// Numbas version: finer_feedback_settings {"name": "Modelos a Escala (Determinar tama\u00f1os de figuras reales desde una figura a escala)", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Recordemos como determinar una raz\u00f3n de homotecia", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/366201593_la_piramide_de_keops.jpg", "/srv/numbas/media/question-resources/366201593_la_piramide_de_keops.jpg"], ["question-resources/Screenshot_1_6ZNS0i4.png", "/srv/numbas/media/question-resources/Screenshot_1_6ZNS0i4.png"], ["question-resources/Screenshot_2_yYPCsZc.png", "/srv/numbas/media/question-resources/Screenshot_2_yYPCsZc.png"], ["question-resources/Screenshot_3_ia8vlqQ.png", "/srv/numbas/media/question-resources/Screenshot_3_ia8vlqQ.png"], ["question-resources/Screenshot_4.png", "/srv/numbas/media/question-resources/Screenshot_4.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Emilio Gonz\u00e1lez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11803/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "
Recordemos lo siguiente antes de avanzar:
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\n\nRespuesta: [[0]]
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\n\nRespuesta [[0]]
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\n\nRespuesta:[[0]]
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\n\nRespuesta: [[0]]
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\n\nRespuesta: [[0]]
\n", "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "R4", "marks": 0, "scripts": {}, "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": ["2", "3", "$\\frac{1}{2}$", "$\\frac{1}{3}$"], "matrix": [0, "1", 0, 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Aprendamos a determinar lados de una figura real por medio de un modelo a escala", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/366201593_la_piramide_de_keops_VBCohhY.jpg", "/srv/numbas/media/question-resources/366201593_la_piramide_de_keops_VBCohhY.jpg"], ["question-resources/Tour_eiffel_at_sunrise_from_the_trocadero_1.jpg", "/srv/numbas/media/question-resources/Tour_eiffel_at_sunrise_from_the_trocadero_1.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Emilio Gonz\u00e1lez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11803/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "La torre Eiffel\u200b (tour Eiffel, en francés), inicialmente llamada tour de ___________ metros , es una estructura de hierro pudelado diseñada por los ingenieros Maurice Koechlin y Émile Nouguier, dotada de su aspecto definitivo por el arquitecto Stephen Sauvestre y construida por el ingeniero francés Alexandre Gustave Eiffel y sus colaboradores para la Exposición Universal de 1889 en París.
\nSituada en el extremo del Campo de Marte a la orilla del río Sena, este monumento parisino, símbolo de Francia y de su capital, es la estructura más alta de la ciudad y el monumento que cobra entrada más visitado del mundo, con 7,1 millones de turistas cada año.\u200b Con una altura de _________ metros, prolongada más tarde con una antena hasta los 324 metros, la torre Eiffel fue la estructura más elevada del mundo durante 41 años.
\n\nLo anterior, lo podemos modelar por medio de Geogebra, de la siguiente manera:
\n{geogebra_applet('https://www.geogebra.org/calculator/c6zagpty')}
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\nObservación: La incógnita a buscar será $x$ en el problema.
\n$\\frac{\\text{Base de la Torre Eiffel}}{\\text{Base de la foto}}$$=$$\\frac{\\text{Altura de la Torre Eiffel}}{\\text{Altura de la foto}}$
\n[[0]] [[3]]
\n------------ $=$ ------------
\n[[2]] [[1]]
\nPero la base de la torre esta en metros y las medidas de la foto en centímetros, pero recordemos que 1 mt = [[5]] cm, obteniendo la ecuación:
\n[[6]] [[3]]
\n------------ $=$ ------------
\n[[2]] [[1]]
\n\nPara despejar $x$ podemos ver que la Altura del Bastón divide a $x$, entonces pasaría a multiplicar la longitud de la sombra de Keops, obteniendo la expresión:
\n[[6]] $\\cdot$ [[1]]
\n---------------------------- $=$ [[3]]
\n[[2]]
\n\nObteniendo que la altura de Keops es igual a: [[4]] metros
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"extensions": [], "custom_part_types": [], "resources": [["question-resources/Screenshot_6_ZpVxASD.png", "/srv/numbas/media/question-resources/Screenshot_6_ZpVxASD.png"], ["question-resources/Screenshot_7_IHnBGv3.png", "/srv/numbas/media/question-resources/Screenshot_7_IHnBGv3.png"], ["question-resources/Screenshot_8_KVG7CFN.png", "/srv/numbas/media/question-resources/Screenshot_8_KVG7CFN.png"], ["question-resources/Screenshot_9_lzLvsRP.png", "/srv/numbas/media/question-resources/Screenshot_9_lzLvsRP.png"], ["question-resources/Screenshot_10_zLOEdN4.png", "/srv/numbas/media/question-resources/Screenshot_10_zLOEdN4.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Emilio Gonz\u00e1lez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11803/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "Ya hemos analizado dos situaciones en la que debemos determinar la longitud de un objeto real, con respecto a las medidas de un objeto con medidas a escala, usando las propiedades de las semejanzas y de proporcionalidad de las homotecias. Ahora, debes hacer lo mismo con los siguientes ejercicios que debes realizar en tu grupo inicial de trabajo, recuerda informar a tu profesor de las dudas que tengas, en caso de que algún problema en Numbas te señale un error. En caso de acierto también informa a tu profesor de tus logros. Éxito.
\n", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Ejercicio (1)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Una persona colecciona figuras de animación japonesa. En particular su última adquisición es una figura a escala de Goku, cuyas dimensiones se observan en la figura adjunta junto a las dimensiones del cuerpo real del personaje de anime. De acuerdo a lo anterior ¿Cuál es la estatura de Goku?
\n\nRespuesta: La estatura de Goku es [[0]] cm.
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\nRespuesta: El alto del celular en el letrero es de [[0]] cm
\n", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "alto letrero", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "165", "maxValue": "165", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["si-fr", "eu", "plain-eu"], "correctAnswerStyle": "si-fr"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Ejercicio (3)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Danilo tiene un tren de juguete cuyo tamaño es a escala con respecto a un tren real. Si el largo y alto del tren de juguete es de 10 y 75 cm rectivamente y el alto real del tren modelado es de 1.5 mt ¿Cuál es el largo del tren real?
\nRespuesta: El largo del tren real es de [[0]] mt.
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\n", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Preguntas del Control", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "En la siguiente imagen se observa un letrero de la ciudad de Bulnes, que se ubica a 85 km de Concepción. Se sabe que todas las letras tienen el mismo ancho y alto y en el diseño a escala, creado en el formato Canvas, las letras tienen un ancho y alto de 5 y 20 cm respectivamente. Si el largo real de cada letra es de 160 cm.
\n\n(1) ¿Cuál es el ancho real de cada letra?
\nRespuesta: El ancho real de cada letra es [[0]] cm
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