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{"name": "Mat 2A - Bab 14 - No 5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Mat 2A - Bab 14 - No 5", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Diberikan persamaan integral-diferensial</p>\n<p style=\"text-align: center;\">$\\displaystyle y'(t)+\\var{a*b}\\int_0^t y(s)\\, ds=\\var{a*b^2}t\\var{a+b}y(t).$</p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-7..-5)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-4..-2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": "0.6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Persamaan ini dapat diubah menjadi persamaan diferensial orde dua $y''+ay'+by=c$ dengan cara menurunkan kedua ruas terhadap variabel $t$. Diperoleh nilai $a$, $b$, dan $c$ berturut-turut adalah $\\ldots$.</p>", "correctAnswer": "matrix([-a-b,a*b,a*b^2])", "correctAnswerFractions": false, "numRows": 1, "numColumns": "3", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "0.6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solusi umum dari persamaan diferensial tersebut adalah $y(t)=C_1e^{\\lambda_1 t}+C_2e^{\\lambda_2 t}+D$ dengan $\\lambda_1&lt;\\lambda_2$. Diperoleh nilai $\\lambda_1$, $\\lambda_2$, dan $D$ berturut-turut adalah $\\ldots$.</p>", "correctAnswer": "matrix([a,b,b])", "correctAnswerFractions": false, "numRows": 1, "numColumns": "3", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Jika $y(0)=\\var{b}$ dan $y'(0)=\\var{a}$, maka nilai $C_1$ dan $C_2$ berturut-turut adalah $\\ldots$.</p>", "correctAnswer": "matrix([1,-1])", "correctAnswerFractions": false, "numRows": 1, "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle \\lim\\limits_{t\\to\\infty}\\dfrac{y(t)}{e^t}=\\ldots$.</p>", "minValue": "0", "maxValue": "0", "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/"}]}