Create the page "Pi over two" on this wiki! See also the search results found.

• 1989 AHSME Problems
  A square is cut into three rectangles along two lines parallel to a side, as shown. If the perimeter of each of the three r ...<math>100</math> does <math> x^{2}+x-n </math> factor into the product of two linear factors with integer coefficients?
  15 KB (2,247 words) - 13:44, 19 February 2020
• 2012 AMC 10A Problems
  A square with side length <math>8</math> is cut in half, creating two congruent rectangles. What are the dimensions of one of these rectangles? ...>4</math> times the reciprocal of the other number. What is the sum of the two numbers?
  13 KB (1,994 words) - 01:31, 22 December 2023
• 2012 AMC 12A Problems
  ...way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of ...as Chelsea. What is the probability that Alex wins three rounds, Mel wins two rounds, and Chelsea wins one round?
  14 KB (2,197 words) - 13:34, 12 August 2020
• 2012 AMC 12A Problems/Problem 16
  ...math> has its center <math>O</math> lying on circle <math>C_2</math>. The two circles meet at <math>X</math> and <math>Y</math>. Point <math>Z</math> in ...angle{OZY} \cong \angle{OZX}</math>, this is a system of two equations and two variables. Solving for <math>r</math> gives <math>r = \sqrt{30}</math>. <ma
  9 KB (1,496 words) - 02:40, 2 October 2022
• 1989 AHSME Problems/Problem 28
  ...\tan^2x-9\tan x+1=0</math> that are between <math>x=0</math> and <math>x=2\pi</math> radians. ...mathrm{(C) \frac{3\pi}{2} } \qquad \mathrm{(D) 3\pi } \qquad \mathrm{(E) 4\pi } </math>
  2 KB (282 words) - 21:14, 2 March 2019
• 1989 AHSME Problems/Problem 19
  ...uad \mathrm{(D) \frac{9}{\pi^2}(\sqrt{3}-1) } \qquad \mathrm{(E) \frac{9}{\pi^2}(\sqrt{3}+3) } </math> ...ac{6}{\pi}</math> for <math>r</math> and evaluating yields <math>\frac{9}{\pi^2}(\sqrt{3}+3)\implies{\boxed{E}}</math>.
  4 KB (649 words) - 10:04, 20 May 2021
• 2012 AMC 10B Problems
  ...y bags as possible, with 6 marbles per bag. How many marbles will be left over? ...e integers are added to the first two integers the sum is 41. Finally when two more integers are added to the sum of the previous four integers the sum is
  18 KB (2,350 words) - 18:48, 9 July 2023
• 2012 AMC 12B Problems/Problem 15
  ...along 2 radii to form 2 sectors, one with a central angle of 120. He makes two circular cones using each sector to form the lateral surface of each cone. ...h>, and the larger is <math>16\pi</math>. Those two arc lengths become the two circumferences of the new cones; so the radius of the smaller cone is <math
  2 KB (259 words) - 13:42, 2 September 2020
• 2010 AMC 8 Problems/Problem 19
  ...erline{AD}</math> has length <math>16</math>. What is the area between the two circles? ...quad\textbf{(C)}\ 64 \pi\qquad\textbf{(D)}\ 81 \pi\qquad\textbf{(E)}\ 100 \pi </math>
  2 KB (279 words) - 09:04, 10 March 2023
• 2012 AMC 10B Problems/Problem 21
  ...)}\ 2\qquad\textbf{(C)}\ \sqrt{5}\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ \pi</math> ...gle inequality: <math>b<2a</math>. The only answer choice that holds these two inequalities is: <math>\sqrt{3}</math>.
  3 KB (432 words) - 20:18, 23 October 2021
• 2015 AIME I Problems
  ...the three sleepers were determined randomly, the probability that exactly two of the sleepers are from the same country is <math>\frac{m}{n}</math>, wher ...2</math> of the remaining <math>8</math> socks at random, and on Wednesday two of the remaining <math>6</math> socks at random. The probability that Wedn
  10 KB (1,615 words) - 21:48, 13 January 2024
• 2012 AIME I Problems
  ...= z,</math> and the imaginary part of <math>z</math> is <math>\sin{\frac{m\pi}{n}}</math>, for relatively prime positive integers <math>m</math> and <mat ...he plane divides the cube into two solids. The volume of the larger of the two solids can be written in the form <math>\tfrac{p}{q},</math> where <math>p<
  10 KB (1,617 words) - 14:49, 2 June 2023
• 2012 AIME II Problems/Problem 13
  ...ath> and <math>\sqrt{11}</math> from point <math>B</math>, so they are the two points where a circle centered at <math>A</math> with radius <math>\sqrt{11 There are two equilateral triangles with <math>\overline{AD_1}</math> as a side; let <mat
  13 KB (2,052 words) - 18:02, 5 February 2024
• 2017 AMC 8 Problems
  ...ves but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are tru ...with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?
  12 KB (1,771 words) - 09:41, 13 June 2024
• Mock AIME I 2012 Problems
  ...math>, <math>\cdots</math>, <math>9\}</math> is called ''golden'' if every two consecutive numbers in the permutation are relatively prime. How many ''gol ...ing (possibly the same string) chosen at random. He continues on by tying two randomly selected untied ends together until there are no more untied ends,
  7 KB (1,309 words) - 11:13, 8 April 2012
• 2015 IMO Problems/Problem 1
  if, for any two different points <math>A</math>, <math>B</math> in <math>\mathcal{S}</math> regular polygons <math>P_n</math> with <math>n</math> sides: given any two vertices <math>A</math> and
  4 KB (773 words) - 08:14, 19 July 2016
• 1988 USAMO Problems/Problem 5
  ...{a_n}</math> are all <math>n</math>th roots of unity. If <math>\omega=e^{2\pi i/n}</math>, then the sum of <math>32</math>nd powers of these roots will b ...mials of degree <math>n</math> over the field <math>\mathbb{F}_2</math> of two elements, and on the left, we have the factorisation of this generating fun
  8 KB (1,348 words) - 09:44, 25 June 2022
• 2006 SMT/General Problems
  A geometric series is one where the ratio between each two consecutive terms is constant (ex. <math> 3, 6, 12, 24,\cdots </math>). The Given two <math> 2 </math>'s, "plus" can be changed to "times" without changing the r
  10 KB (1,477 words) - 16:02, 27 May 2012
• 2006 SMT/Team Problems
  ...e <math> M </math> minus the volume fo cone <math> N </math> is <math> 140\pi </math>, find the length of <math> \overline{BC} </math>. ...ath> S_n=\sum_{i=1}^{n-1}i\cdot S_{n-i} </math>. For example, if the first two elements are <math> 2 </math> and <math> 3 </math>, respectively, the third
  6 KB (910 words) - 17:32, 27 May 2012
• 2006 SMT/Advanced Topics Problems/Problem 1
  ...s the square root of himself, or the square root of <math> i </math>. What two answers should he give? ...math> i=\cos\left(\frac{\pi}{2}\right)+i\sin\left(\frac{\pi}{2}\right)=e^{\pi i/2} </math>.
  1 KB (170 words) - 20:12, 27 May 2012

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)