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• 2021 AIME I Problems/Problem 13
  ...th>x=PT</math>, where the length <math>O_{1}O_{2}</math> splits as <math>u+v</math>. Because the lines <math>PQ</math> and <math>O_{1}O_{2}</math> are p ...u^{2}+(r+x)^{2}-u(r+x) \\ \triangle O_{1}OT&:(r+R_{1})^{2}=v^{2}+(r+x)^{2}+v(r+x)\end{align*}</cmath>
  17 KB (2,852 words) - 03:59, 7 February 2024
• Wood2009
  Lucky Seven V ARE YOU XPERIENCED? V
  3 KB (452 words) - 10:21, 17 November 2022
• 2021 AMC 12A Problems
  Suppose that on a parabola with vertex <math>V</math> and a focus <math>F</math> there exists a point <math>A</math> such
  15 KB (2,383 words) - 09:49, 25 June 2023
• 2022 AIME I Problems/Problem 15
  Denote <math>u = 1 - x</math>, <math>v = 1 - y</math>, <math>w = 1 - z</math>. \sqrt{(1-u)(1+v)} + \sqrt{(1+u)(1-v)} & = 1 \hspace{1cm} (1) \\
  15 KB (2,208 words) - 01:25, 1 February 2024
• 2021 Fall AMC 10B Problems/Problem 25
  ...t{10}} , \sqrt{10} \right)</math>, <math>Q = \left( \sqrt{10} , \frac{10 - v}{\sqrt{10}} \right)</math>. We have <math>m_{HP} = \frac{3}{6 - u}</math> and <math>m_{PQ} = - \frac{v}{u}</math>.
  16 KB (2,274 words) - 09:02, 10 December 2022
• 2021 Fall AMC 10A Problems/Problem 22
  Let <math>O</math> be the center of the base, <math>V</math> be the vertex of the base.
  8 KB (1,314 words) - 03:54, 5 July 2022
• 2021 Fall AMC 10A Problems/Problem 24
  pair A, B, C, D, E, F, G, H, A1, B1, C1, D1, E1, F1, G1, H1, V; V = (3,0);
  24 KB (3,567 words) - 18:14, 30 August 2022
• Cubic Equation
  Now here comes the smart part. Substitute <math>y = \sqrt[3]{u} - \sqrt[3]{v}</math>. ...<math>u - 3\sqrt[3]{u^2v} + 3\sqrt[3]{uv^2} - v + p\sqrt[3]{u} - p\sqrt[3]{v} + q = 0</math>. Simplification:
  6 KB (1,059 words) - 14:42, 11 December 2020
• 2021 AIME II Problems/Problem 1
  Let <math>u = 10 – y, v = 9 – x.</math> https://www.youtube.com/watch?v=jDP2PErthkg
  5 KB (794 words) - 15:36, 30 August 2022
• 2020 IMO Problems/Problem 6
  ...3}</math> then we can find a line <math>\ell</math> perpendicular to <math>v</math> such that <math>\ell</math> separates <math>S</math>, and any point Suppose there is no such direction <math>v</math>, then <math>S</math> is contained in a box with side length <math>n^
  3 KB (574 words) - 11:30, 14 May 2021
• 2021 AMC 12A Problems/Problem 20
  Suppose that on a parabola with vertex <math>V</math> and a focus <math>F</math> there exists a point <math>A</math> such ...d <math>Y</math> be the orthogonal projections of <math>F</math> and <math>V</math> onto <math>AQ</math>. Because <math>AF < AV</math>, there are two po
  4 KB (796 words) - 17:33, 13 July 2021
• 2021 AMC 12A Problems/Problem 23
  ...ur squares on the middle of the edges after n moves, and <math>V_n</math> (V for vertex) be the probability that Frieda is on a corner after n moves. Th https://youtube.com/watch?v=kHLR57iP0cU
  17 KB (2,801 words) - 07:29, 4 November 2022
• Tree (graph theory)
  ...<math>u</math> and <math>v</math> in <math>G</math>. Every tree on <math>|V|=n</math> vertices has exactly <math>n-1</math> edges.
  401 bytes (75 words) - 16:51, 2 November 2020
• 2021 AMC 10A Problems/Problem 13
  V&=\frac16\cdot AB\cdot AD\cdot BD \\
  3 KB (496 words) - 19:12, 28 October 2022
• Quartic Equation
  ...tuy + vy^2 + svy + tv</math>, simplifying to <math>y^4 + (s + u)y^3 + (t + v + su)y^2 + (sv + tu)y + tv</math>. [[Equating coefficients]] gives the foll ...begin{cases} s + u = 0 \text{ since the } y^3 \text{ term is 0} \\ p = t + v + su \\ q = sv + tu \\ r = tv \end{cases}</math>
  13 KB (2,376 words) - 16:56, 19 February 2024
• 2013 Mock AIME I Problems
  ...</math> and <math>2</math> along <math>\textbf{u}</math> and <math>\textbf{v}</math> respectively, then find <cmath>\sum_{i=1}^{n}\|\textbf{r}_i\|^2.</c
  7 KB (1,149 words) - 17:16, 15 December 2020
• Nhakhoaparis
  ...đến sâu răng, mất răng. Vì vậy, cần phát hiện kịp thời và điều trị đúng cách mòn cổ răng. ...rãnh này, lâu dần tạo mảng bám, gây viêm nhiễm, tụt lợi và ảnh hưởng tới thẩm mỹ. Cổ răng mòn nhiều thậm chí có
  5 KB (1,261 words) - 05:15, 7 January 2021
• 1986 IMO Problems/Problem 4
  ...math> OV</math> (but not in <math> \vec{OV}</math>) for some vertex <math> V</math> of the polygon. Each two of these lines are obtained one from anothe
  2 KB (284 words) - 11:02, 30 January 2021
• 1985 AJHSME Problem 11
  label("V",(1.5,.3),N); ...>\text{(A)}\ \text{Z} \qquad \text{(B)}\ \text{U} \qquad \text{(C)}\ \text{V} \qquad \text{(D)}\ \ \text{W} \qquad \text{(E)}\ \text{Y}</math>
  1,023 bytes (167 words) - 15:57, 4 July 2023
• 1956 AHSME Problems/Problem 40
  If <math>V = gt + V_0</math> and <math>S = \frac {1}{2}gt^2 + V_0t</math>, then <math> <math> \textbf{(A)}\ \frac{2S}{V+V_0}\qquad
  737 bytes (129 words) - 22:53, 12 February 2021

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