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{"version":3,"file":"3A14-0-JrFwACbC.js","sources":["../../src/exercices/3e/3A14-0.js"],"sourcesContent":["import { point } from '../../lib/2d/points.js'\nimport { polygone } from '../../lib/2d/polygones.js'\nimport { segment } from '../../lib/2d/segmentsVecteurs.js'\nimport { texteParPosition } from '../../lib/2d/textes.js'\nimport { choice } from '../../lib/outils/arrayOutils'\nimport { createList } from '../../lib/format/lists.ts'\nimport { egalOuApprox } from '../../lib/outils/ecritures'\nimport { numAlpha } from '../../lib/outils/outilString.js'\nimport { decompositionFacteursPremiers, premierAvec } from '../../lib/outils/primalite.js'\nimport { texteGras } from '../../lib/format/style'\nimport { texNombre, stringNombre } from '../../lib/outils/texNombre.js'\nimport Exercice from '../Exercice.js'\nimport { context } from '../../modules/context.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { mathalea2d, fixeBordures, colorToLatexOrHTML } from '../../modules/2dGeneralites.js'\nimport { pyramide3d, pave3d, point3d, polygone3d } from '../../modules/3d.js'\n\nexport const titre = 'Arithmetic & volumes'\n\n/**\n * diviseurs communs, calcul de volume\n * @author Jean-Claude Lhote\n * Référence dnb06_2022_5\n */\nexport const uuid = '2e22a'\nexport const ref = '3A14-0'\nexport default function DesChocolatsDansDesBoites () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.titre = titre\n this.introduction = 'According to Brevet des Collèges - Foreign centers - June 2022'\n this.consigne = ''\n context.isHtml ? this.spacing = 1 : this.spacing = 2\n context.isHtml ? this.spacingCorr = 2 : this.spacingCorr = 2\n this.nbQuestions = 1\n this.nbQuestionsModifiable = false\n this.nbCols = 1\n this.nbColsCorr = 1\n\n this.nouvelleVersion = function () {\n context.anglePerspective = 50\n const premier1 = choice([2, 3, 5, 7])\n const premier2 = choice([2, 3, 5, 7])\n const nbBoites = premier1 * premier2\n const nbTruffesCafeParBoite = randint(5, 12)\n const nbTruffesCocoParBoite = premierAvec(nbTruffesCafeParBoite)\n const nbTruffesParBoite = nbTruffesCocoParBoite + nbTruffesCafeParBoite\n const nbTruffesCafe = nbBoites * nbTruffesCafeParBoite\n const nbTruffesCoco = nbBoites * nbTruffesCocoParBoite\n const nbTruffes = nbTruffesCafe + nbTruffesCoco\n let texte = 'To celebrate the 25th anniversary of his shop, a chocolatier wants to offer the first customers of the day a box containing chocolate truffles.<br><br>'\n texte += `${texteGras('1.')} He made $${nbTruffes}$ truffles: $${nbTruffesCafe}$ coffee flavored truffles and $${nbTruffesCoco}$ coconut coated truffles. He wants to make these boxes so that:`\n\n if (context.isHtml) {\n texte += createList({\n items: ['The number of coffee flavored truffles is the same in each box;',\n 'The number of coconut-coated truffles is the same in each box;',\n 'All truffles are used.'],\n style: 'arrows',\n classOptions: 'style=\"color: red; backgroundColor: red\"'\n }).outerHTML\n } else {\n texte += createList({\n items: ['The number of coffee flavored truffles is the same in each box;',\n 'The number of coconut-coated truffles is the same in each box;',\n 'All truffles are used.'],\n style: 'arrows',\n classOptions: 'style=\"color: red; backgroundColor: red\"'\n })\n }\n\n if (context.isHtml) {\n texte += `${numAlpha(0)} Decompose $${nbTruffesCafe}$ and $${nbTruffesCoco}$ into product of prime factors.<br>`\n texte += `${numAlpha(1)} Deduce the list of divisors common to $${nbTruffesCafe}$ and $${nbTruffesCoco}$.<br>`\n texte += `${numAlpha(2)} What maximum number of boxes can he make?