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User:5849206328x: Difference between revisions

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<asy>
<asy>
import slopefield;
size(216);


//size(288);
pair A,B,P,Q,X,Y;
A = (0,0); B = (25,0);
P = (4/25) * (-7,24); Q = B + (11/25) * (-7,24);
X = (4/5) * (3,4); Y = B - (11/5) * (3,4);


real e  = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
dot(A); dot(B);
real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286;
draw(circle(A,4)); draw(circle(B,11));
draw(P--Q); draw(X--Y);


// Label f;
label("$A$",A,W); label("$B$",B,E);
// f.p=fontsize(6);
label("$C$",P,NNW); label("$D$",Q,NNW);
//xaxis(0,5);
label("$E$",X,ENE); label("$F$",Y,WSW);
//yaxis(-2,3);
</asy>


//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); }


draw(graph(g,-150,150));
<asy>
size(216);


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


draw((-25,0)--(25,0)); draw((16,-25)--(16,25)); draw((0,0)--(0,16),dashed);
dot((0,3),blue); dot((3,6),blue); draw((0,3)--(3,6),blue);
dot((0,0)); draw((0,0)--A--(A + (-2.5,4.1)),EndArrow); dot(A);
label("$ct_1$",(0,3),W,blue); label("$ct_2'$",(3,6),NW,blue);
</asy>


label("$O$",(0,0),S); label("$l/2$",(4,0),S); label("$l/2$",(12,0),S); label("$l$",(0,8),W);
<asy>
label("$\mathbf{r}$",A/2,NW); label("$\theta$",(0.7,0),NE); label("$m$",A,NE);
size(216);


limits((-25,-25),(25,25),Crop);
pair[] nodes;
for (int i = 0; i < 10; ++i) {
  nodes.push(dir(36 * i));
  dot(dir(36 * i));
  label(string(i), 1.1 * dir(36 * i));
}
draw(circle(nodes[0] - 0.1, 0.1), Arrow);
draw(nodes[1] -- nodes[7], Arrow);
draw(nodes[2] -- nodes[4], Arrow);
draw(nodes[3] -- nodes[1], Arrow);
draw(nodes[4] -- nodes[8], Arrow);
draw(arc(nodes[5] + 0.1, 0.1, 180, 540), Arrow);
draw(nodes[6] -- nodes[2], Arrow);
draw(nodes[7] -- nodes[9], Arrow);
draw(nodes[8] -- nodes[6], Arrow);
draw(nodes[9] -- nodes[3], Arrow);
</asy>
 
<asy>
unitsize (1 cm);
 
pair A, B, C;
 
A = (3,2);
B = intersectionpoint(arc(A,4,200,340),C--(10,0));
C = (0,0);
 
draw(B--A--C--(8,0), Arrow(6));
draw(arc(A,4,200,340), dashed);
 
label("$A$", A, N);
label("$B$", B, SE);
label("$C$", C, NNW);
label("$b$", (A + C)/2, NW);
label("$c$", (A + B)/2, NE);
label("$\theta$", (1,0.3));
</asy>
</asy>

Latest revision as of 16:54, 1 July 2025

[asy] size(216); pair A,B,P,Q,X,Y; A = (0,0); B = (25,0); P = (4/25) * (-7,24); Q = B + (11/25) * (-7,24); X = (4/5) * (3,4); Y = B - (11/5) * (3,4); dot(A); dot(B); draw(circle(A,4)); draw(circle(B,11)); draw(P--Q); draw(X--Y); label("$A$",A,W); label("$B$",B,E); label("$C$",P,NNW); label("$D$",Q,NNW); label("$E$",X,ENE); label("$F$",Y,WSW); [/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]

[asy] size(216); pair[] nodes; for (int i = 0; i < 10; ++i) { nodes.push(dir(36 * i)); dot(dir(36 * i)); label(string(i), 1.1 * dir(36 * i)); } draw(circle(nodes[0] - 0.1, 0.1), Arrow); draw(nodes[1] -- nodes[7], Arrow); draw(nodes[2] -- nodes[4], Arrow); draw(nodes[3] -- nodes[1], Arrow); draw(nodes[4] -- nodes[8], Arrow); draw(arc(nodes[5] + 0.1, 0.1, 180, 540), Arrow); draw(nodes[6] -- nodes[2], Arrow); draw(nodes[7] -- nodes[9], Arrow); draw(nodes[8] -- nodes[6], Arrow); draw(nodes[9] -- nodes[3], Arrow); [/asy]

[asy] unitsize (1 cm); pair A, B, C; A = (3,2); B = intersectionpoint(arc(A,4,200,340),C--(10,0)); C = (0,0); draw(B--A--C--(8,0), Arrow(6)); draw(arc(A,4,200,340), dashed); label("$A$", A, N); label("$B$", B, SE); label("$C$", C, NNW); label("$b$", (A + C)/2, NW); label("$c$", (A + B)/2, NE); label("$\theta$", (1,0.3)); [/asy]

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