// Numbas version: finer_feedback_settings
{"name": "Achilles und die Schildkr\u00f6te", "extensions": [], "custom_part_types": [], "resources": [["question-resources/achilles-tortoise.svg", "/srv/numbas/media/question-resources/achilles-tortoise.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Achilles und die Schildkr\u00f6te", "tags": [], "metadata": {"description": "<p>Eine ganz olle Kamelle ; )</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Angenommen ein&nbsp;gesunder Achilles l&auml;uft {factor}-mal so schnell wie die Schildkr&ouml;te, der wir einen Vorsprung von {distance} Ellen geben.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/achilles-tortoise.svg\"/></p>\n<p>Die Schildkr&ouml;te&nbsp;lege zudem eine Elle in {speed} Sekunden zur&uuml;ck.</p>", "advice": "<p>Wir ermitteln zun&auml;chst die <strong>Entfernung</strong> &uuml;ber die (unendliche) geometrische Reihe:</p>\n<p>$\\var{distance}\\cdot\\displaystyle\\sum_{k=0}^\\infty\\frac{1}{\\var{factor}}^k=\\frac{\\var{distance}}{1-\\frac{1}{\\var{factor}}}=\\var[fractionNumbers]{meet}=\\var[fractionNumbers,mixedFractions]{meet}\\approx\\var{meeta}$</p>\n<p>Die <strong>Zeit</strong> l&auml;sst sich nun entweder dadurch ermitteln, dass man diese Entfernung durch die Geschwindigkeit von Achilles ($\\frac{\\var{factor}}{\\var{speed}}$ Ellen pro Sekunde) dividiert:</p>\n<p>$\\var[fractionNumbers]{meet}:\\frac{\\var{factor}}{\\var{speed}}=\\var[fractionNumbers]{meet}\\cdot\\frac{\\var{speed}}{\\var{factor}}=\\var[fractionNumbers]{meet*speed/factor}=\\var[fractionNumbers,mixedFractions]{meet*speed/factor}\\approx=\\var{timea}$</p>\n<p>oder erneut &uuml;ber eine geometrische Reihe:</p>\n<p>$\\var[fractionNumbers]{distance/speed}\\cdot\\displaystyle\\sum_{k=0}^\\infty\\frac{1}{\\var{factor}}^k=\\frac{\\var[fractionNumbers]{distance/speed}}{1-\\frac{1}{\\var{factor}}}=\\var[fractionNumbers]{time}=\\var[fractionNumbers,mixedFractions]{time}\\approx\\var{timea}$</p>", "rulesets": {}, "extensions": [], "variables": {"factor": {"name": "factor", "group": "Ungrouped variables", "definition": "random(2..6)*10", "description": "", "templateType": "anything"}, "distance": {"name": "distance", "group": "Ungrouped variables", "definition": "factor*10", "description": "", "templateType": "anything"}, "meet": {"name": "meet", "group": "Ungrouped variables", "definition": "distance/(1-1/factor)", "description": "", "templateType": "anything"}, "speed": {"name": "speed", "group": "Ungrouped variables", "definition": "10-random(3..7)", "description": "", "templateType": "anything"}, "time": {"name": "time", "group": "Ungrouped variables", "definition": "meet/((1/speed)*factor)", "description": "", "templateType": "anything"}, "meeta": {"name": "meeta", "group": "Ungrouped variables", "definition": "precround(meet,2)", "description": "", "templateType": "anything"}, "timea": {"name": "timea", "group": "Ungrouped variables", "definition": "precround(time,2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["factor", "distance", "meet", "speed", "time", "meeta", "timea"], "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>Achilles wird dann die Schildkr&ouml;te nach&nbsp;[[1]] Sekunden <br/>und einer Entfernung von&nbsp;[[0]] Ellen eingeholt haben.</p>\n<p><em>Beistrich (,) als Dezimaltrennzeichen verwenden!</em></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "meeting", "marks": "2.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{meeta}-0.005", "maxValue": "{meeta}+0.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, 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"penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}]}], "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}