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• V Olimpiada Iberoamericana de Matemáticas (OIM)
  458 bytes (44 words) - 17:51, 14 December 2023

Page text matches

• Physics
  <math>\delta x'(t)=v(t)</math> <math>v'(t)=a(t)</math>
  9 KB (1,355 words) - 07:29, 29 September 2021
• 2020 CIME II Problems/Problem 10
  Case V) <math>a+b=5c\Rightarrow (5a-1)(5b-1)=126</math> for which there are 2 solu
  2 KB (332 words) - 09:37, 30 December 2021
• Cauchy-Schwarz Inequality
  ...ly if there exists a scalar <math>t</math> such that <math>\overrightarrow{v} = t \overrightarrow{w}</math>, or if one of the vectors is zero. This form ...{R} </math> be an [[inner product]]. Then for any <math> \mathbf{a,b} \in V </math>,
  13 KB (2,048 words) - 15:28, 22 February 2024
• Constructive counting
  ...math>, which is less than <math>2 \cdot 99999</math>. Therefore, <math>u + v</math> must be equal to <math>99999</math>. ...eft is which number in each pair goes to <math>u</math> and which to <math>v</math>; there are <math>2</math> ways we can divvy a pair up, which means t
  12 KB (1,896 words) - 23:55, 27 December 2023
• Base numbers
  ...system at all, used certain letters to represent certain values (e.g. I=1, V=5, X=10, L=50, C=100, D=500, M=1000). Imagine how difficult it would be to
  4 KB (547 words) - 17:23, 30 December 2020
• Vector
  ...\,\,y\,\,z\,\,...)</math>. The magnitude of a vector, denoted <math>\|\vec{v}\|</math>, is found simply by ...d by them, <math>\|\vec{v}+\vec{w}\|^2=\|\vec{v}\|^2+\|\vec{w}\|^2+2\|\vec{v}\|\|\vec{w}\|\cos\theta</math>.
  7 KB (1,265 words) - 13:22, 14 July 2021
• Rational approximation
  ...aQ</math> and <math>|qx-(\tilde\beta P-\tilde\alpha v)|\le\tilde\alpha|ux+v|+\tilde\beta|Qx-P|\le ...\le \frac {6a^2}q</math>. Thus, setting <math>p=\tilde\beta P-\tilde\alpha v</math>, we get <math>\left|x-\frac pq\right|<\frac {6a^2}{q^2}</math>.
  7 KB (1,290 words) - 12:18, 30 May 2019
• Algebraic geometry
  ...and let <math>I</math> be a [[prime ideal]] of <math>R</math>. Then <math>V(I)=\{p\in\mathbb{A}^n\mid f(p)=0\mathrm{\ for\ all\ } f\in I\}</math> is ca
  2 KB (361 words) - 01:59, 24 January 2020
• Euler's Polyhedral Formula
  ...of [[vertex|vertices]], [[edge]]s, and [[face]]s, respectively. Then <math>V-E+F=2</math>.
  1,006 bytes (134 words) - 14:15, 6 March 2022
• Mock AMC
  ! scope="row" | '''Mock AMC V'''
  51 KB (6,175 words) - 20:58, 6 December 2023
• 2004 AMC 12A Problems
  Let <math>U=2\cdot 2004^{2005}</math>, <math>V=2004^{2005}</math>, <math>W=2003\cdot 2004^{2004}</math>, <math>X=2\cdot 20 <math>\text{(A) } U-V \qquad \text{(B) } V-W \qquad \text{(C) } W-X \qquad \text{(D) } X-Y \qquad \text{(E) } Y-Z \qqu
  13 KB (1,953 words) - 00:31, 26 January 2023
• 2002 AMC 12B Problems
  ...ngles of a pentagon. Suppose that <math>v < w < x < y < z</math> and <math>v, w, x, y, </math> and <math>z</math> form an arithmetic sequence. Find the
  10 KB (1,547 words) - 04:20, 9 October 2022
• 2004 AIME I Problems/Problem 11
  Our original solid has volume equal to <math>V = \frac13 \pi r^2 h = \frac13 \pi 3^2\cdot 4 = 12 \pi</math> and has [[surf Our original solid <math>V</math> has [[surface area]] <math>A_v = \pi r^2 + \pi r \ell</math>, where
  5 KB (839 words) - 22:12, 16 December 2015
• 1993 AIME Problems
  ...>P^{}_{}</math> pentagonal faces meet. What is the value of <math>100P+10T+V\,</math>?
