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• 2009 AIME II Problems/Problem 15
  Let <math>V = \overline{NM} \cap \overline{AC}</math> and <math>W = \overline{NM} \cap
  11 KB (1,849 words) - 19:43, 2 January 2023
• 2009 USAMO Problems/Problem 5
  ...h> intersect <math>\omega</math> at <math>K</math> and another point <math>V</math>, as shown: pair V = IP(L(P, S, 10, 10), circle, 1);
  6 KB (973 words) - 19:24, 18 October 2018
• 1991 AJHSME Problems/Problem 21
  <cmath>T=32-3k\Rightarrow V=24-4k.</cmath>
  807 bytes (122 words) - 00:08, 5 July 2013
• Differentiation Rules
  If <math>y(x) = u(x)+v(x)</math> then <math>\frac{dy}{dx} = \frac{du}{dx} + \frac{dv}{dx}</math>. ...x) = u(x) \cdot v(x)</math> then <math>\frac{dy}{dx} = u(x)\frac{dv}{dx} + v(x)\frac{du}{dx}</math>.
  2 KB (288 words) - 00:53, 26 March 2018
• Tower law
  ...ath> is a basis for <math>L</math> over <math>K</math>, we can write <math>v = \sum_ia_i\alpha_i</math>, where <math>a_1,a_2,\ldots,a_n\in K</math>. And <cmath>v = \sum_ia_i\alpha_i = \sum_i\left(\sum_jb_{ij}\beta_j\right)\alpha_i = \sum
  3 KB (567 words) - 08:42, 21 August 2009
• Unit (ring theory)
  ...[[inverse]] in <math>R</math>, that is, if there is another element <math>v\in R</math> such that <math>uv=vu=1</math>.
  446 bytes (86 words) - 20:16, 23 August 2009
• 2010 AMC 12A Problems/Problem 7
  ...times more water than Logan's miniature. The volume of a sphere is: <math>V=\dfrac{4}{3}\pi r^3</math>. Since we are comparing the heights (m), we shou
  1 KB (198 words) - 18:08, 28 June 2021
• 2010 AMC 12A Problems/Problem 21
  <cmath>= x^6-2ux^5+(u^2+2v)x^4-(2uv+2w)x^3+(2uw+v^2)x^2-2vwx+w^2</cmath> v &= 2\\
  5 KB (969 words) - 21:33, 22 June 2022
• Kirchhoff's rules
  <math>\sum_{closed loop} \Delta V = 0</math>
  406 bytes (67 words) - 20:36, 7 March 2014
• Characteristic polynomial
  ...non-zero vector that satisfies the relation <math>A\bold{v} = \lambda\bold{v}</math>, for some scalar <math>\lambda \in K</math>. In other words, applyi ...bold{v} = \lambda \bold{v}</math>, then <math>\lambda I \bold{v} - A \bold{v} = \bold{O}</math>. But then, the column vectors of <math>\lambda I - A</ma
  19 KB (3,412 words) - 14:57, 21 September 2022
• Eigenvalue
  ...r constant <math>\lambda</math> such that <math>L \bold{v} = \lambda \bold{v}</math>. Here, <math>\lambda</math> is known as the '''eigenvalue''' associ
  821 bytes (138 words) - 19:32, 2 March 2010
• Connected set
  ...h>, there exists a connected open set <math>V</math> such that <math>x \in V \subset C</math>. <math>X</math> is locally connected if it is locally conn ...here exists a path-connected open set <math>V</math> such that <math>x \in V \subset C</math>. <math>X</math> is locally path-connected if it is locally
  3 KB (497 words) - 16:27, 15 March 2010
• Separation axioms
  ...el("$y$",(A+C)/2 + shiftfactor,(1.2,-1.2)); label("$U$",B,(1,-1)); label("$V$",B+shiftfactor,(1,-1)); ...sets <math>U, V</math> such that <math>x \in U, y \in V</math> and <math>U,V</math> are [[disjoint]].
  5 KB (672 words) - 13:28, 4 June 2018
• Linearly independent
  ...[[vector]]s <math>v_1, v_2, \ldots, v_n</math> in a [[vector space]] <math>V</math> over a field <math>K</math> are '''linearly independent''' if there ...ndependent [[iff]] their [[determinant]] <math>D(\bold{v}_1, \ldots, \bold{v}_n) = 0</math>.
  2 KB (300 words) - 23:35, 16 March 2010
• 2010 IMO Problems/Problem 6
  :<math>a_{n} = max_{\text{(T is valid n-type)}} v(t)</math> ...ch n} \not\le \text{s we pick a valid n-type } T_{n} \text{ with } a_{n} = v(T_{n})</math>
  4 KB (786 words) - 08:46, 12 March 2024
• 2013 IMO Problems/Problem 3
  V=D("V",circumcenter(Ia,Ib,Ic),SE); D(circumcircle(B,C,V),linetype("2 2")+rgb(0.6,0,1));
  3 KB (553 words) - 09:41, 17 January 2016
• 2010 AMC 10B Problems/Problem 16
  pair V=(0,0.5); draw(V--O);
  3 KB (544 words) - 20:54, 24 March 2024
• 2011 AMC 10A Problems/Problem 22
  ...so we can color it in k ways. We then move on to the vertices adjacent to v, etc, and at the end we multiply all these together. For example, the chrom
  14 KB (2,425 words) - 09:13, 5 November 2023
• KGS math club/solution 11 2
  main(int a, char **v) { int n=atoi(v[1]),
  1 KB (188 words) - 18:08, 21 February 2011
• 2011 AMC 12B Problems
  A segment through the focus <math>F</math> of a parabola with vertex <math>V</math> is perpendicular to <math>\overline{FV}</math> and intersects the pa
  13 KB (1,978 words) - 16:28, 12 July 2020

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