lehrkraefte:blc:miniaufgaben:kw20-2017

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lehrkraefte:blc:miniaufgaben:kw20-2017 [2017/05/11 14:48] – created Ivo Blöchligerlehrkraefte:blc:miniaufgaben:kw20-2017 [2020/08/09 13:16] (current) – external edit 127.0.0.1
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 +==== 1. Mai 2017 bis 5. Mai 2017 ====
 +=== Freitag 5. Mai 2017 ===
 +Keine Miniaufgabe
 +
 +==== 8. Mai 2017 bis 12. Mai 2017 ====
 +=== Dienstag 9. Mai 2017 ===
 +<JS>
 +function generate(jQuery, idex, idsol) {
 +
 +    var randi = function(m) {
 + return Math.floor(Math.random()*m);
 +    };
 +
 +    var dispVec = function(a) {
 + return "\\begin{pmatrix}"+a[0]+"\\\\ "+a[1]+"\\\\ "+a[2]+" \\end{pmatrix}";
 +    };
 +    var dispPoint = function(a) {
 + return "\\left("+a[0]+", "+a[1]+", "+a[2]+" \\right)";
 +    };
 +    var vecDiff = function(a,b) {
 + return [a[0]-b[0], a[1]-b[1], a[2]-b[2]];
 +    };
 +    var vecSum = function(a,b) {
 + return [a[0]+b[0], a[1]+b[1], a[2]+b[2]];
 +    };
 +    var lensq = function(a) {
 + return a[0]*a[0]+a[1]*a[1]+a[2]*a[2];
 +    };
 +    var quadrFactor = function(w) {
 + var f = 1;
 + for (var i=2; i*i<=w; i++) {
 +     while (w % (i*i) == 0) {
 + w/=i*i;
 + f*=i;
 +     }
 + }
 + return f;
 +    }
 +    var normalform = function(w) {
 + var r = "\\sqrt{"+w+"}";
 + var f = quadrFactor(w);
 + w = w/(f*f);
 + if (f!=1) {
 +     if (w!=1) {
 + r+="="+f+"\\sqrt{"+w+"}";
 +     } else {
 + r+="="+f;
 +     }
 + }
 + return r;
 +    };
 +
 +    var nicePoints = function(maxComp) {
 + var vecs;
 + var pts;
 + for (var k=0; k<2000; k++) {
 +     vecs = [];
 +     for (var i=0; i<2; i++) {
 + vecs[i]=[];
 + for (var j=0; j<3; j++) {
 +     vecs[i].push((randi(maxComp)+1));
 + }
 + if (i==0) {
 +     vecs[i][0] = -vecs[i][0];
 + } else {
 +     vecs[i][1] = -vecs[i][1];
 +     vecs[i][2] = -vecs[i][2];
 + }
 +     }
 +     var pts = [[randi(maxComp)+1, -randi(maxComp)-1, randi(maxComp)+1]];
 +     pts.push(vecSum(pts[0],vecs[0]));
 +     pts.push(vecSum(pts[1],vecs[1]));
 +     var v3 = vecSum(vecs[0], vecs[1]);
 +     if (quadrFactor(lensq(vecs[0]))>1 &&
 + quadrFactor(lensq(vecs[1]))>1 &&
 + quadrFactor(lensq(v3))>1 &&
 + v3[0]*v3[1]*v3[2]!=0 &&
 + quadrFactor(lensq(vecs[0]))*quadrFactor(lensq(vecs[0]))!=lensq(vecs[0]) &&
 + quadrFactor(lensq(vecs[1]))*quadrFactor(lensq(vecs[1]))!=lensq(vecs[1]) &&
 + quadrFactor(lensq(v3))*quadrFactor(lensq(v3))!=lensq(v3)) {
 +
 + return pts;
 +     }
 + }
 + console.log("Sorry...");
 + return pts;
 +    };
 +    
 +    var vecs=nicePoints(7);
 +    
 +    var pnames = ["A","B", "C"];
 +    var ex = "Gegeben sind drei Punkte: ";
 +    for (var i=0; i<3; i++) {
 + ex+="$"+pnames[i]+"="+dispPoint(vecs[i])+"$"+(i==2 ? "." : ", ");
 +    }
 +    ex += "<br>Berechnen Sie die Komponenten und die Länge (Wurzeln in Normalform) von<br>\
 +1. $\\vec{AB}$<br>\
 +2. $\\vec{AC}$<br>\
 +3. $\\vec{BC}$";
 +    jQuery(idex).append(ex);
 +    var sol = ""
 +    var n = 1;
 +    for (var i=0; i<2; i++) {
 + for (var j=i+1; j<3; j++) {
 +     var diff = vecDiff(vecs[j],vecs[i])
 +     sol+=n+". $"+dispVec(diff)+"$";
 +     sol+=", Länge $"+normalform(lensq(diff))+"$<br>";
 +     n++;
 + }
 +    }
 +    jQuery(idsol).append(sol);
 +}
 +jQuery = jQuery ? jQuery : $,1
 +jQuery(function() {generate(jQuery, "#exos","#sol");});
 +
 +</JS>
 +<HTML><div id="exos"></div></HTML>
 +<hidden Lösungen>
 +<HTML><div id="sol"></div></HTML>
 +</hidden>
 +=== Donnerstag 11. Mai 2017 ===
 +Vereinfachen Sie:
 +  - $$\left(x^{\frac{2}{5}}\right)^{-\frac{35}{6}}\cdot x^{\frac{7}{2}}$$
 +  - $$\left(x^{-\frac{4}{3}}\right)^{-\frac{23}{10}}: x^{\frac{2}{5}}$$
 +  - $$\left(x^{\frac{3}{2}}: x^{\frac{7}{3}}\right)^{-\frac{2}{5}}$$
 +
 +<hidden Lösungen>
 +  - $$x^{\frac{7}{6}}$$
 +  - $$x^{\frac{8}{3}}$$
 +  - $$x^{\frac{1}{3}}$$
 +</hidden>