tag:blogger.com,1999:blog-86420520466843094022024-02-19T09:03:42.958-08:00DUNIA KULIAHMelangkah Lebih Awalmeraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.comBlogger16125tag:blogger.com,1999:blog-8642052046684309402.post-57477234255813320662010-11-17T07:05:00.000-08:002010-11-17T07:05:02.446-08:00Free Download buku kalkulus lengkap (james stewart)<div style="text-align: justify;">kalkulus adalah salah satu Matakuliah yang bisa dikatakan cukup sulit. bagi temen-temen yang ingin mempunyai buku panduannya bisa mendownload disini yaitu buku James stewart, saya sendiri belum selesai membaca buku ini, buku ini terdiri dari 1300 halaman yang berbentuk file Pdf. selain materi kalkulus buku ini juga berisi tentang aljabar linier, Pdm, dan lain sebagainyal. tetapi yang perlu teman-teman ketahui bahwa buku ini bebahasa inggris jadi sedikit kurang di mengerti,,hehehe, jadi temen-temen juga harus jago berbahasa inggris.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSbpQYZF_8JiZLKXH_Rz8nsLVcKqq_aV2uWe0622pANyaQIjiUoreAcQlRM_Me3MIiJHvGO_pYw165swRPZgEjcJo-NPtNm5mXpxTu1ogg8BxR_k3fuKrSS9FVVMdzODGDJGeG7gB7FoKl/s1600/Screenshot+%252822h+01m+02s%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSbpQYZF_8JiZLKXH_Rz8nsLVcKqq_aV2uWe0622pANyaQIjiUoreAcQlRM_Me3MIiJHvGO_pYw165swRPZgEjcJo-NPtNm5mXpxTu1ogg8BxR_k3fuKrSS9FVVMdzODGDJGeG7gB7FoKl/s640/Screenshot+%252822h+01m+02s%2529.jpg" width="496" /></a></div>silahkan download di link ini :<br />
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<span>Tetap Semangat teman-teman,,,</span><br />
<span>:)</span>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com5tag:blogger.com,1999:blog-8642052046684309402.post-62398560706358916062010-11-15T13:38:00.000-08:002010-11-15T13:38:54.344-08:00TTS Probabilitas<div style="font-family: Times,"Times New Roman",serif;"><span style="font-size: large;">Bagi temen-temen yg pingin lihat panduan TTS probabilitas soal nomor 3 dan 4 bisa di baca di bawah ini, karena saya males mengetik sebagian besar saya format dalam bentuk jpg, mari kita berbagi dengan segala ilmu yang kita miliki walaupun hanya sedikit.</span></div><div style="font-family: Times,"Times New Roman",serif;"><span style="font-size: large;">soal nomor 3 : </span></div><div style="font-family: Times,"Times New Roman",serif;"><span style="font-family: Times,"Times New Roman",serif; font-size: large;"><span style="color: black;">1. Sebuah</span><span style="color: black;"> </span><span style="color: black;">kantong</span><span style="color: black;"> pertama </span><span style="color: black;">berisi</span><span style="color: black;"> 4 bola </span><span style="color: black;">merah</span><span style="color: black;"> </span><span style="color: black;">dan</span><span style="color: black;"> 3 </span><span style="color: black;">ola</span><span style="color: black;"> </span><span style="color: black;">hitam</span><span style="color: black;">, </span><span style="color: black;">kantong</span><span style="color: black;"> </span><span style="color: black;">kedua</span><span style="color: black;"> </span><span style="color: black;">berisi</span><span style="color: black;"> 3 bola </span><span style="color: black;">merah</span><span style="color: black;"> </span><span style="color: black;">dan</span><span style="color: black;"> 5 bola </span><span style="color: black;">hitam</span><span style="color: black;">. </span><span style="color: black;">Satu</span><span style="color: black;"> bola </span><span style="color: black;">diambil</span><span style="color: black;"> </span><span style="color: black;">dari</span><span style="color: black;"> </span><span style="color: black;">kantong</span><span style="color: black;"> </span><span style="color: black;">pertama</span><span style="color: black;">, </span><span style="color: black;">dan</span><span style="color: black;"> </span><span style="color: black;">dimasukan</span><span style="color: black;"> </span><span style="color: black;">ke</span><span style="color: black;"> </span><span style="color: black;">kantong</span><span style="color: black;"> </span><span style="color: black;">kedua</span><span style="color: black;"> </span><span style="color: black;">tanpa</span><span style="color: black;"> </span><span style="color: black;">melihat</span><span style="color: black;"> </span><span style="color: black;">hasilnya</span><span style="color: black;">. </span><span style="color: black;">Berapa</span><span style="color: black;"> </span><span style="color: black;">probabilitasnya</span><span style="color: black;"> </span><span style="color: black;">jika</span><span style="color: black;"> </span><span style="color: black;">kita</span><span style="color: black;"> </span><span style="color: black;">mengambil</span><span style="color: black;"> bola </span><span style="color: black;">hitam</span><span style="color: black;"> </span><span style="color: black;">dari</span><span style="color: black;"> </span><span style="color: black;">kantong</span><span style="color: black;"> </span><span style="color: black;">kedua</span><span style="color: black;">?.</span></span></div><div style="font-family: Times,"Times New Roman",serif;"><span style="font-family: Times,"Times New Roman",serif; font-size: large;"><span style="color: black;">penyelesaian :</span></span></div><div style="font-family: Times,"Times New Roman",serif;"> </div><div style="direction: ltr; font-family: Times,"Times New Roman",serif; margin-bottom: 0pt; margin-top: 0pt; text-align: left; unicode-bidi: embed; vertical-align: baseline;"><span style="font-size: large;"><span style="color: black;">Misalkan</span><span style="color: black;">:<span> H1,H2 dan M1 </span></span><span style="color: black;">masing-masing</span><span style="color: black;"> </span><span style="color: black;">menyatakan</span><span style="color: black;"> </span><span style="color: black;">pengambilan</span><span style="color: black;"><span> </span>1 bola</span></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1JPqCFkhPoJH1_7Oy-PPptlk_wbxoL-O_65YsrgTniifH6Ql4624ZQXiQCxznn1oJXzRmMTSwJqL1Hzo0EGnkjpWlrSKuppPFD164IhMkCvMsbvn4VB6z3I_TfyudH2z6WNs9v6vgKOZU/s1600/Screenshot+%252804h+22m+59s%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="411" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1JPqCFkhPoJH1_7Oy-PPptlk_wbxoL-O_65YsrgTniifH6Ql4624ZQXiQCxznn1oJXzRmMTSwJqL1Hzo0EGnkjpWlrSKuppPFD164IhMkCvMsbvn4VB6z3I_TfyudH2z6WNs9v6vgKOZU/s640/Screenshot+%252804h+22m+59s%2529.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmXfC7t6MId5yLyTNAOLR0Qc5c9K1Z8sQZ7ZIKmHmMauTRtmF-VZZ0JMEoNbAc6IZCt1D1kCJyYqZyQNs8u7mCOEBLx2N_QMo5HCBzdok7Ot6A9bbZtQD1XlgIUClqvgFm7s50nlBbNIfB/s1600/Screenshot+%252804h+25m+14s%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="194" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmXfC7t6MId5yLyTNAOLR0Qc5c9K1Z8sQZ7ZIKmHmMauTRtmF-VZZ0JMEoNbAc6IZCt1D1kCJyYqZyQNs8u7mCOEBLx2N_QMo5HCBzdok7Ot6A9bbZtQD1XlgIUClqvgFm7s50nlBbNIfB/s640/Screenshot+%252804h+25m+14s%2529.jpg" width="640" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-top: 0pt; text-align: left; unicode-bidi: embed; vertical-align: baseline;"><span style="color: black; font-family: Arial;"> <span style="font-size: large;">soal no 4 :</span></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitmjOXDW9yCtVf2i6kTeaGCWHE700iTikPYFUE6_Di05lVrw3LK-FxZaBTzBIB9jT6X03_zI4KdthKGAgv09IR2qHJTvs1ULYllXg5ZRNiepZFZVTjrjU8CSKkNX0Hppw9_BnxWM_DUkWl/s1600/Screenshot+%252804h+27m+14s%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="404" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitmjOXDW9yCtVf2i6kTeaGCWHE700iTikPYFUE6_Di05lVrw3LK-FxZaBTzBIB9jT6X03_zI4KdthKGAgv09IR2qHJTvs1ULYllXg5ZRNiepZFZVTjrjU8CSKkNX0Hppw9_BnxWM_DUkWl/s640/Screenshot+%252804h+27m+14s%2529.jpg" width="640" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-top: 0pt; text-align: left; unicode-bidi: embed; vertical-align: baseline;"><span style="color: black; font-family: Arial;">penyelesaian : </span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBGj6yR0NZtjsg-YfBmHHP7NVuyezFvRWSOvjRC6jXZFUrUYRi_jB71jJC23LQzWPL6kNwKo1cboMKQAII8CoSBuhB_HCqnlzbYh9VY_d0diPCWQAxhWN6Rc2ZU4VmaHWtFTzFOavGhdpx/s1600/Screenshot+%252804h+28m+46s%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="420" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBGj6yR0NZtjsg-YfBmHHP7NVuyezFvRWSOvjRC6jXZFUrUYRi_jB71jJC23LQzWPL6kNwKo1cboMKQAII8CoSBuhB_HCqnlzbYh9VY_d0diPCWQAxhWN6Rc2ZU4VmaHWtFTzFOavGhdpx/s640/Screenshot+%252804h+28m+46s%2529.jpg" width="640" /></a></div><div style="direction: ltr; font-family: Times,"Times New Roman",serif; margin-bottom: 0pt; margin-top: 0pt; text-align: left; unicode-bidi: embed; vertical-align: baseline;"><span style="font-size: large;"><span style="color: black;">Demikian soal panduan yang dapat saya berikan teman-teman semoga bermanfaat buat kita semua.</span></span></div><div style="direction: ltr; font-family: Times,"Times New Roman",serif; margin-bottom: 0pt; margin-top: 0pt; text-align: left; unicode-bidi: embed; vertical-align: baseline;"><span style="font-size: large;"><span style="color: black;">Tapi bagi teman-teman yang ingin mempunya filenya langsung silahkan download <a href="http://www.4shared.com/file/hH89-Nx5/probability-091205063835-phpap.html">disini</a> atw di alamat berikut: http://www.4shared.com/file/hH89-Nx5/probability-091205063835-phpap.html</span></span></div><div style="direction: ltr; font-family: Times,"Times New Roman",serif; margin-bottom: 0pt; margin-top: 0pt; text-align: left; unicode-bidi: embed; vertical-align: baseline;"><span style="font-size: large;"><span style="color: black;">atw langsung minta softfile ke rangga pradeka.</span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-top: 0pt; text-align: left; unicode-bidi: embed; vertical-align: baseline;"><span style="color: black; font-family: Arial;"><span style="font-size: large;"><span style="font-family: Times,"Times New Roman",serif;">terima kasih, Tetap semangat......</span></span><br />
