// Numbas version: finer_feedback_settings
{"name": "Golden Gate Bridge", "extensions": [], "custom_part_types": [], "resources": [["question-resources/golden-gate-bridge.png", "/srv/numbas/media/question-resources/golden-gate-bridge.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Golden Gate Bridge", "tags": [], "metadata": {"description": "<p>An application of quadratic functions based on the Golden Gate Bridge in San Francisco, USA. Student is given an equation representing the suspension cable of the bridge and asked to find the width between the towers and the minimum height of the cable above the roadway. Requires and understanding of the quadratic function and where and how to apply correct formulae.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>To find the distance between the towers first note that at \\(x=0\\) (the location of the first tower) the height of the cable is \\(\\frac{3}{8000}\\times 0^2-\\frac{9}{20}\\times 0+155=155\\) m. To find the location of the other tower we need to find the other \\(x\\) value with \\(y=155\\), that is we need to solve <br/>\\[155=\\frac{3}{8000}x^2-\\frac{9}{20}x+155<br/>\\]<br/>or equivalently<br/>\\[\\frac{3}{8000}x^2-\\frac{9}{20}x=0.<br/>\\]<br/>This can be done by factorising the above equation to<br/>\\[\\frac{3}{8000}x\\left(x-1200\\right)=0<br/>\\]<br/>and reading the roots as \\(x=0\\) and \\(x=1200\\). Hence the second tower is at a distance of \\(1200\\) m from the first tower.</p>\n<p></p>\n<p>We need to find the minimum value of the quadratic equation \\(y=\\frac{3}{8000}x^2-\\frac{9}{20}x+155\\). (The value will be a minimum since \\(a\\), the coefficient of \\(x^2\\) is greater than \\(0\\))<br/>The minimum height will occur at \\(\\displaystyle{t=\\frac{-b}{2a}}\\), that is \\(\\displaystyle{t=\\frac{9\\times 8000}{20\\times 2\\times 3}= 600}\\) m.<br/>The minimum height is <br/>\\begin{align}h&amp;=c-\\frac{b^2}{4a}\\\\&amp;=155-\\frac{\\left(9/20\\right)^2}{12/8000}\\\\&amp;= 20 \\quad\\text{metres}\\end{align}<br/>(This value could also be found by substituting the value of \\(x\\) found above into the function.)</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The Golden Gate bridge in San Francisco is a large suspension bridge. The cable joining the two towers of the bridge (see illustration) can be modeled by the equation \\[y=\\frac{3}{8000}x^2-\\frac{9}{20}x+155\\] where \\(y\\) is the height of the cable above the bridge deck in metres and \\(x\\) is the horizontal distance from the left tower in metres.</p>\n<p><img src=\"resources/question-resources/golden-gate-bridge.png\"/></p>\n<p>What is the distance between the towers? (Hint: both towers are the same height. The left hand tower is at \\(x=0\\)) <strong>Show full working on your handwritten working.</strong></p>\n<p>Width between towers = [[0]] metres.</p>\n<p>What is the minimum height of the cable above the deck of the bridge? <strong>Show full working on your handwritten notes.</strong></p>\n<p>Minimum height of cable above deck = [[1]] metres.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "width", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1200", "maxValue": "1200", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Height", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "20", "maxValue": "20", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}