jpg?w=640&h=237" style="margin-left: auto; margin-right: auto;" title="pythagoras set" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><br /></td></tr></tbody></table><div style="text-align: justify;">Perlu diketahui sobat allmipa. Bahwa tripel bilangan (5, 4, 3) dan kelipatannya, seperti (10, 8, 6), (15, 12, 9), dan seterusnya, merupakan <a name='more'></a>contoh Tripel Pythagoras. Dalam hal ini, tripel (5, 4, 3) merupakan Tripel Pythagoras Dasar. Contoh Tripel Pythagoras Dasar lainnya adalah (13, 12, 5). Perhatikan bahwa faktor persekutuan bersama dari suatu Tripel Pythagoras Dasar adalah 1.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Lalu bagaimana dengan Tripel Pecahan Satuan? Ternyata tripel (k, k + 1, k<sup>2</sup> + k ) merupakan Tripel Pecahan Satuan Dasar, tetapi banyak tripel lainnya yang juga merupakan Tripel Pecahan Satuan Dasar.</div><br />Kemudian untuk memperoleh bentuk umum Tripel Pecahan Satuan Dasar, maka pertama catat bahwa jika kita mempunyai suatu Tripel Pecahan Satuan, maka kelipatannya juga merupakan Tripel Pecahan Satuan. Selanjutnya, misalkan (k, m, n) adalah suatu Tripel Pecahan Satuan, yakni:<br /><br /><div style="text-align: center;"><img src="https://bermatematikadotnet.files.wordpress.com/2016/08/tripel-pecahan-satuan-dasar-1.png?w=93&h=48" /></div><br />Di sini m, n > k. Misalkan m = k + j. Maka<br /><br /><div style="text-align: center;"><img src="https://bermatematikadotnet.files.wordpress.com/2016/08/tripel-pecahan-satuan-dasar-2.png?w=193&h=52" /></div><br /><br />Dari sini kita melihat dua kasus. Kasus pertama, k merupakan kelipatan j, sebutlah k = ij, sehingga<br /><br /><br /><div style="text-align: center;"><img src="https://bermatematikadotnet.files.wordpress.com/2016/08/tripel-pecahan-satuan-dasar-3.png?w=185&h=51" /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Jadi kita peroleh (k, m, n) = (ji, j(i + 1), ji(i + 1)), yang hanya merupakan kelipatan dari tripel (i, i + 1, i(i + 1)).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><img alt="rumus-rumus" src="https://lh3.googleusercontent.com/-1FZZlo9SM_s/UTdnnXVSfwI/AAAAAAAAAEM/j2S6YptHYhU/s0-d/formulas-math-equations-hd-wallpaper-facebook-cover.jpg" title="rumus-rumus" /></div><div style="text-align: justify;">Kasus kedua, yang lebih umum daripada kasus pertama, <span style="text-align: justify;">k</span><sup style="text-align: justify;">2</sup> merupakan kelipatan j, sebutlah <span style="text-align: justify;">k</span><sup style="text-align: justify;">2</sup> = lj. Dalam hal ini, kita peroleh (k, m, n) = (k, k + j, k + l), yang tidak harus merupakan kelipatan dari suatu tripel (i, i + 1, i(i + 1)). Sebagai contoh, untuk k = 6, j = 4, dan l = 9, kita peroleh tripel (6, 10, 15), dan tripel ini merupakan Tripel Pecahan Satuan Dasar.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Dengan bantuan faktorisasi prima, tripel (k, k + j, k + l) merupakan Tripel Pecahan Satuan Dasar jika dan hanya jika j dan l merupakan bilangan kuadrat, sebutlah j = a<sup>2</sup> dan l = b<sup>2</sup> dengan a dan b relatif prima. Jadi, kita peroleh bentuk umum Tripel Pecahan Satuan Dasar, yaitu  (ab, a(a + b), b(a + b)), dengan a dan b relatif prima. Perlu diingat bahwa bentuk ini mencakup tripel (b, b + 1, b(b + 1)) yang telah kita identifikasi sebagai suatu Tripel Pecahan Satuan Dasar sejak awal. Jadi, sobat allmipa sudah tahu semua kan mengenai tripel pythagoras? </div></div>

Perlu diketahui sobat allmipa. Bahwa tripel bilangan (5, 4, 3) dan kelipatannya, seperti (10, 8, 6), (15, 12, 9), dan seterusnya, merupakan contoh Tripel Pythagoras. Dalam hal ini, tripel (5, 4, 3) me...