</span></div><span style="font-family: Times,"Times New Roman",serif; font-size: small;"><span style="color: black;"> </span></span>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-14146650345461751622010-11-14T15:08:00.000-08:002010-11-14T15:08:56.472-08:00Ikan di kutub Utara tidak membeku<div style="text-align: justify;">Sumber : www.informasiku.com </div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8XjF7ubXtL1YWdwhwVVuoNOy6IBfm9ZD7HZiOwO0mpRKBqq827U1XgjwC1YtNTgJdw1ITgfnwfQljq93qxDaTFOzrUWVadoDuvDVVAA_NwY8a5ypI60EZm2CrAaHcvF17KFgFAcfB3fqI/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8XjF7ubXtL1YWdwhwVVuoNOy6IBfm9ZD7HZiOwO0mpRKBqq827U1XgjwC1YtNTgJdw1ITgfnwfQljq93qxDaTFOzrUWVadoDuvDVVAA_NwY8a5ypI60EZm2CrAaHcvF17KFgFAcfB3fqI/s1600/images.jpg" /></a></div><div style="text-align: justify;">LONDON--Suhu di Kutub Utara betul-betul ekstrem, dengan rata-rata minus 1,8 ° C. Semestinya, suhu serendah ini cukup untuk membekukan ikan apapun: titik beku darah ikan adalah sekitar minus 0,9 ° C.<br />
Namun di lautan Kutub Utara, di bawah bongkahan es, ikan-ikan bergerak dengan riang gembira. Inilah yang menarik banyak ilmuwan untuk menelitinya.<br />
Sejak sekitar 50 tahun lalu, para ahli telah menemukan, dalam darah ikan itu ditemukan protein pelindung kebekuan. Protein anti-beku ini bekerja dengan sangat sempurna, jauh lebih sempurna dibandingkan dengan mesin anti-beku yang dioperasikan di rumah-rumah tangga Barat saat musim dingin tiba.<br />
Namun bagaimana protein ini bekerja, tak ada yang bisa memberi penjelasan.<br />
Inilah yang mendorong para peneliti setempat bersama satu tim dari Amerika Serikat yang dipimpin ilmuwan lokal Prof Dr Martina Havenith untuk melakukan penelitian mendalam. Hasilnya mereka publikasi dalam jurnal kimia bergengsi Amerika, Journal of American Chemical Society ( JACS).<br />
<br />
Para peneliti menggunakan teknik khusus,<em> terahertz spectroscopy,</em> untuk mengungkap mekanisme dasar. Dengan bantuan radiasi terahertz, gerakan kolektif dari molekul air dan protein dapat direkam. Dengan demikian, kelompok kerja telah mampu menunjukkan bahwa molekul air, yang biasanya melakukan tarian permanen dalam air cair, dan terus-menerus memasukkan obligasi baru, akan lebih teratur dengan adanya protein ini.</div>Adalah ikan khas Kutub Utara, <em>Dissostichus mawson</em>i, sejenis ikan bergigi, yang menjadi objek utama penelitian. Arthur L DeVries, salah seorang peneliti, menyebut, protein pada ikan ini mampu mencegah kristalisasi es, bahkan lebih hebat pada temperatur rendah dari pada suhu kamar. "Aktivitas antibeku tidak tercapai dengan mengikat molekul tunggal antara protein dan air, tetapi dengan adanya protein ini, maka fungsi "pelarutan" akan lebih maksimal," ujarnya.meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-10134528692045084282010-11-11T22:26:00.000-08:002010-11-12T02:32:40.482-08:00Tugas teori graf<div style="color: red; text-align: justify;"><span style="font-size: small;"><b>Exercise 3</b></span></div><div style="color: black; text-align: justify;"><span style="font-size: small;">The direct delivery problem is defined as follows : a transport company residing in city 0 has to carry out n transport orders V1 (i=1,...n). transport order V1 amounts to picking up cargo at place a1 and delivering this a place b1. not possible to combine order. after picking up order i it has to be delivered in b1 immediately.</span><br />
<span style="font-size: small;">the time needed for carrying out task V1 is equal to d(1) which accounts for travel time as well as time loading and unloading etcetera. the time for moving a truck from place j to place k is given by cjk. the tras porter ( who has only one transport vehicle ) leaves place 0 at time zero. the goal to find a solution in which all order are carried out and the transport returns back to place 0 as early as possible.</span><br />
<span style="font-size: small;">for the instance given below, compute an optimal schedule. is your strategy a general one in that it will solve every instance of the direct delevery problem optimally ?</span></div><div class="separator" style="clear: both; color: black; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguV_I0p843c1xZvZPPmHh8YO2N34OToyHFXv5PsH1n8Uu-TixrFLvaozwGW_uYHs-h0S0VTJTjZIsHHFNz1SaiNmby3vH9ZyVd24l9XYtf1Io-vqIcuWDN-4sQhsu3PR0swSdj78WMb9Ij/s1600/Screenshot+%252813h+14m+26s%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="508" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguV_I0p843c1xZvZPPmHh8YO2N34OToyHFXv5PsH1n8Uu-TixrFLvaozwGW_uYHs-h0S0VTJTjZIsHHFNz1SaiNmby3vH9ZyVd24l9XYtf1Io-vqIcuWDN-4sQhsu3PR0swSdj78WMb9Ij/s640/Screenshot+%252813h+14m+26s%2529.jpg" width="640" /></a></span></div><div style="color: red;"><span style="font-size: small;"><i>Translate Indonesia :</i></span></div><div style="color: black; text-align: justify;"><span class="" id="result_box" lang="id" style="font-size: small;"><span title="">Masalah pengiriman langsung didefinisikan sebagai berikut: sebuah perusahaan transportasi yang berada di kota 0 harus melaksanakan perintah n transportasi V1 (i = 1, ... n). </span><span title="">Agar transportasi V1 berjumlah mengambil kargo di tempat a1 dan memberikan tempat ini b1. </span><span title="">tidak mungkin untuk menggabungkan pesanan. </span><span title="">setelah mengambil saya memesannya harus disampaikan dalam b1 segera.</span></span><br />
<span class="" id="result_box" lang="id" style="font-size: small;"><span title="">waktu yang diperlukan untuk melaksanakan tugas V1 sama dengan d (1) yang menyumbang waktu perjalanan serta waktu bongkar muat dan sebagainya. </span><span title="">waktu untuk memindahkan sebuah truk dari satu tempat ke tempat k j diberikan oleh Cjk. </span><span title="">Tras penjaga pintu (yang hanya memiliki satu kendaraan transportasi) daun tempat 0 pada waktu nol. </span><span title="">tujuan untuk mencari solusi yang memerintahkan semua dilakukan dan kembali transportasi kembali ke tempat 0 sedini mungkin.</span></span><br />
<span class="" id="result_box" lang="id" style="font-size: small;"><span title="">untuk contoh diberikan di bawah ini, menghitung jadwal yang optimal. </span><span title="">strategi Anda satu umum dalam bahwa hal itu akan memecahkan setiap contoh dari masalah delevery langsung secara optimal?</span></span></div><div class="separator" style="clear: both; color: black; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguV_I0p843c1xZvZPPmHh8YO2N34OToyHFXv5PsH1n8Uu-TixrFLvaozwGW_uYHs-h0S0VTJTjZIsHHFNz1SaiNmby3vH9ZyVd24l9XYtf1Io-vqIcuWDN-4sQhsu3PR0swSdj78WMb9Ij/s1600/Screenshot+%252813h+14m+26s%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="510" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguV_I0p843c1xZvZPPmHh8YO2N34OToyHFXv5PsH1n8Uu-TixrFLvaozwGW_uYHs-h0S0VTJTjZIsHHFNz1SaiNmby3vH9ZyVd24l9XYtf1Io-vqIcuWDN-4sQhsu3PR0swSdj78WMb9Ij/s640/Screenshot+%252813h+14m+26s%2529.jpg" width="640" /></a></span></div><div style="color: black; text-align: justify;"><div><span style="font-size: small;"><b><span class="" id="result_box" lang="id"><span title=""> <span style="color: red;">Exercise 8</span></span></span></b></span></div><span class="" id="result_box" lang="id" style="font-size: small;"><span title="">A group of 12 boys adn 12 girl decides to following ball room dancing classes. for each boy girls pair, it has been determined whatever or no they could be a dancing couple : see table bellow :</span></span><br />
<div style="text-align: justify;"><span style="font-size: small;"><img border="0" height="458" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi99I7X7iYpy9K2reGcteoxuAz8tSc4eUFTLHr3Hpbl2FpIiiGGLRsE83Lhy1Sv8OntThQi2etubk11a8-P-Kd6ebS6hBkHq7Ydwya3CNZx464owhN0TGj028dEJyWdtK5ELxxBMee8gHOn/s640/Screenshot+%252813h+30m+41s%2529.jpg" width="640" /></span><span style="font-size: small;">(a.) how many couples can be on the dance floor at the same time ?</span><span style="font-size: small;"><br />
</span><br />
<span style="font-size: small;"> (b.) assuming that your answer is less than 12, can you give a convincingargument that no perfect partition into 12 couples exist ?</span></div><div style="text-align: justify;"><span style="color: red; font-size: small;"><i>Translate Indonesia :</i></span><span style="font-size: small;"> </span></div><div style="text-align: justify;"><span class="" id="result_box" lang="id" style="font-size: small;"><span title="">Sekelompok 12 anak laki-laki dan 12 anak perempuan memutuskan untuk kelas menari bola ruangan berikut. </span><span title="">untuk setiap pasangan anak laki-laki perempuan, telah ditetapkan apapun atau tidak ada mereka bisa menjadi pasangan menari: lihat tabel dibawah:</span></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi99I7X7iYpy9K2reGcteoxuAz8tSc4eUFTLHr3Hpbl2FpIiiGGLRsE83Lhy1Sv8OntThQi2etubk11a8-P-Kd6ebS6hBkHq7Ydwya3CNZx464owhN0TGj028dEJyWdtK5ELxxBMee8gHOn/s1600/Screenshot+%252813h+30m+41s%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="458" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi99I7X7iYpy9K2reGcteoxuAz8tSc4eUFTLHr3Hpbl2FpIiiGGLRsE83Lhy1Sv8OntThQi2etubk11a8-P-Kd6ebS6hBkHq7Ydwya3CNZx464owhN0TGj028dEJyWdtK5ELxxBMee8gHOn/s640/Screenshot+%252813h+30m+41s%2529.jpg" width="640" /></a></span></div><div style="text-align: justify;"><span class="" id="result_box" lang="id" style="font-size: small;"><span title="">(A.) berapa banyak pasangan dapat berada di lantai dansa pada saat yang sama?</span><span title="">(B.) asumsi bahwa jawaban Anda kurang dari 12, bisa Anda memberikan convincingargument bahwa tidak ada partisi yang sempurna menjadi 12 pasangan ada?</span></span><br />
