Art of Problem Solving

User:5849206328x: Difference between revisions

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//real f(real x) { return 3 * (-1/x + 1/(2*x^2)); }
//real f(real x) { return 3 * (-1/x + 1/(2*x^2)); }
pair g(real t) { return 16/(1 + cos(pi * t/180)) * dir(t); }
pair g(real t) { return 16/(5/3 * cos(pi * t/180) - 1) * dir(t); }


draw(graph(g,-150,150));
draw(graph(g,-40,45),MidArrow);


pair A = (5, 4 * sqrt(6));
pair A = (48/5,36/5);


draw((-25,0)--(25,0)); draw((16,-25)--(16,25)); draw((0,0)--(0,16),dashed);
draw((-15,-40)--(45,40)); draw((-15,40)--(45,-40));
dot((0,0)); draw((0,0)--A--(A + (-2.5,4.1)),EndArrow); dot(A);
dot((0,0)); draw(A--(0,0)--(15,0),dashed); draw(rightanglemark((0,0),A,(15,0),20));


label("$O$",(0,0),S); label("$l/2$",(4,0),S); label("$l/2$",(12,0),S); label("$l$",(0,8),W);
label("$O$",(0,0),S); label("$b$",A/2,NW); label("$2\alpha$",(16,0),E); label("$\beta$",(15,1),N); label("$ea$",(7,0),S);
label("$\mathbf{r}$",A/2,NW); label("$\theta$",(0.7,0),NE); label("$m$",A,NE);


limits((-25,-25),(25,25),Crop);
limits((-25,-25),(50,25),Crop);
 
// e = 5/3, l = 16, a = 9, b = 12
</asy>
</asy>

Revision as of 20:42, 20 July 2015

[asy] import slopefield;  //size(288);  real e  = 2.718281828459045235360287471352662497757247093699959574966967627724076630353; real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286;  // Label f; // f.p=fontsize(6); //xaxis(0,5); //yaxis(-2,3);  //real f(real x) { return 3 * (-1/x + 1/(2*x^2)); } pair g(real t) { return 16/(5/3 * cos(pi * t/180) - 1) * dir(t); }  draw(graph(g,-40,45),MidArrow);  pair A = (48/5,36/5);  draw((-15,-40)--(45,40)); draw((-15,40)--(45,-40)); dot((0,0)); draw(A--(0,0)--(15,0),dashed); draw(rightanglemark((0,0),A,(15,0),20));  label("$O$",(0,0),S); label("$b$",A/2,NW); label("$2\alpha$",(16,0),E); label("$\beta$",(15,1),N); label("$ea$",(7,0),S);  limits((-25,-25),(50,25),Crop);  // e = 5/3, l = 16, a = 9, b = 12 [/asy]