Show pageOld revisionsBacklinksBack to top This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. === Donnerstag 4. Mai 2017 === **Achtung**: Diese Aufgabe wird bei jedem Neuladen der Seite zufällig neu generiert. <HTML> <div id="exos"></div> </HTML> Bestimmen Sie die Koeffizienten $a$, $b$, $c$ der obigen quadratischen Gleichung, wenn nach - $x$ - $y$ - $z$ aufgelöst wird. <JS> function contFrac(v) { var eps = 0.00001; var res=[Math.floor(v)]; v = v-res[0]; for (var i=0; i<5; i++) { if (v<eps || v>1-eps) { if (v>1-eps) res[res.length-1]++; return res; } v = 1/v; res[res.length] = Math.floor(v); v = v-res[res.length-1]; } return res; } function cFtoTex(cf) { var denom = 1; var num = 0; for (var i = cf.length-1; i>=0 ; i--) { num = cf[i]*denom+num; var tmp = num; num = denom; denom = tmp; } return "\\frac{"+denom+"}{"+num+"}" } function getFraction(v) { var cf = contFrac(Math.abs(v)); if (cf.length==1) return v; return (v < 0 ? "-" : "") + cFtoTex(cf); } function coeff(c,v, op) { if (c==0) return ""; if (v!="") { if (c==1) return (op ? "+" : "")+v; if (c==-1) return "-"+v; if (c>0) return (op ? "+" : "")+getFraction(c)+v; return ""+getFraction(c)+v; } else { return ((op && (c>0)) ? "+" : "")+getFraction(c); } } function generate(jQuery, num) { var randi = function(m) { return Math.floor(Math.random()*m); }; var randCoeff = function(exps) { if (exps[0]==0) { exps[0]=randi(10)-4; if (exps[0]<1) { exps[0]-=1; } } for (var i=1; i<exps.length; i++) { if (exps[i]==-1) { exps[i] = randi(3); } } return exps; }; var randExp = function() { var res = []; for (var i=1; i<3; i++) { res.push(randCoeff([0,i,-1,-1])); res.push(randCoeff([0,-1,i,-1])); res.push(randCoeff([0,-1,-1,i])); } for (var i=0; i<res.length; i++) { for (var j=i+1; j<res.length; j++) { if (res[i][1]==res[j][1] && res[i][2]==res[j][2] && res[i][3]==res[j][3]) { res[i][0] += res[j][0]; res.splice(j,1); j-=1; if (res[i][0]==0) { res.splice(i,1); i-=1; j=res.length; } } } } return res; } var pow = function(base, exp) { if (exp==0) { return ""; } else if (exp==1) { return base; } return base+"^{"+exp+"}"; } for (var i=0; i<num; i++) { var e = randExp(); var ex = ""; for (var j=0; j<e.length; j++) { var name = pow("x", e[j][1])+pow("y", e[j][2])+pow("z", e[j][3]); ex += coeff(e[j][0], name, j!=0); } ex = "$$"+ex+"=0$$"; jQuery("#exos").append(ex); sol = "" for (var v=1; v<4; v++) { sol += "Nach $"+["","x", "y", "z"][v]+"$ auflösen: "; for (var exp=2; exp>=0; exp--) { var abc = ""; for (var j=0; j<e.length; j++) { if (e[j][v]==exp) { var name = ""; for (var k=1; k<=3; k++) { if (k!=v) { name += pow(["","x","y","z"][k],e[j][k]); } } abc += coeff(e[j][0], name, abc!=""); } } if (abc=="") { abc="0"; } sol += "$"+["c", "b", "a"][exp]+"="+abc+"$"+(exp!=0 ? ", " : ""); } sol += "<br>\n"; } jQuery("#sol").append(sol); } } jQuery(function() {generate(jQuery ? jQuery : $,1);}); </JS> <hidden Lösungen> <HTML> <div id="sol"></div> </HTML> </hidden> lehrkraefte/blc/miniaufgaben/kw19-2017.txt Last modified: 2020/08/09 15:16(external edit)