<div style="color: red;"><span class="" id="result_box" lang="id" style="font-size: small;"><span title=""><b>Exercise 9 </b></span></span></div><span class="" id="result_box" lang="id" style="font-size: small;"><span title="">consider the network below. the number along the arcs give the value of the current flow, and the capacity of the arc, respectively. compute the maximum flow throught this network, and prove maximality by using a minimum capacity cut. decribe each step of your procedure.</span></span><br />
<div style="color: red;"><span class="" id="result_box" lang="id" style="font-size: small;"><span title=""><i>translate to Indonesia:</i></span></span></div><span style="font-size: small;"><span class="" id="result_box" lang="id"><span title="">mempertimbangkan jaringan di bawah ini. </span><span title="">nomor sepanjang busur memberikan nilai arus, dan kapasitas busur masing-masing. </span><span title="">menghitung aliran pemikiran maksimum jaringan ini, dan membuktikan maximality dengan menggunakan potongan kapasitas minimum. </span><span title="">menggambarkan setiap langkah prosedur Anda.</span></span></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_ib6i2p86wAtY_Alp4WDp511bkwThQocSV5ZZXikuVquU0tyuJyQH9ZbxaismuqOktv5_aZRkf7QZNakRvRD2iM1CxVGvdQdlONQEiH0mfcnUV37Bq4rC8B-I6qs1L4L0BBQNnz01hZCx/s1600/Screenshot+%252817h+23m+48s%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_ib6i2p86wAtY_Alp4WDp511bkwThQocSV5ZZXikuVquU0tyuJyQH9ZbxaismuqOktv5_aZRkf7QZNakRvRD2iM1CxVGvdQdlONQEiH0mfcnUV37Bq4rC8B-I6qs1L4L0BBQNnz01hZCx/s640/Screenshot+%252817h+23m+48s%2529.jpg" width="640" /></a></span></div><div style="text-align: justify;"><span style="font-size: small;"><span class="" id="result_box" lang="id"><span title=""> </span></span></span></div><div style="text-align: justify;"><span style="font-size: small;"><br />
</span></div></div>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-89200053808135131642010-11-10T14:14:00.000-08:002010-11-10T14:14:42.913-08:00Misteri Bilangan Prima<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSN3HnrXMv_nRSfUz7EnAvYn7oe150arVZLItRCEE0sz76xEJ23mNYY3FgpZzdxpY4PH_6od_Lg5H4ZtLgew5gjKADCDjsUDsuguZ2dQv8nXOfkctabUR7vxX9QJDibBvlalvmZvJy5r2I/s1600/nah.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSN3HnrXMv_nRSfUz7EnAvYn7oe150arVZLItRCEE0sz76xEJ23mNYY3FgpZzdxpY4PH_6od_Lg5H4ZtLgew5gjKADCDjsUDsuguZ2dQv8nXOfkctabUR7vxX9QJDibBvlalvmZvJy5r2I/s1600/nah.jpg" /></a></div><h3>Bilangan Prima dan Rencana Penciptaan</h3><br />
Salah satu teka-teki lama yang belum sepenuhnya terpecahkan adalah bilangan prima. <span style="font-weight: bold;">Bilangan prima</span> adalah bilangan yang hanya dapat habis dibagi oleh bilangan itu sendiri dan angka 1. Angka 12 bukan merupakan bilangan prima, karena dapat habis dibagi oleh angka lainnya 2, 3, dan 4. Bilangan prima adalah 2, 3, 5, 7, 11, 13, .... dan seterusnya. Banyak bilangan prima tidak terhingga. Tidak peduli berapa banyak kita menghitung, pasti kita akan menemukan bilangan prima, walaupun mungkin makin jarang_ Hal ini menjadi teka-teki kita, jika kita ingat bilangan ini tidak dapat dibagi oleh angka lainnya. Salah satu hal yang menakjubkan, dalam era komputer kita memberikan kodetifikasi semua hal yang penting dan rahasia, di bank, asuransi, dan perhitungan-perhitungan peluru kendali, <span style="font-style: italic;">security system</span> dengan enkripsi, dalam angka jutaan bilangan-bilangan yang tidak habis dibagi oleh angka lainnya. Ini diperlukan karena dengan penggunaan angka lain, kodetifikasi tadi dapat dengan mudah ditembus.<br />
<br />
Fenomena inilah yang ditemukan ilmuwan dari Duesseldorf (Dr. Plichta), sehubungan dengan penciptaan alam, yaitu distribusi misterius bilangan prima. Para ilmuwan sudah lama percaya bahwa bilangan prima adalah bahasa universal yang dapat dimengerti oleh semua makhluk (spesies) berintelegensia tinggi, sebagai komunikasi dasar antarmereka. Bahasa ini penuh misteri karena berhubungan dengan perencanaan universal kosmos.<br />
<br />
Bilangan lain yang perlu diketahui adalah sisa dari bilangan prima, yakni <span style="font-weight: bold;">bilangan komposit</span>, kecuali angka 1, yaitu 4, 6, 8, 9,10,12,14,15, .... dan seterusnya. Dengan kata lain, bilangan komposit adalah bilangan yang terdiri dari minimal dua faktor prima. Misalnya : <br />
<br />
6 = 2 x 3 = 2 . 3<br />
30 = 2 x 3 x 5 = 2 . 3 . 5<br />
85 = 5 x 17 = 5 . 17<br />
<br />
Selain itu, dikenal pula <span style="font-weight: bold;">bilangan khusus</span>, yang disebut <span style="font-weight: bold;">prima kembar</span>, yaitu bilangan prima yang angkanya berdekatan dengan selisih 2. Misalnya : <br />
<br />
(3,5)<br />
(5,7)<br />
(11,13)<br />
(17,19)<br />
<br />
dan seterusnya.<br />
<br />
Mayoritas ahli astrofisika juga percaya bahwa di alam semesta terdapat "kode kosmos" atau yang disebut <span style="font-style: italic;">cosmic code based on this order,</span> yang dikenal juga sebagai <span style="font-style: italic;">Theory of Everything</span> (TOE), yang artinya terdapat konstanta-konstanta alam semesta yang saling berhubungan berdasarkan perintah pendesain. Sekali perintah tersebut dapat dipecahkan, maka hal ini akan membuka pandangan sains lainnya yang berhubungan.meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-79214355425752756602010-11-10T14:00:00.000-08:002010-11-10T14:00:52.041-08:00Rumus Dasar Trigometri<div style="text-align: justify;"><!--[if !mso]> <style>
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</style> <![endif]--> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: normal; text-align: justify;"><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">PENJUMLAHAN DUA SUDUT (</span></b><b><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + </span></b><b><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">)</span></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> <br />
<br />
sin(</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) = sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b<br />
</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">cos(</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) = cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b<br />
</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">tg(</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a + b </span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) = <u>tg </u></span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + tg </span></u><u><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> <br />
1 - tg<sup>2</sup></span><span style="color: black; font-family: Symbol; font-size: 9pt;">a </span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
<br />
<b>SELISIH DUA SUDUT (</b></span><b><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - </span></b><b><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">)</span></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
<br />
sin(</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) = sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b<br />
</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">cos(</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) = cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b<br />
</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">tg(</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a </span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">-</span><span style="color: black; font-family: Symbol; font-size: 9pt;"> b </span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) = <u>tg </u></span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - tg </span></u><u><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> <br />
1 + tg<sup>2</sup></span><span style="color: black; font-family: Symbol; font-size: 9pt;">a </span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
<br />
<b>SUDUT RANGKAP <br />
<br />
</b>sin 2</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = 2 sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
cos 2</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = cos<sup>2</sup></span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - sin<sup>2</sup> </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
<img height="8" src="file:///C:/Users/rangga/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" width="44" />= 2 cos<sup>2</sup></span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - 1<br />
<img height="8" src="file:///C:/Users/rangga/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" width="44" />= 1 - 2 sin<sup>2</sup></span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
tg 2</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = <u> 2 tg 2</u></span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> </span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
1 - tg<sup>2</sup></span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = ½ sin 2</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
cos<sup>2</sup></span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = ½(1 + cos 2</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">)<br />
sin2</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = ½ (1 - cos 2</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">)<b><br />
<br />
Secara umum :</b><br />
<br />
sin n</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = 2 sin ½n</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos ½n</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
cos n</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = cos<sup>2</sup> ½n</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - 1<br />
<img height="8" src="file:///C:/Users/rangga/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" width="49" />= 2 cos<sup>2</sup> ½n</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - 1<br />
<img height="8" src="file:///C:/Users/rangga/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" width="49" />= 1 - 2 sin<sup>2 </sup>½n</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
tg n</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = <u> 2 tg ½n</u></span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> </span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
