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• 2007 AMC 12B Problems/Problem 19
  <math>V = \pi \left(\frac{3}{\pi}\right)^2\cdot 6\sin\theta</math>
  1 KB (166 words) - 16:35, 15 February 2021
• 1985 AJHSME Problems
  label("V",(1.5,.3),N); ...bf{(A)}\ \text{Z} \qquad \textbf{(B)}\ \text{U} \qquad \textbf{(C)}\ \text{V} \qquad \textbf{(D)}\ \ \text{W} \qquad \textbf{(E)}\ \text{Y}</math>
  12 KB (1,670 words) - 17:42, 24 November 2021
• Mock AIME 5 Pre 2005 Problems
  ...>. Y is on <math>\overline {ST}</math>, dividing <math>SY:YT = 2:1</math>. V is on <math>\overline {XY}</math>, dividing <math>XV:VY = 1:2</math>. It is
  6 KB (909 words) - 07:27, 12 October 2022
• 1974 USAMO Problems/Problem 5
  ...le ADB = \angle BDC = \angle CDA = 120^\circ</math>. Prove that <math>x=u+v+w</math>. label("$v$",(B+D)/2,N);
  7 KB (1,221 words) - 18:57, 3 July 2013
• 2005 USAMO Problems/Problem 3
  ...math> Substituting in <math>P</math> yields <cmath>-a^2p(1-p)+vp=0\implies v = a^2(1-p).</cmath> Substituting in <math>B_1</math> yields
  6 KB (1,117 words) - 01:17, 11 October 2021
• Cone
  ...me of a pyramid, <math>V = \frac{1}{3} \cdot B \cdot h</math>, where <math>V</math> is the volume, <math>B</math> is the area of the base and <math>h</m
  7 KB (1,128 words) - 20:12, 27 September 2022
• 2008 USAMO Problems/Problem 6
  ...space]] of all such functions. Define the linear operator <math>A : V \to V</math> as <cmath>(Af)(v) = \sum_{v \sim w} f(v) - f(w)</cmath>
  13 KB (2,414 words) - 14:37, 11 July 2016
• 2008 Mock ARML 1 Problems/Problem 3
  pair v(int n){ return dir(n * 60); } ...0))--MP("B",v(1),N)--MP("C",v(2),N)--MP("D",v(3),SW)--MP("E",v(4))--MP("F",v(5))--cycle);
  3 KB (425 words) - 22:32, 5 December 2020
• Schrodinger Equation
  ...ing the Hamiltonian, usually of the form <math>-\frac{\hbar^2}{2m}\Delta + V</math> where <math>\Delta</math> is the relevant Laplace(-Beltrami) operato
  417 bytes (69 words) - 14:32, 21 April 2018
• Jean-Victor Poncelet
  *Didion 1870. ''Notice sur la vie et les ouvrages du général J. V. Poncelet''
  2 KB (253 words) - 11:41, 19 December 2018
• 1988 IMO Problems/Problem 1
  ...ble positions of the midpoints <math>U</math> of <math>AB</math> and <math>V</math> of <math>AC</math> as <math>A</math> varies?</li> We claim that all points <math>U,V</math> lie on a circle centered at the midpoint of <math>OP</math>, <math>M
  3 KB (545 words) - 11:32, 30 January 2021
• 1997 PMWC Problems/Problem T1
  ...uilateral triangle with sides of length three units. <math>U</math>, <math>V</math>, <math>W</math>, <math>X</math>, <math>Y</math>, and <math>Z</math> label("$V$",(-1/3,sqrt(3)/6),NW);
  1 KB (188 words) - 14:38, 20 April 2014
• Category (category theory)
  ...nd there is a morphism <math>U \to V</math> if and only if <math>U \subset V</math>.