21Jan2017

Peran, Fungsi, dan Karakteristik Matematika di Sekolah

January 21, 2017 fungsi , karakteristik , Matematika , pembelajaran , peran , sekolah , tujuan

<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"></div><div style="margin-left: 1em; margin-right: 1em; text-align: justify;"><br /></div><br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img alt="Pembelajaran di Sekolah" height="352" src="http://gambarterbaru.com/wp-content/uploads/2013/10/gambar-animasi-kartun-anak-sekolah-555x306.jpg" style="margin-left: auto; margin-right: auto;" title="Pembelajaran di Sekolah" width="640" /></td></tr><tr><td class="tr-caption" style="text-align: center;">Pembelajaran di Sekolah</td></tr></tbody></table><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Sesuai dengan tujuan diberikannya ilmu matematika di sekolah, kita dapat melihat bahwa matematika sekolah memegang<a name='more'></a>  peranan sangat penting. Anak didik memerlukan matematika untuk memenuhi kebutuhan praktis dan memecahkan masalah dalam kehidupan sehari-hari. Misalnya, dapat berhitung, dapat menghitung isi dan berat, dapat mengumpulkan, mengolah, menyajikan dan menafsirkan data, dapat menggunakan kalkulator dan komputer. Selain itu, agar mampu mengikuti pelajaran matematika lebih lanjut, membantu memahami bidang studi lain seperti fisika, kimia, arsitektur, farmasi, geografi, ekonomi, dan sebagainya, dan agar para siswa dapat berpikir logis, kritis, dan praktis, beserta bersikap positif dan berjiwa kreatif.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Sebagai warga negara Indonesia yang berhak mendapatkan pendidikan seperti yang tertuang dalam susunan UUD 1945, tentunya harus memiliki pengetahuan umum minimum. Pengetahuan minimum itu diantaranya adalah ilmu matematika. Oleh sebab itu, matematika sekolah sangat berarti baik bagi para siswa yang melanjutkan studi maupun yang tidak.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Bagi mereka yang tidak melanjutkan studi, matematika dapat diproyeksikan dalam berdagang dan berbelanja, dapat berkomunikasi melalui tulisan atau gambar seperti membaca grafik dan persentase, dapat membuat catatan-catatan dengan angka, dan lain-lain. Juka diperhatikan pada berbagai media massa, seringkali informasi disajikan dalam bentuk persen, tabel, bahkan dalam bentuk diagram. Dengan demikian, agar orang dapat memperoleh informasi yang benar dari apa yang dibacanya itu, mereka harus memiliki pengetahuan mengenai persen, cara membaca tabel, dan juga diagram. Dalam hal inilah matematika memberikan peran pentingnya.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img alt="Pembelajaran Matematika di Sekolah" height="320" src="http://dinidinidini.files.wordpress.com/2012/09/kartun-ngajar2.jpg" style="margin-left: auto; margin-right: auto;" title="Pembelajaran Matematika di Sekolah" width="313" /></td></tr><tr><td class="tr-caption" style="text-align: center;">Pembelajaran Matematika di Sekolah</td></tr></tbody></table><div style="text-align: justify;">Sejalan dengan kemajuan zaman, tentunya pengetahuan semakin berkembang. Supaya suatu negara bisa lebih maju, maka negara tersebut perlu memiliki manusia-manusia yang melek teknologi.Perlu diketahui sobat allmipa, untuk keperluan ini tentunya mereka perlu belajar matematika sekolah terlebih dahulu karena matematika memegang peranan yang sangat penting bagi perkembangan teknologi itu sendiri. Tanpa bantuan matematika tidak mungkin terjadi perkembangan teknologi seperti sekarang ini.</div></div>

Pembelajaran di SekolahSesuai dengan tujuan diberikannya ilmu matematika di sekolah, kita dapat melihat bahwa matematika sekolah memegang peranan sangat penting. Anak didik memerlukan matematika untu...