1 - tg<sup>2</sup> ½n</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
<br />
JUMLAH SELISIH DUA FUNGSI YANG SENAMA<br />
<br />
<br />
<i>BENTUK PENJUMLAHAN </i></span></b><b><span style="color: black; font-family: Symbol; font-size: 9pt;">®</span></b><b><i><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> PERKALIAN<br />
</span></i></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
</span></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = 2 sin </span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> +</span></u><u><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> -</span></u><u><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
2 2 <br />
sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> - sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = 2 cos </span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> +</span></u><u><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> sin </span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> -</span></u><u><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
2 2 <br />
cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = 2 cos </span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> +</span></u><u><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> -</span></u><u><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
2 2 <br />
cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = - 2 sin </span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> +</span></u><u><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> sin </span><u><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></u><u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> -</span></u><u><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span></u><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
2 2 <br />
<br />
<b><i>BENTUK PERKALIAN </i></b></span><b><span style="color: black; font-family: Symbol; font-size: 9pt;">®</span></b><b><i><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> PENJUMLAHAN <br />
</span></i></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
2 sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">(a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> +</span><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) + sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">(a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> -</span><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;">)</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
2 cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">(a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> +</span><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) - sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">(a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> -</span><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;">)</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
2 cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">(a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> +</span><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) + cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">(a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> -</span><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;">)</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
- 2 sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">(a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> +</span><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) - sin </span><span style="color: black; font-family: Symbol; font-size: 9pt;">(a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> -</span><span style="color: black; font-family: Symbol; font-size: 9pt;"> b</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;">)</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
<br />
<br />
</span></div><div> </div><div class="MsoNormal" style="line-height: normal; text-align: justify;"><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">PENJUMLAHAN FUNGSI YANG BERBEDA<br />
</span></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
Bentuk <b>a cos x + b sin x<br />
</b><br />
Merubah bentuk <b><i>a cos x + b sin x</i></b> ke dalam bentuk <b><i>K cos (x - </i></b></span><b><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></b><b><i><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">)</span></i></b><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div><div style="text-align: justify;"> </div><div class="MsoNormal" style="line-height: normal; text-align: justify;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
<b>a cos x + b sin x = K cos (x-</b></span><b><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">)</span></b><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div><div style="text-align: justify;"> </div><div class="MsoNormal" style="line-height: normal; text-align: justify;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">dengan : <b> <u> </u><br />
K = </b></span><b><span style="color: black; font-family: Symbol; font-size: 9pt;">Ö</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">a<sup>2</sup> + b<sup>2</sup> dan tg </span></b><b><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = b/a </span></b><b><span style="color: black; font-family: Symbol; font-size: 9pt;">Þ a</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> = ... ?<br />
</span></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
Kuadran dari a ditentukan oleh kombinasi tanda a dan b sebagai berikut</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div><div style="text-align: justify;"> </div><table border="1" cellpadding="0" class="MsoNormalTable" style="margin-left: 0px; margin-right: 0px; text-align: left; width: 40%;"><tbody>
<tr> <td style="background: none repeat scroll 0% 0% rgb(204, 204, 204); padding: 0.75pt; width: 20%;" width="20%"><br />
</td> <td style="background: none repeat scroll 0% 0% rgb(204, 204, 204); padding: 0.75pt; width: 20%;" width="20%"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">I</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="background: none repeat scroll 0% 0% rgb(204, 204, 204); padding: 0.75pt; width: 20%;" width="20%"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">II</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="background: none repeat scroll 0% 0% rgb(204, 204, 204); padding: 0.75pt; width: 20%;" width="20%"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">III</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="background: none repeat scroll 0% 0% rgb(204, 204, 204); padding: 0.75pt; width: 20%;" width="20%"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">IV</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> </tr>
<tr> <td style="background: none repeat scroll 0% 0% rgb(204, 204, 204); padding: 0.75pt; width: 20%;" width="20%"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">a</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="padding: 0.75pt;"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">+</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="padding: 0.75pt;"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">-</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="padding: 0.75pt;"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">-</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="padding: 0.75pt;"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">+</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> </tr>
<tr> <td style="background: none repeat scroll 0% 0% rgb(204, 204, 204); padding: 0.75pt; width: 20%;" width="20%"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">b</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="padding: 0.75pt;"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">+</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="padding: 0.75pt;"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">+</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="padding: 0.75pt;"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">-</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> <td style="padding: 0.75pt;"> <div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">-</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div></td> </tr>
</tbody></table><div style="text-align: justify;"> </div><div class="MsoNormal" style="line-height: normal; text-align: justify;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">keterangan :<br />
a = koefisien cos x<br />
b = koefisien sin x </span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"></span></div><div style="text-align: justify;"> </div><div class="MsoNormal" style="line-height: normal; text-align: justify;"><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
<b>PERSAMAAN</b><br />
<b>I.</b> <b>sin x = sin </b></span><b><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> </span><span style="color: black; font-family: Symbol; font-size: 9pt;">Þ</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> x1 = </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + n.360°<br />
x2 = (180° - </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) + n.360°<br />
<b> cos x = cos </b></span><b><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> </span><span style="color: black; font-family: Symbol; font-size: 9pt;">Þ</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> x = ± </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + n.360°<br />
<b>tg x = tg a</b> </span><span style="color: black; font-family: Symbol; font-size: 9pt;">Þ </span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">x = a + n.180° (n = bilangan bulat)<br />
<b>II.</b> <b>a cos x + b sin x = c</b><br />
a cos x + b sin x = C<br />
K cos (x-</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) = C<br />
