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• 2021 AIME II Problems/Problem 12
  ...$c$", D--C, N); label("$d$",D--A,W); label("$u$",D--B,2*dir(170)); label("$v$",A--C,S); ...c, d</math>, be the sides, <math>s</math> the semiperimeter, and <math>u, v</math>, the diagonals. Then the area, <math>K</math>, is given by <cmath>K
  10 KB (1,669 words) - 17:33, 12 January 2024
• 2021 USAMO Problems/Problem 6
  Denote <math>D' – A' = 2\vec V.</math> ...\triangle A'C'E'</math> into <math>\triangle D'F'B'</math> is <math>2\vec {V.}</math>
  5 KB (875 words) - 00:26, 23 May 2023
• 2021 USAJMO Problems/Problem 1
  ...<math>n=2k+1</math>, just take <math>(u,v)= (k+1,k)</math> which <math>u^2-v^2=n</math>. Thus the only answer is <math>\boxed{f\equiv 1}</math> and we a https://www.youtube.com/watch?v=Q1NUBUYvOJc
  8 KB (1,492 words) - 00:23, 24 February 2024
• G285 2021 MC10A
  ...th>t</math> is square free and <math>gcd(u,v,w) = 1</math>, find <math>t+u+v+w</math> if <math>x=\cos 20^o</math> and <math>y=\sin 20^o</math>.
  8 KB (1,385 words) - 12:55, 23 June 2021
• 2022 AIME II Problems/Problem 4
  We could assume a variable <math>v</math> which equals to both <math>\log_{20x} (22x)</math> and <math>\log_{2 So that <math>(20x)^v=22x \textcircled{1}</math>
  5 KB (778 words) - 18:14, 30 January 2024
• 2022 AIME II Problems/Problem 9
  ...s, plus the outer region, <math>E</math> is the number of edges, and <math>V</math> is the number of vertices. Temporarily disregarding the intersection <math>V=V_{i}+210=222</math>
  12 KB (2,025 words) - 14:56, 25 January 2024
• 1978 AHSME Problems/Problem 25
  ...\qquad \text{(iii) }x+y\ge a\\ \\ \qquad \text{(iv) }x+a\ge y\qquad \text{(v) }y+a\ge x</math>
  665 bytes (119 words) - 18:31, 28 August 2023
• 1972 AHSME Problems/Problem 26
  ...t,st),E); label("M",(cu,su),N);label("P",(cu,st),S); label("C",(cos(v),sin(v)),W); //Credit to Zimbalono for the diagram </asy>
  864 bytes (169 words) - 16:47, 23 June 2021
• 2021 Fall AMC 12B Problems/Problem 17
  ...th>C(1) = 0</math> and our recursive rules for <math>C(n)</math> and <math>V(n)</math> as follows: n & V(n) & C(n) \\ \hline
  8 KB (1,309 words) - 00:31, 6 January 2023
• 2021 Fall AMC 12A Problems/Problem 13
  .../math> bisects the angle between <math>\mathbf{u}</math> and <math>\mathbf{v}</math>.
  16 KB (2,526 words) - 00:53, 6 May 2023
• 2021 Fall AMC 12A Problems/Problem 21
  ...h>. Hence, <math>B = \left( - 1 , u \right)</math>, <math>D = \left( 0 , - v \right)</math>. The slope of <math>AD</math> is <math>m_{AD} = \frac{v}{3}</math>.
  5 KB (756 words) - 03:40, 23 January 2023
• OrenSH
  v v
  2 KB (265 words) - 22:25, 15 April 2024
• Matrix Tree Theorem
  Let <math>G</math> be a graph with the set of vertices <math>V=\{v_1,v_2,v_3,\ldots, v_n\}</math>. We define its adjacency matrix <math>\
  1 KB (264 words) - 11:26, 3 March 2022
• Variance
  ...> the formula for variance if <math>X</math> is a [[population]] is <cmath>V = \frac{1}{n}\sum_{i=1}^n (x_i - \overline{x})^2.</cmath> Additionally, <math>V = \sigma^2</math> where <math>\sigma</math> is the population [[standard de
  749 bytes (122 words) - 19:16, 3 March 2022
• Newton's method
  ...>, (2) <math>\hat{x}\equiv x\pmod{p^{n-k}}</math> and (3) <math>k=v(p'(x))=v(p'(\hat{x}))</math>. <center><cmath>v=u+p^{n-2k}zs\in u+p\mathbb{Z}_p\subset \mathbb{Z}_p^{\times}</cmath></cente
  13 KB (2,298 words) - 23:34, 28 May 2023
• 2023 AIME I Problems
  pair o = (0, 0), u = (1, 0), v = 0.8*dir(40), w = dir(70); draw(o--u--(u+v));
  7 KB (1,154 words) - 12:54, 20 February 2024
• Rank Nullity Theorem
  ...t{R}(\text{T}))</math> where <math>\text{R}(\text{T})=\{\text{T}(x)~|~x\in V\}</math>. In other words, rank is the dimension of the linear transformati ...aim that if <math>\beta=\{v_1,v_2,\ldots, v_n\}</math> is a basis of <math>V</math>, then
  5 KB (893 words) - 22:41, 28 May 2022
• Kimberling’s point X(24)
  ...math> In accordance with Claim, <math>\angle BVD = \angle HVE \implies B', V,</math> and <math>B</math> are collinear.
  10 KB (1,751 words) - 15:34, 25 November 2022
• Vector analysis
  ...mathbf{n}\,dS,</cmath> where <math>R</math> is a region whose volume <math>V(R)</math> shrinks to <math>0</math> about the point <math>p</math>, <math>\ ...mathbf{n}\,dS,</cmath> where <math>R</math> is a region whose volume <math>V(R)</math> shrinks to <math>0</math> about the point <math>p</math>, <math>\
  7 KB (1,189 words) - 06:00, 21 December 2022
• 2022 AMC 10A Problems/Problem 16
  ...the three roots of the polynomial. The lengthened prism's volume is <cmath>V = (a+2)(b+2)(c+2) = abc+2ac+2ab+2bc+4a+4b+4c+8 = abc + 2(ab+ac+bc) + 4(a+b+ We can substitute these into the expression, obtaining <cmath>V = \frac{6}{10} + 2\left(\frac{29}{10}\right) + 4\left(\frac{39}{10}\right)
  7 KB (1,111 words) - 21:00, 21 February 2024

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