  5 KB (792 words) - 19:01, 7 April 2012
• 1991 IMO Problems/Problem 4
  ...each step in the process we remove a number of vertices from the set <math>V</math> if their exists an edge sorrounding it which is labelled. Additiona ...of the vertices not in <math>V</math>. Notice that since <math>v_1,v_n\in V</math> the edge connecting <math>v_0</math> and <math>v_1</math> and the ed
  4 KB (668 words) - 17:45, 30 January 2021
• 2001 IMO Problems/Problem 4
  ..., there exists a <math>v\in\{1,2,...,m!\}</math> such that <math>t\equiv f(v)\pmod{m!}</math>. So, let <math>t\equiv f(v_t)\pmod{m!}</math>. Consider
  2 KB (416 words) - 20:01, 19 May 2023
• Acceleration
  ...known to be constant, then <cmath>\textbf{a} = \frac{\textbf{v}_2 -\textbf{v}_1 }{t_2 - t_1}</cmath> Note that velocity is a vector, so the magnitudes c ...instance, <cmath>\textbf{a} = \lim_{h\to 0} \frac{v(t+h)-v(t)}{(t+h)-t} = v'(t)</cmath>
  2 KB (277 words) - 14:04, 24 April 2022
• 2001 USAMO Problems/Problem 3
  ...h>b = 2\sin u</math> and <math>c = 2\sin v</math>, where <math>0^\circ < u,v < 90^\circ</math>. Then <cmath>a = 2(-\sin u\sin v + \cos u\cos v) = 2\cos (u + v),</cmath>
  4 KB (807 words) - 10:45, 9 April 2023
• Time dilation
  <math>\dfrac{t_1}{\sqrt{1-v^2/c^2}}=t_2</math> <math>v</math> is the relative velocity the ovject is moving to the observer.
  1 KB (261 words) - 00:19, 31 January 2021
• Lorentz Factor
  It is equivalent to <math>\gamma=\dfrac{1}{\sqrt{1-v^2/c^2}}</math>
  226 bytes (34 words) - 11:23, 5 October 2012
• 1992 USAMO Problems/Problem 4
  By another person ^v^
  5 KB (807 words) - 18:37, 25 June 2021
• 1974 USAMO Problems
  ...le ADB = \angle BDC = \angle CDA = 120^\circ</math>. Prove that <math>x=u+v+w</math>. label("$v$",(B+D)/2,N);
  3 KB (427 words) - 18:55, 3 July 2013
• 1962 IMO Problems/Problem 3
  Answer: the rhombus CUVW, where U is the center of ABCD, V is the center of ABB'A, and W is the center of BCC'B'. ...x/2 + 1/2, x/2, 1/2) = x (1, 1/2, 1/2) + (1-x) (1/2, 0, 1/2) = x W + (1-x) V, so M traces out the line VW.
  3 KB (581 words) - 02:00, 6 May 2023
• 1962 IMO Problems/Problem 7
  ...n the direction of <math>V{i}</math> to <math>V{j}</math> and beyond <math>V{j}</math> for <math>i=1,2,3,4</math>; <math>j=1,2,3,4</math>; and <math>i \ ...trahedron opposite of vertex <math>V_{4}</math> below <math>\Delta V{1}V{2}V{3}</math>
  11 KB (1,928 words) - 20:52, 21 November 2023
• 2001 AMC 10 Problems
  ...and diagonal are the same. Five of these numbers are represented by <math> v </math>, <math> w </math>, <math> x </math>, <math> y </math>, and <math> z label("$v$",(0.5,2.5));
  14 KB (1,983 words) - 16:25, 2 June 2022
• 1976 USAMO Problems/Problem 4
  ...ath>. Let the volume of the tetrahedron be <math>V</math>. Therefore <math>V=\frac{abc}{6}</math>. ...{6V}</math>, or <math>6V\leq \frac{S^3(\sqrt{2}-1)^3}{27}</math>, or <math>V\leq \frac{S^3(\sqrt{2}-1)^3}{162}</math>, with equality only when <math>a=b
  2 KB (358 words) - 23:15, 18 July 2016
• 1985 AJHSME Problems/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>
  2 KB (279 words) - 09:25, 10 January 2023
• 2009 AMC 12B Problems/Problem 20
  <math>v = \frac{200}{b}</math> ...gain <math>b</math> more edges. So the total number of new edges is <math>v*b \Rightarrow \frac{200}{b}*b \Rightarrow 200</math>. It doesn't matter how
  9 KB (1,567 words) - 13:43, 19 August 2023
• 2009 AIME I Problems/Problem 10
  ...of sittings is in the form <math>N*(5!)^3</math> because for each <math>M, V, E</math> sequence we have <math>5!</math> arrangements within the Ms, Vs, ...members must sit in cycles of M, V, E, but not necessarily with one M, one V, and one E in each cycle(for example, MMVVVE, MVVVEEE, MMMVVVEE all count a
  4 KB (590 words) - 16:49, 27 September 2023
• 2009 AIME II Problems/Problem 9
  ...en <math>1</math> and <math>167</math>, inclusive, and for each such <math>v</math> we have exactly one valid <math>x</math>. Hence in this case there a
  5 KB (845 words) - 15:45, 28 December 2020
• 2008 IMO Problems/Problem 6
  V be the foot of the projection of K to AC.
  1 KB (283 words) - 01:15, 19 November 2023
• 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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