Difference between revisions of "User:5849206328x"

Latest revision as of 16:35, 1 June 2023

$[asy] size(216); draw((0,10)--(0,0)--(10,0)); draw((5,10)--(0,0)--(10,5)); label("$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$", (1,0.3)); [/asy]$

Page

Toolbox

Search

Difference between revisions of "User:5849206328x"

Latest revision as of 16:35, 1 June 2023

@@ Line 1: / Line 1: @@
 <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);
+</asy>
-// Label f;
+<asy>
-// f.p=fontsize(6);
+size(216);
-//xaxis(0,5);
-//yaxis(-2,3);
-//real f(real x) { return 3 * (-1/x + 1/(2*x^2)); }
+pair[] nodes;
-pair g(real t) { return 16/(1 + 5/3 * cos(pi * t/180)) * dir(t); }
+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>
-draw(graph(g,-105,105));
+<asy>
+unitsize (1 cm);
-pair A = (4, 8 * sqrt(10)/3);
+pair A, B, C;
-draw((-25,0)--(25,0)); draw((15,-25)--(15,25)); draw((0,0)--(0,16),dashed);
+A = (3,2);
-dot((0,0)); draw((0,0)--A--(A + (-1.7,4.1)),EndArrow); dot(A);
+B = intersectionpoint(arc(A,4,200,340),C--(10,0));
-draw((-15,-40)--(30,20),dashed); draw((-15,40)--(30,-20),dashed);
+C = (0,0);
-draw((6,0)--(6,12)); draw((0,0)--(48/5,-36/5),dashed); draw(rightanglemark((0,0),(48/5,-36/5),(15,0),20));
-label("$O$",(0,0),S); label("$ea$",(6,-1),SE); label("$a$",(10,0),N); label("$b$",(6,6),E); label("$l$",(0,8),W); label("$b$",(4,-3),SW);
+draw(B--A--C--(8,0), Arrow(6));
-label("$\mathbf{r}$",A/2,NW); label("$\theta$",(0.5,0),NE); label("$m$",A,NE);
+draw(arc(A,4,200,340), dashed);
-limits((-25,-25),(25,25),Crop);
+label("$A$", A, N);
+label("$B$", B, SE);
-// e = 5/3, l = 16, a = 9, b = 12
+label("$C$", C, NNW);
-// (x - 15)^2/81 - y^2/144 = 1, y^2/144 = 40/81, 40 * 144/81, sqrt(40) * 12/9 = 8sqrt(10)/3
+label("$b$", (A + C)/2, NW);
+label("$c$", (A + B)/2, NE);
+label("$\theta$", (1,0.3));
 </asy>