// Numbas version: exam_results_page_options {"name": "Set Soal Matematika IIB - Bab 6 - 8", "metadata": {"description": "", "licence": "None specified"}, "duration": 3600, "percentPass": 0, "showQuestionGroupNames": true, "showstudentname": true, "question_groups": [{"name": "PG + Isian", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questionNames": ["", "", "", "", "", ""], "questions": [{"name": "Mat 2B - UTS - No 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Jika diberikan hasil perkalian matriks berikut

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$\\begin{bmatrix} 1&2&a&2\\\\ 1&5&0&1\\\\1&0&-1&-1\\\\2&0&0&2 \\end{bmatrix} \\begin{bmatrix} 1&-1&2&3\\\\1&1&-1&d\\\\0&0&2&3\\\\3&1&c&5 \\end{bmatrix}=\\begin{bmatrix} 9&3&-6&4\\\\b&5&-3&8\\\\-2&-2&0&-5\\\\e&0&4&16 \\end{bmatrix},$

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maka pernyataan yang benar tentang variabel $a$, $b$, $c$, $d$, dan $e$ adalah $\\ldots$.

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Pilihlah semua pernyataan yang benar tentang sistem persamaan diferensial berikut.

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$\\begin{cases} \\dfrac{dp}{dt}=(p^2-4p-q)(q-5)\\\\[10pt] \\dfrac{dq}{dt}=(q-4p+p^2)(p-2) \\end{cases}$

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Daerah $R$ dibatasi oleh $y=\\var{a}x$, $y=-\\var{a}x$ dan $y=\\var{a}$.

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Pernyataan berikut yang benar adalah $\\ldots$.

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Luas daerah di antara kurva $y=a^2-x^2$ dan $y=x^2-a^2$ adalah $\\dfrac{\\simplify{8*{a}^3}}{3}$. Maka nilai $a=\\ldots$.

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Diberikan medan arah dari persamaan diferensial $\\dfrac{dy}{dt}=g(y)$ sebagai berikut.

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Misalkan $y(t)$ merupakan solusi persamaan diferensial tersebut, dengan $y(\\var{a})=\\var{b}$. Tentukan nilai dari $\\lim\\limits_{t \\to \\infty} y(t)$.

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Perhatikan diagram matriks berikut.

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Misalkan $\\begin{bmatrix} A_{t+1}\\\\B_{t+1}\\\\C_{t+1} \\end{bmatrix}=H\\begin{bmatrix} A_{t}\\\\B_{t}\\\\C_{t} \\end{bmatrix}$.

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Maka matriks $H$ adalah $\\ldots$.

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Misal laju transkripsi berubah secara eksponensial terhadap fungsi $e^{\\var{b} t }$ dan mRNA mempunyai laju peluruhan konstan $\\var{k}$. Banyaknya molekul transkrip mRNA, dinotasikan $T$, berubah melalui persamaan diferensial

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$\\dfrac{dT}{dt}=e^{\\var{b} t}-\\var{k}T.$

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Misalkan $T(0)=\\dfrac{1}{\\simplify{{k}+{b}}}$. Dengan ketelitian $3$ angka di belakang koma, tentukan nilai dari $T\\left( \\dfrac{1}{2} \\right)$.

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Petunjuk: Gunakan substitusi $y(t)=e^{\\var{k}t}T(t)$ agar dapat masalah nilai awal tersebut dapat diselesaikan dengan metode separasi variabel

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Dengan menggunakan Metode Euler untuk $h=0.25$, akan diperoleh $T_1(0.25) \\approx\\ldots$.

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Titik kedua yang diperoleh dari Metode Euler adalah $T_2(0.5) \\approx\\ldots$.

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Tentukan galat mutlak Metode Euler, $|T(0.5)-T_2(0.5)|$.

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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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