  8 KB (1,275 words) - 06:55, 2 September 2021
• 1997 AIME Problems
  .... Let <math>m/n</math> be the probability that <math>\sqrt{2+\sqrt{3}}\le |v+w|</math>, where <math>m</math> and <math>n</math> are relatively prime pos
  7 KB (1,098 words) - 17:08, 25 June 2020
• 2000 AIME I Problems
  ...he area of pentagon <math>ABCDE</math> is <math>451</math>. Find <math>u + v</math>.
  7 KB (1,204 words) - 03:40, 4 January 2023
• 2001 AIME II Problems
  ...ine{UV}</math> with <math>U</math> on <math>\overline{PQ}</math> and <math>V</math> on <math>\overline{QR}</math> such that <math>\overline{UV}</math> i
  8 KB (1,282 words) - 21:12, 19 February 2019
• 1983 AIME Problems/Problem 11
  ...Using the formula for the volume of a regular tetrahedron, which is <math>V = \frac{\sqrt{2}S^3}{12}</math>, where S is the side length of the tetrahed <math>V = \frac{1}{2} \cdot \frac{\sqrt{2} \cdot (12\sqrt{2})^3}{12} = \boxed{288}<
  5 KB (865 words) - 21:11, 6 February 2023
• 1985 AIME Problems/Problem 12
  ...rom vertex <math>V</math> and ending at vertex <math>A,</math> where <math>V\in\{A,B,C,D\}</math> and <math>k</math> is a positive integer. We wish to f ...math>V</math> to <math>A</math> and the paths from <math>A</math> to <math>V</math> have one-to-one correspondence. So, we must get <cmath>A_k+B_k+C_k+D
  17 KB (2,837 words) - 13:34, 4 April 2024
• 1986 AIME Problems/Problem 14
  ...th>h = 15</math>, <math>l = 5</math>, <math>w = 10</math>. Therefore <math>V = 5 \cdot 10 \cdot 15 = \boxed{750}</math>
  2 KB (346 words) - 13:13, 22 July 2020
• 1986 AIME Problems/Problem 11
  ...>C = \{1, (x+1), (x+1)^2, ..., (x+1)^{17} \}</math> be two bases for <math>V</math>. ...e polynomial given in the problem, and it is easy to see that <math>[ \vec{v} ]_B = \langle 1, -1, 1, -1, ... , 1, -1 \rangle.</math>
  6 KB (872 words) - 16:51, 9 June 2023
• 1988 AIME Problems/Problem 13
  ...(x)</math> are also roots of <math>f(x)</math>. Let these roots be <math>u,v</math>. We get the system If we multiply the first equation by <math>v^{16}</math> and the second by <math>u^{16}</math> we get <cmath>\begin{alig
  10 KB (1,585 words) - 03:58, 1 May 2023
• 1988 AIME Problems/Problem 10
  ...lies on exactly one vertex of a square/hexagon/octagon, we have that <math>V = 12 \cdot 4 = 8 \cdot 6 = 6 \cdot 8 = 48</math>. ...h of its endpoints, the number of edges <math>E</math> is <math>\frac{3}{2}V = 72</math>.