cos (x-</span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) = C/K<br />
syarat persamaan ini dapat diselesaikan<br />
<b>-1 </b></span><b><span style="color: black; font-family: Symbol; font-size: 9pt;">£</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> C/K </span></b><b><span style="color: black; font-family: Symbol; font-size: 9pt;">£</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> 1 atau K² </span></b><b><span style="color: black; font-family: Symbol; font-size: 9pt;">³</span></b><b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> C²</span></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> (bila K dalam bentuk akar)<br />
<br />
misalkan C/K = cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
cos (x - </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) = cos </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"><br />
(x - </span><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">) = ± </span><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;"> + n.360° </span><span style="color: black; font-family: Symbol; font-size: 9pt;">®</span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"> </span><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">x =</span><b><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"> (</span></b><b><span style="color: black; font-family: Symbol; font-size: 9pt;">a</span></b><b><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"> </span></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">±</span><b><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;"> </span></b><b><span style="color: black; font-family: Symbol; font-size: 9pt;">b</span></b><b><span style="color: black; font-family: "Times New Roman","serif"; font-size: 9pt;">) </span></b><span style="color: black; font-family: "Verdana","sans-serif"; font-size: 9pt;">+<b> n.360°</b></span><span style="color: black; font-size: 9pt;"></span></div>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-16318793680783624852010-11-09T01:54:00.000-08:002010-11-09T01:59:05.282-08:00free download materi teori graf<div style="text-align: justify;">Teori graf adalah salah satu mata kuliah jurusan matematika, matakuliah ini biasanya di ambil semester 3.</div><div style="text-align: justify;">bagi temen-temen yang belum mempunyai materi tentang teori graf dapat di download di link berikut ini.<br />
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</div><div style="text-align: justify;"><br />
</div><div style="text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div align="center" class="MsoNormal" style="color: #20124d; margin-bottom: 0.0001pt; text-align: center;"><b><span style="font-family: "Times New Roman","serif";">TEORI GRAF DAN APLIKASINYA</span></b></div><div class="MsoNormal" style="color: #20124d; margin-bottom: 0.0001pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #20124d; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: -0.25in;"><b><span style="font-family: "Times New Roman","serif";">a.<span style="font: 7pt "Times New Roman";"> </span></span></b><b><span style="font-family: "Times New Roman","serif";">Definisi</span></b></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Times New Roman","serif";">Secara informal, suatu graf adalah himpunan benda-benda yang disebut verteks (atau <i>node</i>) yang terhubung oleh sisi (atau <i>edge </i>atau <i>arc</i>). Graf digunakan untuk merepresentasikan objek-objek diskrit dan hubungan antara objek-objek tersebut. Representasi visual dari graf adalah dengan menuyatakan objek dinyatakan sebagai noktah, bulatan, atau titik, sedangkan hubungan antara objek dinyatakan dengan garis.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Secara formal, Graf <i>G </i>didefinisikan sebagai pasangan himpunan (<i>V</i>, <i>E</i>), yang dalam hal ini:</span></div><div class="MsoListParagraphCxSpFirst" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">-<span style="font: 7pt "Times New Roman";"> </span></span><i><span style="font-family: "Times New Roman","serif";">V </span></i><span style="font-family: "Times New Roman","serif";">= himpunan tidak-kosong dari simpul-simpul (<i>vertices </i>atau <i>node</i>) = { <i>v</i>1 , <i>v</i>2 , ... , <i>vn </i>}</span></div><div class="MsoListParagraphCxSpLast" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">-<span style="font: 7pt "Times New Roman";"> </span></span><i><span style="font-family: "Times New Roman","serif";">E </span></i><span style="font-family: "Times New Roman","serif";">= himpunan sisi (<i>edges </i>atau <i>arcs</i>) yang menghubungkan sepasang simpul = {<i>e</i>1 , <i>e</i>2 , ... , <i>en</i>}</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman","serif";">atau dapat ditulis singkat notasi <i>G </i>= (<i>V</i>, <i>E</i>).</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Times New Roman","serif";">Definisi diatas menyatakan bahwa <i>V </i>tidak boleh kosong, sedangkan <i>E </i>boleh kosong. Jadi, sebuah graf dimungkinkan tidak mempunyai sisi satu buah pun, tetapi simpulnya harus ada, minimal satu. Graf yang hanya mempunyai satu buah simpul tanpa sebuah sisi pun dinamakan <b>graf trivial</b>. Sedangkan garis yang hanya berhubungan dengan satu simpul disebut <b>loop</b>.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: -0.25in;"><b><span style="font-family: "Times New Roman","serif";">b.<span style="font: 7pt "Times New Roman";"> </span></span></b><b><span style="font-family: "Times New Roman","serif";">Komponen-komponen graf</span></b></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Ada beberapa terminologi dari teori graf yang digunakan untuk menjelaskan apa yang dilihat ketika melihat suatu graf. Graf dapat dilihat dari komponen-komponen penyusunnya.</span></div><ol start="1" style="color: #20124d; margin-top: 0in;" type="1"><li class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><b><i><span style="font-family: "Times New Roman","serif";">Verteks</span></i></b></li>
</ol><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><i><span style="font-family: "Times New Roman","serif";">Verteks </span></i><span style="font-family: "Times New Roman","serif";">(simpul atau titik) yang disimbolkan dengan V adalah himpunan simpul yang terbatas dan tidak kosong. Dalam <i>gambar a.1</i> , <i>v<sub>1</sub>, v<sub>2</sub>, v<sub>3</sub>, … , v<sub>6</sub> </i>adalah simpul-simpul penyusun graf. Jumlah simpul pada graf dapat dinyatakan dengan <i>n </i>= |<i>V|</i>. </span></div><ol start="2" style="color: #20124d; margin-top: 0in;" type="1"><li class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><b><i><span style="font-family: "Times New Roman","serif";">Edge</span></i></b></li>
</ol><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><i><span style="font-family: "Times New Roman","serif";">edge</span></i><span style="font-family: "Times New Roman","serif";"> (sisi, busur atau rusuk) yang disimbolkan dengan E adalah himpunan rusuk yang menghubungkan sepasang simpul. Dalam <i>gambar a.1, </i>pada gambar b), <i>v<sub>1</sub> dan v<sub>2 </sub></i>dihubungkan oleh <i>e<sub>1</sub></i> dan <i>e<sub>2</sub></i>. Dalam hal ini,<i> e<sub>1</sub></i> dan <i>e<sub>2 </sub></i>adalah rusuk. Jumlah rusuk dam graf dinyatakan dengan <i>m </i>= </span><span style="font-family: "Times New Roman","serif";">|</span><i><span style="font-family: "Times New Roman","serif";">E</span></i><span style="font-family: "Times New Roman","serif";">|</span><span style="font-family: "Times New Roman","serif";">.</span></div><ol start="3" style="color: #20124d; margin-top: 0in;" type="1"><li class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><b><i><span style="font-family: "Times New Roman","serif";">Degree</span></i></b></li>
</ol><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><i><span style="font-family: "Times New Roman","serif";">Degree </span></i><span style="font-family: "Times New Roman","serif";">(derajat) suatu simpul yang disimbolkan dengan <i>d(v) </i>adalah jumlah rusuk yang berada pada simpul tersebut. Dalam <i>gambar a.1,</i> pada gambar b), <i>d(v<sub>1</sub>), d(v<sub>2</sub>) = </i>2<i>.</i> Dalam teori graf loop dihitung 2 kali sehingga pada gambar c), <i>d(v<sub>1</sub>)= </i>4 dan <i>d(v<sub>2</sub>), d(v<sub>3</sub>) = </i>2.</span></div><ol start="4" style="color: #20124d; margin-top: 0in;" type="1"><li class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><b><i><span style="font-family: "Times New Roman","serif";">Size</span></i></b></li>
</ol><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><i><span style="font-family: "Times New Roman","serif";">Size </span></i><span style="font-family: "Times New Roman","serif";">(ukuran) dari suatu graf adalah banyaknya simpul yang dimiliki.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: -0.25in;"><b><span style="font-family: "Times New Roman","serif";">c.<span style="font: 7pt "Times New Roman";"> </span></span></b><b><span style="font-family: "Times New Roman","serif";">Keterhubungan</span></b></div><ol start="1" style="color: #20124d; margin-top: 0in;" type="1"><li class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><b><i><span style="font-family: "Times New Roman","serif";">Walk </span></i></b></li>
</ol><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Misalkan G suatu Graf dengan <i>V<sub>i</sub></i> dan <i>V<sub>j</sub></i> adalah 2 titik dalam G<i>. Walk </i>(jalan) dari <i>V<sub>i</sub> ke V<sub>j</sub></i> adalah barisan simpul dan rusuk yang berhubungan secara bergantian, diawali dari simpul <i>V<sub>i</sub></i> dan diakhiri simpul <i>V<sub>j</sub></i>. Simpul <i>V<sub>i </sub></i>dan<i> V<sub>j</sub></i> adalah simpul awal dan simpul akhir. Sedangkan simpul-simpul yang berada diantara <i>V<sub>i </sub></i>dan<i> V<sub>j</sub></i> adalah simpul-simpul internal.</span></div><ol start="2" style="color: #20124d; margin-top: 0in;" type="1"><li class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><b><i><span style="font-family: "Times New Roman","serif";">Trail </span></i></b></li>
