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• 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

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