import{E as A,ag as D,ke as H,h as c,T as C,az as d,w as e,f as w,m as y,aK as E,U as N,a as Q,s as v,bp as P,W,F as R,l as S}from"./index-ajJ0B2-K.js";import{d as m}from"./deprecatedFractions-MjvQvhWQ.js";import{p as U,a as k}from"./Personne-zmVSe1SX.js";const V=!0,B="mathLive",j="Use or find plan scales",J="10/08/2022",X="edb61",Y="5P13";function Z(){A.call(this),this.sup=4,this.titre=j,this.spacing=2,this.spacingCorr=2,this.nbQuestions=3,this.nouvelleVersion=function(){this.autoCorrection=[],this.listeQuestions=[],this.listeCorrections=[];const q=["each","This"];this.consigne="Solve",this.consigne+=this.nbQuestions===1?q[1]:q[0],this.consigne+=" problem, linked to a scale on a plan.";const G=D({max:3,defaut:4,melange:4,nbQuestions:this.nbQuestions,saisie:this.sup}),x=["father","brother","cousin","grandfather","neighbor"],L=["mother","sister","cousin","Grandmother","aunt","neighbor"],T=[];for(let a=0;a<x.length;a++)T.push([x[a],"her","of"]);for(let a=x.length;a<x.length+L.length;a++)T.push([L[[a-x.length]],"her","of the"]);const F=[[100],[200],[250],[1e3],[1500],[5e3],[1e5],[2e5],[25e4],[2e6],[25e5],[5e6]],I=["of the House","neighborhood","from the city","from the country"];for(let a=0;a<F.length;a++)F[a].push(I[H(a,3)]);const M=["mm","cm","dm","m","dam","hmm","km"];for(let a=0,s,i,t,p,o,n,u,f,b,$,l,g,r,h;a<this.nbQuestions;a++){switch(g="",r="",G[a]){case 1:$=c(T),l=c([U(),k()]),o=c(C(3,17,[10])),s=M[Math.floor(Math.log10(o))],n=o/Math.pow(10,d(Math.floor(Math.log10(o)))),t=c(F),u=o*t[0],i=M[Math.floor(d(Math.log10(u),6))],b=W(u/Math.pow(10,d(Math.floor(Math.log10(o)),6)),3),f=W(u/Math.pow(10,d(Math.floor(Math.log10(u)),6)),3),h=new R(o,u),g+=`On the ${t[1]} of ${$[1]} ${$[0]} plan, ${l} finds that $${e(n)}$ ${s} on the plan corresponds to $${e(f)}$ ${i} in reality.`,g+=" What is the scale of the plan?",r+=`$${e(n,2)}$ ${s} on the plan represents $${e(f,2)}$ ${i} in reality.`,r+=`To find the scale, we must first put these two distances in the same unit.<br>Let's choose the smaller of the two, the ${s}, and thus $${e(f,2)}$ ${i} = $${e(b)}$ ${s}.<br>`,r+=`$${e(n,2)}$ ${s} on the plan then represents $${e(b,2)}$ ${s} in reality and the scale of the plan is therefore $${m(n,b)}.$<br>`,r+="This answer is accepted but we are used to finding a fraction with integer numerator and denominator and if possible, one of which is equal to 1.<br>",r+=`Now, $${m(n,b)}=${m(e(n)+w(2)+y("\\div"+w(2)+e(n),"blue"),e(b,2)+w(2)+y("\\div"+w(2)+e(n,2),"blue"))}=${h.simplifie().texFraction}$.`,r+=`So the scale of the ${t[1]} ${$[2]} ${$[0]} of ${l} plan is: $${m(y(1),y(e(h.simplifie().den)))}$.<br>`,r+=`Note: This means that, on the ${t[1]} ${$[2]} ${$[0]} of ${l} plan, $1$ ${s} represents $${e(h.simplifie().den)}$ ${s} in reality, and therefore $1$ ${s} represents $${e(h.simplifie().den/Math.pow(10,d(Math.floor(Math.log10(h.simplifie().den)),6)),2)}$ ${i} in reality.