</ol><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><i><span style="font-family: "Times New Roman","serif";">Trail </span></i><span style="font-family: "Times New Roman","serif";">(jejak) adalah jalan dengan rusuk-rusuk yang berbeda atau tanpa rusuk berulang.</span></div><ol start="3" style="color: #20124d; margin-top: 0in;" type="1"><li class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><b><i><span style="font-family: "Times New Roman","serif";">Path </span></i></b><b><span style="font-family: "Times New Roman","serif";"></span></b></li>
</ol><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><i><span style="font-family: "Times New Roman","serif";">Path </span></i><span style="font-family: "Times New Roman","serif";">(lintasan) adalah jalan dengan simpul dan rusuk yang berbeda atau jejak dengan simpul yang berbeda.</span></div><ol start="4" style="color: #20124d; margin-top: 0in;" type="1"><li class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><b><i><span style="font-family: "Times New Roman","serif";">Sirkuit</span></i></b><b><span style="font-family: "Times New Roman","serif";"></span></b></li>
</ol><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><i><span style="font-family: "Times New Roman","serif";">Sirkuit </span></i><span style="font-family: "Times New Roman","serif";">adalah Jejak tertutup. Jejak tertutup adalah jejak dengan simpul awal dan simpul akhir sama.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify; text-indent: -0.25in;"><b><span style="font-family: "Times New Roman","serif";">a.<span style="font: 7pt "Times New Roman";"> </span></span></b><b><i><span style="font-family: "Times New Roman","serif";">Sirkuit</span></i></b><b><span style="font-family: "Times New Roman","serif";"> <i>Euler</i></span></b></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><i><span style="font-family: "Times New Roman","serif";">Sirkuit</span></i><span style="font-family: "Times New Roman","serif";"> <i>Euler </i>adalah sirkuit dimana setiap simpul dalam G yang muncul paling sedikit sekali dan setiap rusuk dalam G muncul tepat satu kali. </span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify; text-indent: -0.25in;"><b><span style="font-family: "Times New Roman","serif";">b.<span style="font: 7pt "Times New Roman";"> </span></span></b><b><i><span style="font-family: "Times New Roman","serif";">Sirkuit Hamilton</span></i></b><b><span style="font-family: "Times New Roman","serif";"></span></b></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><i><span style="font-family: "Times New Roman","serif";">Sirkuit</span></i><span style="font-family: "Times New Roman","serif";"> <i>Hamilton </i>adalah sirkuit dimana setiap simpul dalam G yang dilalui tepat satu kali dan setiap garis dalam G tidak harus dilalui.</span></div><ol start="5" style="color: #20124d; margin-top: 0in;" type="1"><li class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><b><i><span style="font-family: "Times New Roman","serif";">Cycle</span></i></b><b><span style="font-family: "Times New Roman","serif";"></span></b></li>
</ol><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><i><span style="font-family: "Times New Roman","serif";">Cycle </span></i><span style="font-family: "Times New Roman","serif";">adalah sebuah jejak tertutup dengan simpul awal dan semua simpul internalnya berbeda.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><table align="left" cellpadding="0" cellspacing="0"><tbody>
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</tbody></table><span style="font-family: "Times New Roman","serif";"></span></div><i style="color: #20124d;"><span style="font-family: "Times New Roman","serif";">Contoh<b> :</b></span></i> <br />
<div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify; text-indent: 0.5in;"><span style="font-family: "Times New Roman","serif";">Salah satu <i>walk</i> dari <i>v<sub>1</sub></i> ke <i>v<sub>3</sub></i> = {<i>v<sub>1</sub>,e<sub>1</sub>,v<sub>2</sub>,e<sub>7</sub>,v<sub>6</sub>,e<sub>10</sub>,v<sub>1</sub>,e<sub>5</sub>,v<sub>5</sub>,e<sub>4</sub>,v<sub>4,</sub>e<sub>4,</sub>v<sub>5,</sub>e<sub>10,</sub>v<sub>6,</sub>e<sub>8,</sub>v<sub>3</sub></i>}</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify; text-indent: 0.5in;"><span style="font-family: "Times New Roman","serif";">Salah satu <i>trail </i>dari <i>v<sub>1</sub></i> ke <i>v<sub>4</sub> </i>={<i>v<sub>1</sub>,e<sub>1</sub>,v<sub>2</sub>,e<sub>7</sub>,v<sub>6</sub>,e<sub>10</sub>,v<sub>1</sub>,e<sub>5</sub>,v<sub>5</sub>,e<sub>4</sub>,v<sub>4</sub></i>}</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify; text-indent: 0.5in;"><span style="font-family: "Times New Roman","serif";">Salah satu <i>path </i>dari <i>v<sub>1</sub></i> ke <i>v<sub>4</sub> =</i>{<i> v<sub>1</sub>,e<sub>1</sub>,v<sub>2</sub>,e<sub>7</sub>,v<sub>6</sub>,e<sub>8</sub>,v<sub>3</sub>,e<sub>3</sub>,v<sub>4</sub></i>}</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify; text-indent: 0.5in;"><span style="font-family: "Times New Roman","serif";">Salah satu <i>sirkuit </i>dari <i>v<sub>1</sub></i> ke <i>v<sub>4 </sub>= </i>{<i>v<sub>1</sub>,e<sub>1</sub>,v<sub>2</sub>,e<sub>7</sub>,v<sub>6</sub>,e<sub>9</sub>,v<sub>4</sub>,e<sub>3</sub>,v<sub>3</sub>,e<sub>8</sub>,v<sub>6</sub>,e<sub>6</sub>,v<sub>1</sub></i>}</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify; text-indent: 0.5in;"><span style="font-family: "Times New Roman","serif";">Salah satu <i>sirkuit </i>dari <i>v<sub>1</sub></i> ke <i>v<sub>4 </sub>= </i>{<i>v<sub>1</sub>,e<sub>1</sub>,v<sub>2</sub>,e<sub>7</sub>,v<sub>6</sub>,e<sub>9</sub>,v<sub>4</sub>,e<sub>3</sub>,v<sub>3</sub>,e<sub>8</sub>,v<sub>6</sub>,e<sub>6</sub>,v<sub>1</sub></i>}</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify; text-indent: 0.5in;"><span style="font-family: "Times New Roman","serif";">Salah satu <i>cycle =</i> {<i>v<sub>1</sub>,e<sub>1</sub>,v<sub>2</sub>,e<sub>7</sub>,v<sub>6</sub>,e<sub>10</sub>,v<sub>1</sub></i>}</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify; text-indent: 0.5in;"><table cellpadding="0" cellspacing="0"><tbody>
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<div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: -0.25in;"><b><span style="font-family: "Times New Roman","serif";">d.<span style="font: 7pt "Times New Roman";"> </span></span></b><b><span style="font-family: "Times New Roman","serif";">Jenis-Jenis Graf</span></b><b><span style="font-family: "Times New Roman","serif";"></span></b></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Pengelompokan graf dapat dipandang berdasarkan ada tidaknya sisi ganda atau sisi kalang, berdasarkan jumlah simpul, atau berdasarkan orientasi arah pada sisi.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">1.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-family: "Times New Roman","serif";">Berdasarkan ada tidaknya gelang atau sisi ganda pada suatu graf, maka secara umum graf dapat digolongkan menjadi dua jenis:</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">a.<span style="font: 7pt "Times New Roman";"> </span></span><b><span style="font-family: "Times New Roman","serif";">Graf sederhana </span></b><span style="font-family: "Times New Roman","serif";">(<i>simple graph</i>).</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Graf yang tidak mengandung loop maupun rusuk paralel. </span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">b.<span style="font: 7pt "Times New Roman";"> </span></span><b><span style="font-family: "Times New Roman","serif";">Graf tak-sederhana </span></b><span style="font-family: "Times New Roman","serif";">(<i>unsimple-graph</i>).</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Graf yang mengandung loop atau rusuk paralel Ada dua macam graf tak-sederhana, yaitu </span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">1). <b>Graf Ganda </b>(<i>multigraph</i>)</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 1in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Graf ganda adalah graf yang mengandung rusuk paralel</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">2). <b>Graf Semu </b>(<i>pseudograph</i>). </span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify; text-indent: 0.5in;"><span style="font-family: "Times New Roman","serif";">Graf semu adalah graf yang mengandung <i>loop</i>. </span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">2.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-family: "Times New Roman","serif";">Berdasarkan jumlah simpul pada suatu graf, maka secara umum graf dapat digolongkan menjadi dua jenis:</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">a.<span style="font: 7pt "Times New Roman";"> </span></span><b><span style="font-family: "Times New Roman","serif";">Graf berhingga </span></b><span style="font-family: "Times New Roman","serif";">(<i>limited graph</i>)</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Times New Roman","serif";">Graf berhingga adalah graf yang jumlah simpulnya, <i>n</i>, berhingga. </span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">b.<span style="font: 7pt "Times New Roman";"> </span></span><b><span style="font-family: "Times New Roman","serif";">Graf tak-berhingga </span></b><span style="font-family: "Times New Roman","serif";">(<i>unlimited graph</i>)</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Times New Roman","serif";">Graf yang jumlah simpulnya, <i>n</i>, tidak berhingga banyaknya.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">3. Berdasarkan orientasi arah pada rusuk, maka secara umum graf dibedakan atas 2 jenis:</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">a. <b>Graf tak-berarah </b>(<i>undirected graph</i>)</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Graf yang sisinya tidak mempunyai orientasi arah disebut graf tak-berarah. Pada graf tak-berarah, urutan pasangan simpul yang dihubungkan oleh sisi tidak diperhatikan.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Jadi, (<i>v<sub>i</sub></i>,<i>v<sub>j</sub></i>) = (<i>v<sub>j</sub></i>,<i>v<sub>i</sub></i>) adalah sisi yang sama. </span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">c.<span style="font: 7pt "Times New Roman";"> </span></span><b><span style="font-family: "Times New Roman","serif";">Graf berarah </span></b><span style="font-family: "Times New Roman","serif";">(<i>directed graph </i>atau <i>digraph</i>)</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><table cellpadding="0" cellspacing="0"><tbody>