<br>`\n texte += `${numAlpha(3)} In this case, how many truffles of each type will there be in each box?<br><br>`\n } else {\n texte += `${numAlpha(0)} Decompose $${nbTruffesCafe}$ and $${nbTruffesCoco}$ into product of prime factors.<br>`\n texte += `${numAlpha(1)} Deduce the list of divisors common to $${nbTruffesCafe}$ and $${nbTruffesCoco}$.<br>`\n texte += `${numAlpha(2)} What maximum number of boxes can he make?<br>`\n texte += `${numAlpha(3)} In this case, how many truffles of each type will there be in each box?<br><br>`\n }\n const largeurCadre = 30\n const hauteurCadre = 20\n const cadrePrincipal = polygone([point(0, 0), point(largeurCadre, 0), point(largeurCadre, hauteurCadre), point(0, hauteurCadre)])\n const ligne1 = segment(point(0, hauteurCadre / 3), point(largeurCadre, hauteurCadre / 3))\n const ligne2 = segment(point(largeurCadre / 2, hauteurCadre), point(largeurCadre / 2, 0))\n const text1 = texteParPosition('type A', largeurCadre / 4 - 1, hauteurCadre - 1, 'medium', 'black', 2)\n const text2 = texteParPosition('type B', 3 * largeurCadre / 4 - 1, hauteurCadre - 1, 'medium', 'black', 2)\n text1.epaisseur = 4\n text1.contour = true\n text1.couleurDeRemplissage = colorToLatexOrHTML('black')\n text2.epaisseur = 4\n text2.contour = true\n text2.couleurDeRemplissage = colorToLatexOrHTML('black')\n const sommetPyramide = point3d(largeurCadre / 4 - 2, 4, hauteurCadre - 4)\n const base = polygone3d([\n point3d(largeurCadre / 4 - 6, 0, hauteurCadre / 3 + 1),\n point3d(largeurCadre / 4 + 2, 0, hauteurCadre / 3 + 1),\n point3d(largeurCadre / 4 + 2, 8, hauteurCadre / 3 + 1),\n point3d(largeurCadre / 4 - 6, 8, hauteurCadre / 3 + 1)\n ])\n const pyramide = pyramide3d(base, sommetPyramide)\n const sommetsPave = [\n point3d(3 * largeurCadre / 4 - 5, 0, hauteurCadre / 3 + 2),\n point3d(3 * largeurCadre / 4 + 3, 0, hauteurCadre / 3 + 2),\n point3d(3 * largeurCadre / 4 - 5, 0, hauteurCadre - 5),\n point3d(3 * largeurCadre / 4 - 5, 5, hauteurCadre / 3 + 2)\n ]\n const pave = pave3d(...sommetsPave)\n const diametreTruffes = randint(10, 15) / 10\n const volumeTotalTruffe = nbTruffesParBoite * 4 * Math.PI * (diametreTruffes / 2) ** 3 / 3\n const volumeCible = 1.7 * volumeTotalTruffe\n const volumeTropImportant = 2.3 * volumeTotalTruffe\n let basePyramide, hauteurPave\n const longueurPave = randint(4, 5)\n const largeurPave = randint(2, 3) - 0.5\n const hauteurPyramide = randint(4, 6)\n const paveQuiConvient = Math.random() < 0.5\n if (paveQuiConvient) {\n hauteurPave = Number((volumeCible / longueurPave / largeurPave).toFixed(1))\n basePyramide = Number(Math.sqrt(3 * volumeTropImportant / hauteurPyramide).toFixed(1))\n } else {\n hauteurPave = Math.round(volumeTropImportant / longueurPave / largeurPave)\n basePyramide = Number(Math.sqrt(3 * volumeCible / hauteurPyramide).toFixed(1))\n }\n const volumePave = largeurPave * longueurPave * hauteurPave\n const volumePyramide = (hauteurPyramide * basePyramide ** 2) / 3\n const textA1 = texteParPosition('Pyramid with square base', largeurCadre / 4, hauteurCadre / 3 - 1, 'medium', 'black', 1.5)\n const textA2 = texteParPosition(`side ${stringNombre(basePyramide, 1).replace(',', '.')} cm`, largeurCadre / 4, hauteurCadre / 3 - 2, 'medium', 'black', 1.5)\n const textA3 = texteParPosition(`and height ${stringNombre(hauteurPyramide, 1).replace(',', '.')} cm`, largeurCadre / 4, hauteurCadre / 3 - 3, 'medium', 'black', 1.5)\n const textB1 = texteParPosition('Right pad', 3 * largeurCadre / 4, hauteurCadre / 3 - 1, 'medium', 'black', 1.5)\n const textB2 = texteParPosition(`length ${longueurPave} cm`, 3 * largeurCadre / 4, hauteurCadre / 3 - 2, 'medium', 'black', 1.5)\n const textB3 = texteParPosition(`width ${stringNombre(largeurPave, 1).replace(',', '.')