// Numbas version: exam_results_page_options {"name": "Set Soal Matematika Bisnis II - Bab 7 dan 8", "metadata": {"description": "", "licence": "None specified"}, "duration": 2700, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "PG + Isian", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questionNames": ["", "", "", ""], "questions": [{"name": "Matbis 2 - Bab 7 dan 8 - No 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Solusi khusus dari persamaan diferensial \$$y'-\\var{a}y=\\var{a*c}\$$, \$$y(0)=\\var{b}\$$ adalah \$$\\ldots\$$.

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Diberikan persamaan diferensial tak homogen \$$y''-2y'+y=e^x+x+1\$$. Pemisalan yang tepat untuk menentukan solusi partikularnya adalah \$$\\ldots\$$.

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Pendapatan per kapita meningkat dengan laju \$$\\var{a}\\%\$$. Maka dari itu terbentuk persamaan diferensial \$$p'(t)=\\var{a/100}p(t)\$$. Tentukan waktu yang dibutuhkan agar pendapatannya menjadi \$$\\var{b}\$$ kali lipat pendapatan awal.

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Solusi khusus dari persamaan diferensial \$$y''-\\var{c}y'=0\$$, \$$y(0)=\\var{a}\$$, \$$y'(0)=\\var{b}\$$ adalah \$$y(t)=A+Be^{\\var{c}t}\$$.

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Tentukan nilai $A$ dan $B$ berturut-turut.

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Perubahan harga suatu komoditas (dalam dolar) mengikuti persamaan

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\$p'(t)=(q^D(t)-q^S(t))-\\dfrac{2}{3}\\displaystyle\\int_0^t (q^S(s)-q^D(s))\\, ds.\$

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Diketahui jumlah penawaran komoditas (dalam unit) mengikuti \$$q^S(t)=20+2p(t)\$$ dan jumlah permintaan mengikuti \$$q^D(t)=56-p(t)\$$.

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Jika fungsi \$$p'\$$ diturunkan sekali lagi, akan diperoleh persamaan diferensial orde dua berbentuk \$$p''+ap'+bp=k\$$. Nilai dari \$$a\$$, \$$b\$$, dan \$$k\$$ berturut-turut adalah $\\ldots$.

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Catatan: Ingat Teorema Dasar Kalkulus, $\\dfrac{d}{dt}\\displaystyle\\int_0^t f(s)\\, ds=f(t)$.

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Solusi dari persamaan differensial orde $2$ sebelumnya adalah \$$p_h(t)=C_1e^{\\alpha t}+C_2e^{\\beta t}+\\hat p\$$. Maka \$$\\alpha+\\beta+\\hat p=\\ldots\$$.

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Jika diberikan syarat awal $p(0)=0$ dan $p'(0)=0$, tentukan nilai \$$C_1\\cdot C_2\$$.

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Waktunya 5 menit lagi ya.

Selamat datang!

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Silakan gunakan set soal ini dengan bijak. Kalian bisa mencoba set soal ini terus-menerus.

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Set soal ini dapat digunakan oleh siapapun secara gratis.

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Petunjuk pengerjaan soal:

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• Jawaban dapat dituliskan dalam bentuk desimal maupun pecahan.
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• Jika jawaban dituliskan dalam bentuk desimal, pisahkan dengan tanda titik dan bulatkan hingga dua angka di belakang titik. Contoh: ketik 0.67 untuk menjawab \$$\\frac{2}{3}\$$.
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• Jika jawaban dituliskan dalam bentuk pecahan, pisahkan pembilang dan penyebut dengan garis miring dan jawab dengan pecahan paling sederhana. Contoh: ketik 2/3 untuk menjawab \$$\\frac{2}{3}\$$.
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Jika ada kunci jawaban yang salah, kalian dapat memberitahu kami di Instagram @meongmeongproject atau OA Line @eog7710d.

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