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<span style="font-family: "Times New Roman","serif";">Graf yang setiap sisinya diberikan orientasi arah disebut sebagai graf berarah. Pada graf berarah, (<i>v<sub>i</sub></i>,<i>v<sub>j</sub></i>) dan (<i>v<sub>j</sub></i>,<i>v<sub>i</sub></i>) menyatakan dua buah busur yang berbeda, dengan kata lain (<i>v<sub>i</sub></i>,<i>v<sub>j</sub></i>) </span><span style="font-family: "Times New Roman","serif";">≠ </span><span style="font-family: "Times New Roman","serif";">(<i>v<sub>j</sub></i>,<i>v<sub>i</sub></i>). Untuk busur (<i>v<sub>i</sub></i>,<i>v<sub>j</sub></i>) simpul <i>vj </i>dinamakan simpul asal<b> </b>(<i>initial vertex</i>) dan simpul <i>vk </i>dinamakan simpul terminal<b> </b>(<i>terminal vertex</i>). </span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><br />
</div><div align="center" class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><i><span style="font-family: "Times New Roman","serif"; font-size: 9pt;"></span></i></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-align: justify;"><b><span style="font-family: "Times New Roman","serif";">e. Permasalahan Optimasi</span></b></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-indent: 0.25in;"><b><span style="font-family: "Times New Roman","serif";">1. Penyelesaian Masalah Optimasi</span></b></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Times New Roman","serif";">Secara umum, penyelesaian masalah pencarian jalur terpendek dapat dilakukan dengan menggunakan dua metode, yaitu metode konvensional dan metode heuristik. Metode konvensional diterapkan dengan perhitungan matematis biasa, sedangkan metode heuristik diterapkan dengan perhitungan kecerdasan buatan.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 31.5pt; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif";">1.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-family: "Times New Roman","serif";">Metode Konvensional</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Metode konvensional adalah metode yang menggunakan perhitungan matematis biasa. . Ada beberapa metode konvensional yang biasa digunakan untuk melakukan pencarian jalur terpendek, diantaranya: algoritma Djikstraa, algoritma Floyd-Warshall, dan algoritma Bellman-Ford</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Times New Roman","serif";">2. Metode Heuristik</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.75in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">Metode Heuristik adalah sub bidang dari kecerdasan buatan yang digunakan untuk melakukan pencarian dan optimasi. Ada beberapa algoritma pada metode heuristik yang biasa digunakan dalam permasalahan optimasi, diantaranya algoritma genetika, algoritma semut, logika fuzzy, jaringan syaraf tiruan, pencarian tabu, <i>simulated annealing</i>, dan lain-lain.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin-bottom: 0.0001pt; text-indent: 0.25in;"><b><span style="font-family: "Times New Roman","serif";">2. Permasalahan Jalur Terpendek (<i>Shortest Path Problem</i>)</span></b></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-indent: 0.25in;"><span style="font-family: "Times New Roman","serif";">Jalur terpendek adalah suatu jaringan pengarahan perjalanan dimana sesorang pengarah jalan ingin menentukan jalur terpendek antara dua kota, berdasarkan beberapa jalur alternatif yang tersedia, dimana titik tujuan hanya satu.</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: 0.25in;"><b><i><span style="font-family: "Times New Roman","serif";">Gambar e.2 </span></i></b><i><span style="font-family: "Times New Roman","serif";">Graf ABCDEFG</span></i></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Times New Roman","serif";">Pada gambar diatas, misalkan kita dari kota A ingin menuju Kota G. Untuk menuju kota G, dapat dipilih beberapa jalur yang tersedia :</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><br />
</div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → B → C → D → E → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → B → C → D → F → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → B → C → D → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → B → C → F → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → B → D → E → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → B → D → F → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → B → D → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → B → E → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → C → D → E → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → C → D → F → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in;"><span style="font-family: "Times New Roman","serif";">A → C → D → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.5in; text-align: justify;"><span style="font-family: "Times New Roman","serif";">A → C → F → G</span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Times New Roman","serif";">Berdasarkan data diatas, dapat dihitung jalur terpendek dengan mencari jarak antara jalur-jalur tersebut. Apabila jarak antar jalur belum diketahui, jarak dapat dihitung berdasarkan koordinat kota-kota tersebut, kemudian menghitung jalur terpendek yang dapat dilalui.</span><span style="font-family: "Times New Roman","serif";"> </span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Times New Roman","serif";"></span></div><div class="MsoNormal" style="color: #20124d; line-height: normal; margin: 0in 0in 0.0001pt 0.25in; text-align: justify; text-indent: 0.25in;"><br />
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</div>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com2tag:blogger.com,1999:blog-8642052046684309402.post-72651435923409720522010-11-09T01:31:00.000-08:002010-11-09T01:31:47.413-08:00tugas kampus<ol><li><a name='more'></a>Tugas Bulan November</li>
</ol><ul><li>teori graf ( algoritam dikstra ) </li>
<li>aljabar linier</li>
<li>pdb</li>
<li>dll</li>
</ul>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-10699631978935402102010-11-08T20:18:00.000-08:002010-11-08T20:18:28.031-08:00artikel motivasi<div><div style="background-color: transparent; border: medium none; color: black; overflow: hidden; text-align: left; text-decoration: none;"><table><tbody>
<tr><td valign="top" width="100%"> </td> <td valign="top"> </td> </tr>
</tbody></table><img alt="images" class="alignleft size-full wp-image-878" height="201" src="http://www.resensi.net/wp-content/uploads/2010/11/images.jpeg" title="images" width="250" />Tulisan ini saya tujukan untuk memotivasi diri saya sendiri. Semoga dapat memberi manfaat kepada sahabat yang telah secara rutin dan berkala berkunjung ke halaman-halaman pada web ini ataupun yang kebetulan mampir.<br />
6 Tips motivasi<br />
Secara ringkas, motivasi adalah semangat pendorong untuk melakukan sesuatu. Berikut ini adalah beberapa tips motivasi yang semoga bermanfaat.<br />
<strong>1. Selalu bersyukur akan apa yang kita dapatkan.</strong><br />
Mungkin hal ini adalah sederhana, namun sangat memotivasi diri kita saat kita terpukul atau terjatuh dengan target-target yang dinanti-nanti dan diharapkan untuk terjadi, tapi faktanya meleset. Pengungkapan syukur melalui 3 cara.<span id="more-877"></span><br />
<ul><li><strong>Dengan hati.</strong> Lihatlah sekeliling kita yang ada dibawah kita. Yakin hal ini akan membuat hati kita lembut dan mensyukuri akan nikmat-nikmat yang oleh sebagian orang tidak dapat menikmatinya.</li>
<li><strong>Dengan lisan,</strong> dengan ucapkan alhamdulillah. Nikmat yang kita rasakan tidak akan kita peroleh tanpa seijin dari pemilik tubuh kita, pemilik jasad kita, juga pemilik ruh kita. Trus kita ini siapa? Kita adalah makhluk yang diberi pinjaman untuk dapat berkarya, dan membagikan kebahagiaan kepada orang lain.</li>
<li><strong>Dengan perbuatan.</strong> Syukur dengan membagikan kebahagiaan kepada orang lain. Rasakanlah kebahagiaan yang timbul saat kita dapat melihat kebahagiaan yang muncul melalui tangan kita. Ada rasa menyeruak dalam dada merasakan bahagia meski buliran air mata mengalir tidak terasa. Jika kita pernah merasakannya, ulangi ulangi dan ulangi.</li>
</ul><strong>2. Lakukan apa yang kita minati.</strong><br />
Hal ini akan memotivasi kita untuk melakukannya. Karena dengannya kita merasa enjoy, dan dengannya tak kan ada rasa bosan dan letih. Banyak dari saudara kita yang mereka bekerja karena tuntutan, bukan karena mereka menyukainya. Dari hasilnya kita akan tahu mana yang bekerja karena menyukainya, atau bekerja karena tuntutan. Orang bekerja dengan diikuti rasa senang, akan menambahkan detil-detil secara sukarela.<br />
<strong>3. Jika tidak seperti yang kita inginkan. </strong><br />
Yakinkan pada diri sendiri, jika posisi ini adalah step awal menuju yang kita inginkan. Tentunya ada hikmahnya. Apapun keadaanannya. Tetap lakukan yang terbaik yang kita bisa, karena itu memperlihatkan kualitas kita.<br />
<strong>4. Cermati, perhitungkan, dan tangkap peluang yang ada. </strong><br />
Setiap kita memiliki peluang-peluang menuju sukses. Namun hanya sedikit orang yang mampu memanfaatkan peluang itu. Terkadang kita melihat ada peluang, namun memiliki keterbatasan, misal keterbatasan modal, keterbatasan keahlian dan lain-lain. Itulah gunanya bermasyarakat, adanya berinteraksi, bersosialisasi, dan bertolong-menolong. Dengan bekerja sama tentu akan menghasilkan yang positif sesuai target dan keinginan bersama. Asah terus kemampuan untuk melihat peluang.<br />