} cm`, 3 * largeurCadre / 4, hauteurCadre / 3 - 3, 'medium', 'black', 1.5)\n const textB4 = texteParPosition(`and height ${stringNombre(hauteurPave, 1).replace(',', '.')} cm`, 3 * largeurCadre / 4, hauteurCadre / 3 - 4, 'medium', 'black', 1.5)\n const objets = [cadrePrincipal, ligne1, ligne2, text1, text2, pyramide.c2d, pave.c2d, textA1, textA2, textA3, textB1, textB2, textB3, textB4]\n texte += `${texteGras('2.')} The chocolatier wants to make boxes containing $${nbTruffesParBoite}$ truffles. For this, he has the choice between two types of boxes which can contain the $${nbTruffesParBoite}$ truffles, and whose characteristics are given below:`\n texte += '<br>' + mathalea2d(Object.assign({ scale: 0.5 }, fixeBordures(objets)), objets)\n texte += `In this question, each of the $${nbTruffesParBoite}$ truffles is compared to a ball of diameter $${texNombre(diametreTruffes, 1)}$ cm.<br>`\n texte += 'Inside a box, so that the truffles are not damaged during transport, the volume occupied by the truffles must be greater than the volume not occupied by the truffles.<br>'\n texte += 'What type(s) of box should the chocolatier choose for this condition to be met?'\n this.listeQuestions[0] = texte\n let texteCorr = mathalea2d(Object.assign({ scale: 0.5 }, fixeBordures(objets)), objets)\n texteCorr += `${texteGras('1.')} He made $${nbTruffes}$ truffles: $${nbTruffesCafe}$ coffee flavored truffles and $${nbTruffesCoco}$ coconut coated truffles. He wants to make these boxes so that:`\n // @todo replace this call with a new function allowing you to make bulleted lists depending on the context.\n if (context.isHtml) {\n texteCorr += createList({\n items: ['The number of coffee flavored truffles is the same in each box;',\n 'The number of coconut-coated truffles is the same in each box;',\n 'All truffles are used.'],\n style: 'arrows',\n classOptions: 'style=\"backGroundColor: red\";'\n }).outerHTML\n } else {\n texteCorr += createList({\n items: ['The number of coffee flavored truffles is the same in each box;',\n 'The number of coconut-coated truffles is the same in each box;',\n 'All truffles are used.'],\n style: 'arrows',\n classOptions: 'style=\"backGroundColor: red\";'\n })\n }\n if (context.isHtml) {\n texteCorr += `${numAlpha(0)} $${nbTruffesCafe} = ${decompositionFacteursPremiers(nbTruffesCafe)}$ and $${nbTruffesCoco} = ${decompositionFacteursPremiers(nbTruffesCoco)}$.<br>`\n texteCorr += `${numAlpha(1)} We are looking for the greatest common divisor of $${nbTruffesCafe}$ and $${nbTruffesCoco}$.<br>`\n texteCorr += `In the prime factor decompositions of $${nbTruffesCafe}$ and $${nbTruffesCoco}$, we find $${decompositionFacteursPremiers(nbBoites)}$, so their greatest common divisor is $${decompositionFacteursPremiers(nbBoites)} = ${nbBoites}$.<br>`\n texteCorr += `${numAlpha(2)} The maximum number of boxes he can make is therefore $${nbBoites}$.<br>`\n texteCorr += `${numAlpha(3)} There will therefore be $\\\\dfrac{${nbTruffesCafe}}{${nbBoites}} = ${nbTruffesCafeParBoite}$ coffee truffles per box and $\\\\dfrac{${nbTruffesCoco}}{${nbBoites}} = ${nbTruffesCocoParBoite}$ coconut truffles per box.<br><br>`\n } else {\n texteCorr += `${numAlpha(0)} $${nbTruffesCafe} = ${decompositionFacteursPremiers(nbTruffesCafe)}$ and $${nbTruffesCoco} = ${decompositionFacteursPremiers(nbTruffesCoco)}$.<br>`\n texteCorr += `${numAlpha(1)} We are looking for the greatest common divisor of $${nbTruffesCafe}$ and $${nbTruffesCoco}$.<br>`\n texteCorr += `In the prime factor decompositions of $${nbTruffesCafe}$ and $${nbTruffesCoco}$, we find $${decompositionFacteursPremiers(nbBoites)}$, so their greatest common divisor is $${decompositionFacteursPremiers(nbBoites)} = ${nbBoites}$.