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{"name": "Laplace transform #3 - powers of t by exp", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Laplace transform #3 - powers of t by exp", "variables": {"n": {"definition": "random(2..5#1)", "name": "n", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "b": {"definition": "random(2..11#1)", "name": "b", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "k": {"definition": "random(2..12#0.5)", "name": "k", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "a": {"definition": "random(2..10#1)", "name": "a", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}}, "advice": "", "variable_groups": [], "statement": "<p>What is the Laplace transform for the function:</p>\n<p style=\"padding-left: 30px;\">\\(x(t)=\\var{a}t^{\\var{n}}e^{-\\var{k}t}+\\var{b}.\\)</p>\n<p style=\"padding-left: 30px;\"></p>", "functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"scripts": {}, "type": "gapfill", "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "marks": 0, "gaps": [{"checkingAccuracy": 0.001, "scripts": {}, "type": "jme", "failureRate": 1, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "vsetRange": [0, 1], "showPreview": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "marks": 1, "vsetRangePoints": 5, "answer": "fact{n}*{a}/(s+{k})^{n+1}+{b}/s"}], "unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "prompt": "<p>\\(X(s)=\\)&nbsp;[[0]]</p>"}], "rulesets": {}, "extensions": [], "ungrouped_variables": ["a", "b", "k", "n"], "tags": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": ""}, "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}]}