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| | <asy> | | <asy> |
| − | import slopefield;
| + | size(216); |
| | | | |
| − | size(288);
| + | draw((0,10)--(0,0)--(10,0)); draw((5,10)--(0,0)--(10,5)); |
| | + | label("$ct$",(0,10),N); label("$x$",(10,0),E); |
| | + | label("$ct'$",(5,10),N); label("$x'$",(10,5),E); |
| | | | |
| − | real e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
| + | dot((0,3),blue); dot((3,6),blue); draw((0,3)--(3,6),blue); |
| − | real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286;
| + | label("$ct_1$",(0,3),W,blue); label("$ct_2'$",(3,6),NW,blue); |
| − | | |
| − | //xaxis(0,5);
| |
| − | //yaxis(-2,3);
| |
| − | | |
| − | //real f(real x) { return 3 * (-1/x + 1/(2*x^2)); }
| |
| − | pair g(real t) { return (20/13,48/13) + (1.5 * cos(pi * t/180), -1.5 * sin(pi * t/180)); }
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| − | | |
| − | fill((-12,5)--(-12,3)--(48/5,-5)--(12,-5)--cycle,palegrey); draw((-12,5)--(12,-5)--(2,-5),linewidth(2)); draw(circle((20/13,48/13),4));
| |
| − | dot((20/13,48/13)); draw(graph(g,0,90),EndArrow); draw((92/13,18/13)--(116/13,8/13),EndArrow);
| |
| − | label("$\alpha$",(9,-5),N); label("$\omega$",(20/13 + 3*sqrt(2)/4,48/13 - 3*sqrt(2)/4),SE); label("$v$",(116/13,8/13),ESE); | |
| − | | |
| − | //limits((-25,-25),(50,25),Crop);
| |
| − | </asy>
| |
| − | | |
| − | | |
| − | <!--
| |
| − | 3D graphs
| |
| − | <asy>
| |
| − | import graph3;
| |
| − | import three;
| |
| − | | |
| − | size(288);
| |
| − | | |
| − | real e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
| |
| − | real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286;
| |
| − | | |
| − | currentprojection=orthographic(2,-2,1);
| |
| − | xaxis3("$x$",0,5);
| |
| − | yaxis3("$y$",0,5);
| |
| − | zaxis3("$z$",0,5);
| |
| − | | |
| − | //real f(real x) { return 3 * (-1/x + 1/(2*x^2)); }
| |
| − | //triple g(real t) { return (2 * cos(pi * t/180), 2 * sin(pi * t/180), 2.5); }
| |
| − | //triple rot(real t) { return (0.2 * cos(pi * t/180), 0.2 * sin(pi * t/180), 4.5); }
| |
| − | | |
| − | draw(scale(3,2,2)*unitdisk,palegrey); draw(graph(rot,-180,93),EndArrow3);
| |
| − | draw((0,0,5)--(0,0,0)); draw((0,5,0)--(0,0,0)); draw((5,0,0)--(0,0,0));
| |
| | </asy> | | </asy> |
| − | -->
| |
![[asy] size(216); draw((0,10)--(0,0)--(10,0)); draw((5,10)--(0,0)--(10,5)); label("$ct$",(0,10),N); label("$x$",(10,0),E); label("$ct'$",(5,10),N); label("$x'$",(10,5),E); dot((0,3),blue); dot((3,6),blue); draw((0,3)--(3,6),blue); label("$ct_1$",(0,3),W,blue); label("$ct_2'$",(3,6),NW,blue); [/asy]](http://latex.artofproblemsolving.com/5/a/a/5aa32b4b39ea87966619720471695320b8335aa8.png)
