// Numbas version: exam_results_page_options
{"name": "Mat 2B - UAS - No 7", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Mat 2B - UAS - No 7", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Suatu model sistem persamaan diferensial untuk model kecukupan vaksinasi suatu wabah adalah</p>\n<p style=\"text-align: center;\">$\\begin{cases} \\dfrac{dN}{dt} &amp;= 2(1-p)N+2(1-p)V-N \\\\ \\dfrac{dV}{dt} &amp;= 2pV+2pN-3V \\end{cases}$</p>\n<p style=\"text-align: left;\">dengan $N$ menyatakan banyaknya orang yang belum divaksin, $V$ menyatakan banyaknya orang yang divaksin, serta $p$ adalah fraksi populasi yang telah divaksin.</p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {"k": {"name": "k", "group": "Ungrouped variables", "definition": "random(20..50)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["k"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Perhatikan bahwa titik kesetimbangan model ini adalah di $(0,0)$. Tentukan nilai $p$ terkecil agar titik kesetimbangan ini bersifat stabil. Tuliskan nilainya dalam bentuk pecahan paling sederhana.</p>\n<p><em>Catatan</em>: Nilai $p$ ini disebut juga dengan nilai kritis, yaitu nilai yang dibutuhkan agar wabah dapat mereda.</p>\n<p><em>Petunjuk:</em> Karena $p$ menyatakan fraksi, maka $p\\in[0,1]$.</p>", "minValue": "3/4", "maxValue": "3/4", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Misal $\\mathbf{x}(t)=\\begin{bmatrix} N(t) \\\\ V(t) \\end{bmatrix}$. Dengan menggunakan $p=\\dfrac{15}{16}$, jika diberikan nilai awal $N(0)=\\var{k}$ dan $V(0)=0$, maka solusi khusus dari sistem persamaan diferensial tersebut adalah $\\mathbf{x}(t)=\\begin{bmatrix} c_1e^{\\lambda_1t}+c_2e^{\\lambda_2t} \\\\ c_3e^{\\lambda_1t}+ c_4e^{\\lambda_2t} \\end{bmatrix}$.</p>\n<p style=\"text-align: left;\">Maka $c_1+c_2+c_3+c_4=\\ldots$.</p>", "minValue": "k", "maxValue": "k", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Mengacu pada solusi (b), $\\displaystyle \\lim\\limits_{t\\to\\infty}\\dfrac{V(t)}{N(t)} = \\ldots$.</p>", "minValue": "3", "maxValue": "3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}]}]}], "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}]}