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• 2022 AMC 12A Problems/Problem 25
  ...e R.H.S. is a not a perfect square. Thus, the number of positive <math>(u, v)</math> is equal to the number of positive divisors of <math>2 r^2</math>. ...n if <math>(a, b)</math> with <math>a = 2 r - u</math> and <math>b = 2 r - v</math>.
  7 KB (1,271 words) - 12:09, 4 January 2024
• 2022 AMC 10B Problems/Problem 22
  We denote by <math>\left( u, v \right)</math> the coordinates of circle <math>C_0</math>, and <math>r</mat u^2 + v^2 = \left( 8 - r \right)^2 . \hspace{1cm} (1)
  7 KB (1,202 words) - 01:15, 10 June 2023
• 2023 AMC 12B Problems
  .../math>, define the binary operation <math>\otimes</math> by<cmath>u\otimes v=ac+bdi.</cmath>Suppose <math>z</math> is a complex number such that <math>z
  13 KB (2,107 words) - 22:19, 20 April 2024
• 2024 AMC 8 Problems
  pair P,Q,R,S,T,U,V,W; P=(0,30); Q=(30,30); R=(40,40); S=(10,40); T=(10,10); U=(40,10); V=(30,0); W=(0,0);
  22 KB (2,999 words) - 19:07, 4 June 2024
• Random Problem
  <math>V=\pi{r^2}h</math> <math>V=\pi{r^2}(14-2r)</math>
  4 KB (697 words) - 17:07, 24 March 2023
• 2023 AIME I Problems/Problem 14
  path v=(5,-0.5)--(5,0)--(5,1)--(6,1)--(6,2)--(6,3)--(6,4)--(7,4); draw(v,p);
  11 KB (1,834 words) - 22:01, 4 January 2024
• 2023 AIME I Problems/Problem 13
  pair o = (0, 0), u = (1, 0), v = 0.8*dir(40), w = dir(70); draw(o--u--(u+v));
  13 KB (2,130 words) - 01:52, 31 January 2024
• 2023 AIME II Problems/Problem 14
  <cmath> V = \frac{1}{3} \cdot x \cdot (S_1 + \sqrt{S_1S_2} + S_2) = \frac{1}{3} \cdot Let the volume without water be <math>V,</math> volume of the pyramid <math>SCGJ</math> be <math>U.</math>
  10 KB (1,574 words) - 16:42, 8 March 2024
• 2019 ELMO Problems
  ...en so are <math>f(V)</math>, <math>V+W</math>, <math>V-W</math>, and <math>V \cdot W</math>.
  5 KB (772 words) - 08:50, 23 February 2023
• 2023 USAJMO Problems/Problem 2
  Plugging in <math>A</math> and <math>B</math> gives <math>u=v=0</math>. Plugging in <math>P</math> gives Since it passes through <math>A</math>, for some <math>v, w</math>, the equation of circle <math>(ABP)</math> is,
  7 KB (1,280 words) - 01:22, 6 February 2024
• 2023 USAMO Problems/Problem 1
  Plugging in <math>A</math> and <math>B</math> gives <math>u=v=0</math>. Plugging in <math>P</math> gives
  4 KB (684 words) - 01:55, 6 February 2024
• Pell's equation (simple solutions)
  <cmath>u = 5y - 1, v = 2x - 3y + 1 \implies u^2 - 5 v^2 = - 4 \implies</cmath>
  15 KB (2,351 words) - 08:28, 20 April 2023
• 2023 USAMO Problems/Problem 6
  https://youtube.com/watch?v=LAuyU2OuVzE ...and <math>w=\frac{2b^3cx_0z_0}{c^2y_0^2-b^2z_0^2}</math>, so <cmath>\frac{v}{w}=\frac{b^2z_0}{c^2y_0},</cmath> which is the required condition for <mat
  14 KB (2,600 words) - 23:37, 10 March 2024
• Xosomiennamxsmn
  ...n c&oacute; biết tại sao SXMN lại c&oacute; sức hấp dẫn như vậy hay kh&ocirc;ng, h&atilde;y c&ugrave;ng l&yacute; giải qua b&agrave;i <p><strong><span style="color: #000000;">XSMN ph&aacute;t triển với mục đ&iacute;ch &Iacute;ch nước lợi nh&agrave;</span></strong><
  11 KB (2,230 words) - 23:24, 9 May 2023
• Know the Facts: Gmaas
  231. Gmaas once demanded Epic Games to give him 5,000,000 V-bucks for his 569823rd birthday. EDIT: This is why Gmaas no longer has an E
  88 KB (14,928 words) - 13:54, 29 April 2024
• 1997 IMO Problems/Problem 2
  ...math>AB</math> and <math>AC</math> meet the line <math>AU</math> and <math>V</math> and <math>W</math>, respectively. The lines <math>BV</math> and <ma
  736 bytes (124 words) - 23:58, 28 March 2024
• 1992 IMO Problems/Problem 2
  ...th>f(u) = f(t^{2}+v) = f^{-1}(v)+f(t)^{2}> f^{-1}(v) = f(f(f^{-1}(v))) = f(v)</math>. Hence f is strictly increasing. It is now clear that since <math>f
  1 KB (282 words) - 14:53, 12 March 2024
• 2023 AMC 10B Problems
  ...sed as <math>(2u-3w, v+4w)</math> with <math>0\le u\le1</math>, <math>0\le v\le1,</math> and <math>0\le w\le1</math>?
  13 KB (1,959 words) - 13:42, 14 June 2024
• 2024 AIME I Problems/Problem 14
  <math>V = \sqrt{(a^2 + b^2 - c^2)(b^2 + c^2 - a^2)(a^2 + c^2 - b^2)/72}</math> ...umes <cmath>[ABCI] + [ABDI] + [ACDI] + [BCDI] = V,</cmath> We have <cmath>V = \frac{4AR}{3}.</cmath> Plugging in and simplifying, we get <math>R = \fra
  13 KB (2,042 words) - 09:34, 3 April 2024
• 2023 AMC 12A Problems/Problem 16
  label("$v'$", (0, 2.18), NE); ...eed to find <math>v</math> with the largest imaginary part such that <math>v^2</math> lies on <math>\omega</math>.
  6 KB (1,055 words) - 21:58, 28 February 2024

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