`,this.interactif&&(g+=Q(this,a,"inline",{tailleExtensible:!0}),v(this,a,h,{formatInteractif:"fractionEqual"}));break;case 2:$=c(T),l=c([U(),k()]),o=c(C(3,47,[10,20,30,40])),n=o/Math.pow(10,d(Math.floor(Math.log10(o),6))),t=c(F),p=t[0]/Math.pow(10,d(Math.floor(Math.log10(t[0])),6-Math.floor(Math.log10(o)))),s=M[Math.floor(Math.log10(o))],u=o*t[0],i=M[Math.floor(d(Math.log10(t[0])+Math.floor(Math.log10(o)),6))],f=n*p,h=f,g+=`The ${t[1]} ${$[2]} ${$[0]} plan of ${l} has a scale of $${m(1,t[0])}$. ${l} measures, on this plane, a segment of $${e(n,2)}$ ${s}. What real distance does this segment correspond to?`,r+=`A scale of $${m(1,t[0])}$ means that $1$ ${s} on the plan represents $${e(t[0])}$ ${s} in reality, or $${e(p,2)}$ ${i}.<br>`,r+=`$${e(n)}$ ${s} being $${e(n)}$ times greater than $1$ ${s}, then the real distance is $${e(n)}$ times greater than $${e(p,2)}$ ${i}. ${w(10)}`,r+=`$${e(n)}\\times${e(p,2)}$ ${i} $= ${e(h,2)}$ ${i}.<br>`,r+=`The segment of $${e(n)}$ ${s} measured by ${l} on the ${t[1]} plane of ${$[1]} ${$[0]} therefore corresponds to a real distance of ${E(N(h))} ${E(i)}.`,this.interactif&&(g+=Q(this,a,"width25 inline units[lengths]"),v(this,a,new P(h,i),{formatInteractif:"units"}));break;case 3:$=c(T),l=c([U(),k()]),o=c(C(11,47,[10,20,30,40])),n=o,t=c(F),s=M[1],u=o*t[0],i=M[Math.floor(d(Math.log10(u),6))],p=t[0]/Math.pow(10,d(Math.floor(Math.log10(t[0])),5)),f=o*p,b=u,h=n,g+=`The ${t[1]} ${$[2]} ${$[0]} plan of ${l} has a scale of $${m(1,t[0])}$. ${l} draws, on this plan, a segment which represents $${e(f)}$ ${i} in reality. What is the length of the segment drawn on the plan by ${l}?`,r+=`A scale of $${m(1,t[0])}$ means that $1$ ${s} on the plan represents $${e(t[0])}$ ${s} in reality, or $${e(p,2)}$ ${i}.<br>`,r+=`Let's find out how much to multiply $${e(p,2)}$ ${i} by to get $${e(f,3)}$ ${i}. $${w(10)} ${e(f,2)}\\div${e(p,2)}=${e(n)}$<br>`,r+=`$${m(1,t[0])}=${m(1+y("\\times"+e(n),"blue"),e(t[0])+y("\\times"+e(n),"blue"))}=${m(n,b)}$ and therefore a distance of $${e(b)}$ ${s} ($${e(f)}$ ${i}) is represented by a segment of $${e(n)}$ ${s}.<br>`,r+=`The segment representing $${e(f)}$ ${i} in reality, drawn by ${l}, on the ${t[1]} plane of ${$[1]} ${$[0]}, measures ${E(N(h))} ${E(s)}.`,this.interactif&&(g+=Q(this,a,"width25 inline units[lengths]"),v(this,a,new P(h,s),{formatInteractif:"units"}));break}this.listeQuestions.push(g),this.listeCorrections.push(r)}S(this)},this.besoinFormulaireTexte=["Choice of problems",`Numbers separated by hyphens
1: Find a scale
2: Find a real distance
3: Find a length on the plane
4: Mixture`]}export{J as dateDePublication,Z as default,V as interactifReady,B as interactifType,Y as ref,j as titre,X as uuid};
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