<strong>5. Berkumpul dengan orang yang bermotivasi. </strong><br />
Prinsip ini sama dengan istilah penjual minyak wangi akan berbau wangi dengan sendirinya.<br />
<strong>6. Selalu dekatkan diri pada Allah. </strong><br />
Adakalanya dalam berusaha mengalami pasang surut. Hambatan dan rintangan dalam melangkah. Pastikan pada diri sendiri bahwa semua itu ada hikmahnya. Mungkin sajakan itu adalah cara Allah untuk mendidik kita. Kita tidak akan dididik seperti di bangku sekolah, tapi kita dididik melalui peristiwa-peristiwa. Kita akan mendapatkan pelajaran dari universitas yang skalanya lebih besar. yaitu universitas kehidupan.<br />
Semoga kita termasuk orang-orang yang dapat memberi manfaat kepada orang lain. Semoga Allah mengijinkannya.. Amin..<br />
Tidaklah sesuatu berubah jika tidak mulai bertindak, dan kapankah waktu yang paling sesuai untuk memulainya jika bukan saat ini<br />
<span><br />
<br />
Read more: <a href="http://www.resensi.net/6-tip-motivasi/2010/11/07/#more-877#ixzz14kuA2Ikw" style="color: #003399;">http://www.resensi.net/6-tip-motivasi/2010/11/07/#more-877#ixzz14kuA2Ikw</a></span></div></div>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-34574751608223696202010-11-08T20:14:00.001-08:002010-11-08T20:14:38.487-08:00maaf untuk download buku kuliah blm kami postingmeraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-46790613496834817762010-11-08T20:13:00.000-08:002010-11-08T20:13:01.981-08:00Matakuliah yang kami ambil semester 3<br />
<ol><li>Aljabar Linier</li>
<li>Persamaan deferensial Biasa</li>
<li>Geometri analitika</li>
<li>Probabilitas </li>
<li>Teori bilangan</li>
<li>Teori Graf</li>
</ol>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-50391332206925991462010-11-08T20:11:00.000-08:002010-11-08T20:11:03.790-08:00Matakuliah yang kami ambil Semester 2<br />
<ol><li>Kalkulus 2</li>
<li>Pengantar Teknologi</li>
<li>Fisika Dasar 2</li>
<li>B.inggris</li>
<li>Logika dan Himpunan</li>
<li>Kombinatorik</li>
<li>PKN</li>
</ol>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-63445387835950449222010-11-08T20:08:00.000-08:002010-11-08T20:08:06.989-08:00Daftar matakuliah yang di ambil semester 1 :<br />
<ol><li>Agama </li>
<li>Biologi</li>
<li>Fisika Dasar 1</li>
<li>Ilmu Alam Dasar</li>
<li>Kimia dasar</li>
</ol>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-54509829688027184732010-11-08T20:05:00.000-08:002010-11-08T20:05:43.757-08:00<b><span style="color: red;">Selamat datang di bloq kami</span>,</b><br />
maaf jika banyak kekukargan karena kami beru belajar membuat blog.<br />
blog sukses kuliah ini berisi tentang berita terbaru tentang buku-buku kuliah terbaru khususnya Fakultas Sains Dan Matematika.<br />
SEMANGAT BUAT TEMAN-TEMAN.<br />
email : <i style="background-color: lime;">ranggapradeka@yahoo.co.id</i>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-18147230365712209122010-11-04T09:09:00.000-07:002010-11-04T09:09:07.808-07:00The shortest problemSalah satu subbab dari matakuliah teori graf yaitu tentang lintasan terpendek.<br />
untuk menentukan sebuah lintasan terpendek banyak algoritma yang digunakan.<br />
berikut ini adalah salah satu contoh penyelesai kasus menentukan lintasan terpendek menggunakan algoritma dijkstra.<br />
silahkan teman-teman download dsini kilik <a href="http://www.4shared.com/document/QH0f7LXy/the_shortest_path___teori_graf.html">r2g</a>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0tag:blogger.com,1999:blog-8642052046684309402.post-10015826612582411212010-10-09T21:26:00.000-07:002010-10-09T21:26:26.267-07:00tips sukses kuliah<div class="posttitle"> <h2 class="pagetitle">catatatan : hasil copy paste,,hehe </h2><h2 class="pagetitle">Tips Sukses Kuliah</h2></div><br />
<div class="entry"> <div align="justify"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Kali ini saya pingin berbagi tips2 sukses kuliah versi denok…Tentu aja harus disamakan dulu y persepsinya. Klo dalam pandanganku nih…yg dinamakan orang sukses kuliah tuh harus memenuhi beberapa syarat kayak gini : 1. Lulus tepat waktu (maksimal 4,5 tahun) 2. Dapet Predikat cumlaude or minimal IPK nya diatas 3 lah , 3. Langsung dapat kerjaan (ga pake nganggur) , 4. ga kuper alias banyak temennya , 5. dikenal baik di lingkungannya , 6. komunikatif and kreatif. Banyak banget kan? </span></span></div><div align="justify"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">YuPz..itu sih versikoe.. klo untuk point 1,2 and 3 itu sih standard banget y…nah menurutku klo seseorang bisa memenuhi poin 1,2 and 3 tapi g dapet di 4,5 and 6 nya sama aja boong…alias tong kosong..knapa? Tentu aja karena sebenarnya tujuan kita belajar itu kan y biar bermanfaat buat orang lain..lha klo pinter tapi ga punya temen, ga kenal tetangga and ga bisa berbuat sesuatu sekecil apapun buat lingkungan sekitarnya apa gunanya dunk kuliah sampe sarjana?</span></span></div><div align="justify"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Nah ini nih yang harus diluruskan dulu persepsinya.Kadang kala orang berfikir bahwa parameter orang itu sukses itu adalah KAYA, kerja di perusahaan elit and terkenal. Klo cuman pingin jadi kaya ga kuliah pun klo cerdas,kreatif and inovatif pasti juga bisa,liat aj tuh bill gate (empunya microsoft). Seorang bill Gate tuh ga lulus kuliah lho…tapi jadi orang paling kaya di dunia. </span></span></div><div align="justify"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">so..buat kamu2 yang masih ada di semester awal kuliah, harus punya persepsi yang benar dulu nih mengenai tujuan kita kuliah. Klo dalam persepsi ku, kuliah itu punya 3 tujuan penting, yaitu meng-upgrade ilmu sesuai dengan bidang keahlian kita (menuntut ilmu wajib lho), meng-create pola pikir dan menciptakan semacam social responsibility. Ketika seseorang itu punya ilmu, cerdas (pola pikirnya terasah) dan dekat dengan lingkungannya (mempunyai social responsibility) insya allah yg namanya pekerjaan itu mudah didapatkan. Bahkan sebelum dia mencari sudah dicari ^_^ so sweet kan? </span></span></div><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Buat mewujudkan itu, aku punya beberapa tips yang semoga bermanfaat :</span></span><br />
<ol><li><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Niat dulu *niatin kuliah tuh mo ngapain? Yg jelas bukan buat maen2 doang kan?</span></span></li>
<li><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Perhatikan baik2 apa yang diajarkan dosen *ini kuncinya menurutku, g harus punya catatan deh..asal dengerin bener apa yg disampekan dosen, 70 % nya dah terserap kok di otak..yg di catat poin2 pentingnya aj</span></span></li>
<li><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">menjadikan Belajar sebagai hal yang menyenangkan *jangan menganggap belajar itu adalah beban..enjoy aj lagi…</span></span></li>
<li><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Mencari teman yang baik plus pintar *Penting and wajib bgt deh..klo sampe salah piilih temen bisa berabe lho!!! temen yang baek adalah teman yang tulus and biasanya temen yang kayak gini yang bakal bikin kita jadi selalu termotivasi ^_^</span></span></li>
<li><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Aktif berorganisasi (intra kampus maupun ekstra kampus) *bisa belajar b’sosialisasi dgn orla, blajar memahami orla, bljar menghadapi perbedaan , mbtuk pola pikir,etc –> PENTING bgt!!<br />
</span></span></li>
<li><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">aktif dalam kegiatan social kemasyarakatan *jangan jadi katak dalam tempurung,lihatlah dunia di sekitarmu dan lakukan sesuatu <img alt=":)" class="wp-smiley" src="http://s2.wp.com/wp-includes/images/smilies/icon_smile.gif?m=1245369377g" /> </span></span></li>
<li><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Managemen waktu yang baik *<strong>kUnci dri semuanya </strong>nih</span></span></li>
<li><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Imbangi dengan penguatan ruhiyah (dengan sering ikutin kajian or pengajian or baca2 buku agama) dan jangan lupa always berdoa ^_^ *<strong>kekuatan utama</strong> nih</span></span></li>
</ol><div align="justify"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">itu aja kok..simple kan? Oia satu hal yang harus diingat, yang namanya belajar tuh ga melulu harus SERIUS bgt dengan srtumpuk buku tebal lho…klo kita jeli, kita sbnrnya bisa belajar kapanpun and dimanapun …klo males belajar, ikutan aj kelompok belajar or kelompok study. Mencari temen yg baik bukan berarti pilih2 or gmna gtu…bertemanlah dengan siapa saja..but untuk ‘temen deket’ or ‘sahabat’ wajib BAIK (biasanya orang baik itu juga pintar). Knapa? Karena sahabat adalah orang yg bakal paling mempengaruhi kepribadian kita after keluarga. Yakin deh… klo sampe kmu salah pilih teman bakal bahaya bgt buat masa depan kmu sendiri..so wajib bgt bersahabat dengan Orang yg baek and berusahalah juga untuk jadi orang yang baek <img alt=":)" class="wp-smiley" src="http://s2.wp.com/wp-includes/images/smilies/icon_smile.gif?m=1245369377g" /> </span></span></div><div align="justify"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">tulisan ini dah teruji and aku compare dengan hasil pengamatanku selama ini terhadap anak2 ikoMp UGM angkatan 2002…</span></span></div><div align="justify"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Alhamdulillah allah mempertemukanku dengan temen2 yg super Baiknya super Pinternya super SMART and super Gokil juga (fun banget)..jadinya 3 tahun 10 bulan kuliah di ikomp UGM bener2 menjadi salah satu moment terindah dalam hidupku,</span></span></div><div align="justify"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;">Semoga kalian pun juga bakal nemuin hal yg sama ^_*</span></span></div></div>meraih mimpi by rangga pradekahttp://www.blogger.com/profile/12507828444049279300noreply@blogger.com0