<br>`\n texteCorr += `${numAlpha(2)} The maximum number of boxes he can make is therefore $${nbBoites}$.<br>`\n texteCorr += `${numAlpha(3)} There will therefore be $\\\\dfrac{${nbTruffesCafe}}{${nbBoites}} = ${nbTruffesCafeParBoite}$ coffee truffles per box and $\\\\dfrac{${nbTruffesCoco}}{${nbBoites}} = ${nbTruffesCocoParBoite}$ coconut truffles per box.<br><br>`\n }\n texteCorr += `${texteGras('2.')} In this question, each of the $${nbTruffesParBoite}$ truffles is compared to a ball of diameter $${texNombre(diametreTruffes, 1)}$ cm.<br>`\n texteCorr += 'Inside a box, so that the truffles are not damaged during transport, the volume occupied by the truffles must be greater than the volume not occupied by the truffles.<br>'\n const sousListe1 = {\n items: [`The pyramid has a square base of side $${texNombre(basePyramide, 1)}$ cm, the area of its base is therefore in cm$^2$: $${texNombre(basePyramide, 1)}\\\\times ${texNombre(basePyramide, 1)} = ${texNombre(basePyramide ** 2, 2)}$cm$^2$.`,\n `Its volume in cm$^3$ is: $\\\\dfrac{\\\\text{area of the base}\\\\times\\\\text{height}}{3}=\\\\dfrac{${texNombre(basePyramide ** 2, 2)}\\\\times ${hauteurPyramide}}{3 }${egalOuApprox(volumePyramide, 1)}${texNombre(volumePyramide, 1)}$ cm$^3$.`,\n `The volume of the pyramid is approximately $${texNombre(volumePyramide, 1)}$ cm$^3$; that of truffles is approximately $${texNombre(volumeTotalTruffe, 1)}$ cm$^3$.`,\n `The volume not occupied by the truffles is approximately $${texNombre(volumePyramide, 1)}-${texNombre(volumeTotalTruffe, 1)}$ or $${texNombre(volumePyramide - volumeTotalTruffe, 1)}$ cm$^3$`,\n paveQuiConvient\n ? 'it is greater than the volume of the truffles, so the pyramid-shaped box is not suitable.'\n : 'it is less than the volume of the truffles, so the pyramid-shaped box is suitable.'],\n style: 'arrows',\n introduction: 'The pyramid: '\n }\n const sousListe2 = {\n items: [`The right pad has a volume in cm$^3$ of: $${texNombre(largeurPave, 1)}\\\\times ${texNombre(longueurPave, 1)} \\\\times ${texNombre(hauteurPave, 1)} = ${texNombre(volumePave, 3)}$.`,\n `The volume of the right pad is $${texNombre(volumePave, 1)}$ cm$^3$; that of truffles is approximately $${texNombre(volumeTotalTruffe, 1)}$ cm$^3$.`,\n `The volume not occupied by the truffles is approximately $${texNombre(volumePave, 1)}-${texNombre(volumeTotalTruffe, 1)}$ or $${texNombre(volumePave - volumeTotalTruffe, 1)}$ cm$^3$.`,\n paveQuiConvient\n ? 'it is less than the volume of the truffles, so the box shaped like a straight block is suitable.'\n : 'it is greater than the volume of the truffles, so the box shaped like a straight block is not suitable.'],\n style: 'arrows',\n introduction: 'The right pad: '\n }\n const liste = createList({\n items: [`A truffle is likened to a ball of diameter $${texNombre(diametreTruffes, 1)}$ cm, therefore of radius $${texNombre(diametreTruffes / 2, 2)}$ cm and its volume in cm$^3$ is: $\\\\dfrac{4}{3}\\\\times\\\\pi\\\\ times${texNombre(diametreTruffes / 2, 2)}^3$.`,\n `The volume occupied by $${nbTruffesParBoite}$ truffles is therefore: $${nbTruffesParBoite}\\\\times\\\\dfrac{4}{3}\\\\times\\\\pi\\\\times${texNombre(diametreTruffes / 2, 2)}^3=\\\\dfrac{${texNombre(nbTruffesParBoite * 4 * (diametreTruffes / 2) ** 3, 4)}}{3}\\\\pi $ or approximately $${texNombre(nbTruffesParBoite * 4 * Math.PI * (diametreTruffes / 2) ** 3 / 3, 1)}$cm$^3$.`,\n sousListe1,\n sousListe2\n ],\n style: 'fleas'\n })\n texteCorr += context.isHtml ? liste.outerHTML : liste\n this.listeCorrections[0] = texteCorr\n listeQuestionsToContenu(this)\n 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