21Jan2017

Sejarah Singkat dan Penjelasan Persamaan Diophanthine

January 20, 2017 Alexandria , aljabar , diophantine , diophantus , persamaan , sejarah , singkat , warisan

<div dir="ltr" style="text-align: left;" trbidi="on"><div><img alt="pulau diophanthus" height="316" src="https://cdn3.volusion.com/gnclv.fjgyd/v/vspfiles/photos/DWI0402-2.jpg" title="pulau diophanthus" width="640" /></div><div></div><br /><b>Diophantus</b>, matematikawan Alexandria abad ke-3, terkenal dengan karyanya “<i>Arithmetica</i>” yang terdiri dari<br /><a name='more'></a>13 jilid. (Namun, beberapa jilid di antaranya musnah terbakar ketika Museum dan Perpustakaan Besar-nya diserbu massa, pada abad ke-4 dan abad ke-7.)<br /><div><br /><div class="separator" style="clear: both; text-align: center;"></div><div style="margin-left: 1em; margin-right: 1em; text-align: center;"></div><br /><div class="entry-content" style="box-sizing: border-box; width: 620px;">Salah satu warisan Diophantus adalah persamaan yang kita kenal sekarang sebagai Persamaan Diophantine, yaitu persamaan aljabar dengan koefisien bilangan bulat dan solusi yang dikehendaki juga merupakan bilangan bulat.<br /><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a 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" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Diophantus " border="0" height="320" 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" title="Diophantus " width="251" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Diophantus </td></tr></tbody></table><div style="text-align: justify;">Contoh Persamaan Diophantine yang paling klasik adalah persamaan ax + by = c, dengan a, b, dan c diketahui, misalnya 15x + 11y = 12. Bagaimana mencari solusi persamaan ini?</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Karena 15 dan 11 relatif prima (faktor persekutuan terbesarnya sama dengan 1), kita dapat menemukan bilangan bulat x dan y sedemikian sehingga 15x + 11y = 1 dengan menggunakan Algoritma Euclid:</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: left;">15 = 1(11) + 4</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;">11 = 2(4) + 3</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;">4 = 1(3) + 1</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;">3 = 3(1) + 0.</div><div style="text-align: left;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Bila kita telusuri dari persamaan kedua terakhir, maka kita peroleh:</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">1 = 4 – 1(3)</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">= 4 – 1[11 – 2(4)] = 3(4) – 1(11)</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">= 3[15 – 1(11)] – 1(11) = 3(15) – 4(11).</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Dengan demikian kita dapatkan solusi persamaan 15x + 11y = 1, yaitu x = 3 dan y = -4. (Tetapi ini bukan satu-satunya solusi. Solusi umum dari persamaan 15x + 11y = 1 adalah x = 3 – 11k dan y = -4 + 15k, dengan k bilangan bulat.)</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Nah, solusi dari persamaan 15x + 11y = 12 sekarang dapat kita peroleh dengan mengalikan solusi dari persamaan 15x + 11y = 1 dengan 12. Jadi, solusi yang kita cari adalah x = 36 dan y = -48. Solusi umumnya adalah x = 36 – 11k dan y = -48 + 15k.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Ternyata persamaan Diophantine mudah bukan? kalau sekilas melihat namanya saja pasti terlintas dalam pikiran kita terasa sulit. Namun jika sudah mempelajari dengan seksama pasti akan bisa.</div><div style="background-color: white; box-sizing: border-box; color: #333333; font-family: "lucida grande", "lucida sans unicode", "lucida sans", geneva, verdana, sans-serif; font-size: 13px; margin-bottom: 2.3rem;"><br /></div></div></div></div>

Diophantus, matematikawan Alexandria abad ke-3, terkenal dengan karyanya “Arithmetica” yang terdiri dari13 jilid. (Namun, beberapa jilid di antaranya musnah terbakar ketika Museum dan Perpustakaan Bes...

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