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- ...r centers is <math>84</math>, then the area of the third circle is <math>k\pi</math> for some integer <math>k</math>. Determine <math>k</math>. ...h>, so <math>r=14</math>. Thus the area of the circle is <math>\boxed{196}\pi</math>.795 bytes (129 words) - 10:22, 4 April 2012
- ...the circle. More generally, an arc is a portion of a smooth curve joining two points. ..., in particular, the [[circumference]] of a circle is given by <math>C = 2\pi</math>.1 KB (170 words) - 00:24, 16 December 2023
- ...t starts. The distance <math>x</math> can be expressed in the form <math>a\pi+b\sqrt{c},</math> where <math>a,</math> <math>b,</math> and <math>c</math> If it weren’t for the small tube, the larger tube would travel <math>144\pi</math>. Consider the distance from which the larger tube first contacts the2 KB (407 words) - 16:31, 29 February 2020
- ...ers can produce <math>300</math> widgets and <math>200</math> whoosits. In two hours, <math>60</math> workers can produce <math>240</math> widgets and <ma ...t starts. The distance <math>x</math> can be expressed in the form <math>a\pi+b\sqrt{c},</math> where <math>a,</math> <math>b,</math> and <math>c</math>9 KB (1,435 words) - 01:45, 6 December 2021
- The larger of two consecutive odd integers is three times the smaller. What is their sum? <math>\mathrm{(A)}\ 8.64\qquad \mathrm{(B)}\ 12\qquad \mathrm{(C)}\ 5\pi\qquad \mathrm{(D)}\ 17.28\qquad \mathrm{(E)}\ 18</math>11 KB (1,750 words) - 13:35, 15 April 2022
- ...i/2)--intersectionpoint(incircle(A,B,C),I--I+O-A)-abs(A-O)*expi(angle(A-O)-pi/2), q_a--q_a+O-A); ...i/2)--intersectionpoint(incircle(A,B,C),I--I+A-O)-abs(A-O)*expi(angle(A-O)-pi/2), O--A);7 KB (1,274 words) - 15:11, 31 August 2017
- ...] from a line [[perpendicular]] to both planes. Thus, a '''cylinder''' has two circular flat surfaces--think of a can of soup. Typically, to solve for sur * Surface [[area]]: <math>2 \pi r^2 + 2 \pi r h</math>827 bytes (135 words) - 18:13, 27 July 2023
- ...ent pulleys, that are connected with a strap. If the distances between any two pulley center points are <math>AB=3\,\mathrm{m}</math>, <math>AC=4\,\mathrm ...\qquad \mathrm{(B) \ } (12 + \pi)\,\mathrm{m}\qquad \mathrm{(C) \ } (12+ 4\pi)\,\mathrm{m}\qquad \mathrm{(D) \ } \left(12+\frac\pi5\right)\,\mathrm{m}\qq1 KB (175 words) - 22:21, 23 July 2020
- ...l prove the theorem for a cyclic hexagon, using directed angles mod <math>\pi </math>. '''Lemma.''' Let <math>\omega_1, \omega_2 </math> be two circles which intersect at <math>M, N </math>, let <math>AB </math> be a ch4 KB (712 words) - 21:57, 25 April 2020
- ...the [[equation]] <math>\sin{x}=\sin{(nx)}</math> on the interval <math>[0,\pi]</math>. What is <math>\sum_{n=2}^{2007} F(n)</math>? Notice that the solutions are basically reflections across <math>x = \frac{\pi}{2}</math>.4 KB (588 words) - 14:40, 23 August 2023
- pair A=(0,0),B=(-3^.5,-3),C=(3^.5,-3),D=13*expi(-2*pi/3),E1=11*expi(-pi/3),F=E1+D; Because the ratio of the area of two similar figures is the square of the ratio of the corresponding sides, <mat6 KB (1,033 words) - 02:36, 19 March 2022
- touches its two neighbors and the larger circle. What is the radius of the ...in the list <math>1, 2, 3, 4, 5, \dots, 10000</math> which contain exactly two consecutive <math>9</math>'s such as <math>993, 1992</math> and <math>9929<9 KB (1,449 words) - 20:49, 2 October 2020
- ...>\angle BOA</math> is a right angle. <math>A</math> and <math>B</math> are two points on the circumference of circle of radius <math>OA</math>. Find the a .../3),6sin(4*pi/3))--(0,0))--(-3,-3)--intersectionpoint((8cos(5*pi/6),8sin(5*pi/6))--(0,0),(-3,3)--(-3,-3))--cycle,gray);11 KB (1,738 words) - 19:25, 10 March 2015
- <math>p</math> is the product of two <math>4</math>-digit numbers formed by the digits <math>1,2,3,4,5,6,7,8</ma <math>a</math> and <math>b</math> are two numbers that have prime factors <math>3</math> and <math>5</math> only. <ma11 KB (1,713 words) - 22:47, 13 July 2023
- ...e radian measure of the acute angle formed by the two lines? (Note: <math>\pi</math> radians is <math>180</math> degrees.) ...\pi}{6} \qquad \mathrm{(D) \ } \frac{\pi}{5} \qquad \mathrm{(E) \ } \frac{\pi}{4} </math>3 KB (476 words) - 03:50, 23 January 2023
- ...t response, and 1.5 points for each problem left unanswered. After looking over the 25 problems, Sarah has decided to attempt the first 22 and leave the la ...lengths <math>AB = 5</math>, <math>BC = 6</math>, and <math>AC = 7</math>. Two bugs start simultaneously from <math>A</math> and crawl along the sides of12 KB (1,814 words) - 12:58, 19 February 2020
- The area of <math>T</math> may be computed in two different ways: <cmath>V_1 = \frac{1}{3}\pi R^2 h</cmath>7 KB (1,214 words) - 18:49, 29 January 2018
- ...t[n]{x}=\sqrt[n]{|x|}\left(\cos\frac{\theta+2\pi k}{n}+i\sin\frac{\theta+2\pi k}{n}\right)</math> , where <math>k=0,1,2,...,n-1</math> and <math>x\in\mat ...h>\sqrt[4]{16}=\sqrt[4]{16}\left(\cos\frac{0+2\pi\cdot0}{4}+i\sin\frac{0+2\pi\cdot0}{4}\right)\implies\boxed{2}</math>3 KB (532 words) - 16:52, 20 May 2020
- The larger of two consecutive odd integers is three times the smaller. What is their sum? ...005, <math>78</math> in 2006, and is <math>85</math> in 2007. Between what two consecutive years was there the largest percentage increase?13 KB (2,058 words) - 17:54, 29 March 2024
- ...oint, it moves one point, and if it is on an even-numbered point, it moves two points. If the bug begins on point 5, after 1995 jumps it will be on point ...n attendance. A league official who knows the actual numbers attending the two games notes that:17 KB (2,387 words) - 22:44, 26 May 2021
