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{"name": "Value of Jacobian 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Value of Jacobian 2", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Let $U=X + Y$ and $V=X-Y$</p>\n<p>For $\\var{a}&lt;x&lt;\\var{b}$ and $\\var{a} &lt;y&lt;\\var{b}$</p>\n<p>What is the value of the Jacobian?</p>", "advice": "<p>$|J| = \\Bigg|\\begin{vmatrix}<br/>\\frac{\\partial x}{\\partial u} &amp; \\frac{\\partial x}{\\partial v} \\\\ <br/>\\frac{\\partial y}{\\partial u} &amp; \\frac{\\partial y}{\\partial v}<br/>\\end{vmatrix}\\Bigg| = \\Bigg|\\begin{vmatrix}<br/>\\frac{1}{2} &amp; \\frac{1}{2} \\\\ <br/>\\frac{1}{2} &amp; -\\frac{1}{2}<br/>\\end{vmatrix}\\Bigg| = \\bigg|-\\frac{1}{4} - \\frac{1}{4}\\bigg| = \\bigg|-\\frac{1}{2}\\bigg| = \\frac{1}{2}$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(1 .. 5#0.25)", "description": "<p>Upper range for x</p>", "templateType": "randrange", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5 .. 5#0.25)", "description": "", "templateType": "randrange", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "a+x", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "a<b", "maxRuns": "1500"}, "ungrouped_variables": ["x", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "// Reveal answers, score and advice\nthis.display.revealAnswer();\nthis.display.showScore();\nNumbas.controls.getAdvice();", "order": "before"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$|J| = \\big|-\\frac{1}{2}\\big| = \\frac{1}{2}$", "$|J| = |u+v| = u+v$ as $v&gt; \\var{a}$ and $u&gt;\\var{a}$", "$|J| = \\big|-\\frac{1}{4}\\big| = \\frac{1}{4}$"], "matrix": ["1", 0, 0], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "adam bretherton", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18177/"}]}]}], "contributors": [{"name": "adam bretherton", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18177/"}]}