  5 KB (811 words) - 19:10, 25 January 2021
• 1990 AIME Problems/Problem 14
  Finally, we substitute <math>h</math> into the volume equation to find <math>V = 6\sqrt{133}\left(\frac{99}{\sqrt{133}}\right) = \boxed{594}</math>. ...ave the base area as <math>18\sqrt {133}</math>. Thus, the volume is <math>V = \frac {1}{3}\cdot18\sqrt {133}\cdot\frac {99}{\sqrt {133}} = 6\cdot99 = 5
  7 KB (1,086 words) - 08:16, 29 July 2023
• 1993 AIME Problems/Problem 12
  ...th>(u,v)</math> and <math>(p,q)</math>, then <math>u=2r-p</math> and <math>v=2s-q</math>. So we start with the point they gave us and work backwards. We
  4 KB (611 words) - 13:59, 15 July 2023
• 1993 AIME Problems/Problem 10
  ...<math>P</math> pentagonal faces meet. What is the value of <math>100P+10T+V</math>? ...ge). Thus, <math>E=60</math>. Finally, using Euler's formula we have <math>V=E-30=30</math>.
  4 KB (716 words) - 20:50, 17 April 2022
• 1994 AIME Problems/Problem 6
  ...(-20/sqrt(3),0)-2*u+i*u--(0,20)--(20/sqrt(3),0)+2*d-i*d;draw(shift(0,-2*i)*v);} ...(-20/sqrt(3),0)-2*u+i*u--(0,20)--(20/sqrt(3),0)+2*d-i*d);draw(shift(0,2*i)*v);}
  4 KB (721 words) - 16:14, 8 March 2021
• 1995 AIME Problems/Problem 12
  ...as <math>\vec{u}\cdot \vec{v} = \parallel \vec{u}\parallel \parallel \vec{v}\parallel \cos \theta</math>, we will be able to solve for <math>\cos \thet <cmath>\vec{v} = \overrightarrow{OB}\times \overrightarrow{OC} - \left|\begin{array}{ccc}
  8 KB (1,172 words) - 21:57, 22 September 2022
• 1997 AIME Problems/Problem 14
  ...c{m}{n}</math> be the [[probability]] that <math>\sqrt{2+\sqrt{3}}\le\left|v+w\right|</math>, where <math>m</math> and <math>n</math> are [[relatively p Now, let <math>v</math> be the root corresponding to <math>m\theta=2m\pi/1997</math>, and le
  5 KB (874 words) - 22:30, 1 April 2022
• 1999 AIME Problems/Problem 15
  ...coordinates of the vertex of the resulting pyramid. Call this point <math>V</math>. Clearly, the height of the pyramid is <math>z</math>. The desired v ...= QC</math>. We then use distance formula to find the distances from <math>V</math> to each of the vertices of the medial triangle. We thus arrive at a
  7 KB (1,107 words) - 20:34, 27 January 2023
• 2000 AIME I Problems/Problem 8
  (Computational) The volume of a cone can be found by <math>V = \frac{\pi}{3}r^2h</math>. In the second container, if we let <math>h',r'< From the formula <math>V=\frac{\pi r^2h}{3}</math>, we can find that the volume of the container is
  4 KB (677 words) - 16:33, 30 December 2023
• 2000 AIME I Problems/Problem 2
  ...rea of [[pentagon]] <math>ABCDE</math> is <math>451</math>. Find <math>u + v</math>. D(D(MP("A\ (u,v)",A,(1,0)))--D(MP("B",B,N))--D(MP("C",C,N))--D(MP("D",D))--D(MP("E",E))--cy
  3 KB (434 words) - 22:43, 16 May 2021
• 2001 AIME I Problems/Problem 12
  ...ath>P</math> perpendicular to plane <math>ABC</math> can be found as <math>V=(A-C)\times(B-C)=\langle 8, 12, 24 \rangle</math> ...r each pyramid(base times height divided by 3) we have <math>\dfrac{rF}{3}=V</math>. The surface area of the pyramid is <math>\dfrac{6\cdot{4}+6\cdot{2}
  6 KB (1,050 words) - 18:44, 27 September 2023
• 2014 USAJMO Problems
  ...line{CA}</math> and <math>\overline{AB}</math>, respectively. Let <math>U,V</math> be the intersections of line <math>EF</math> with line <math>MN</mat
  3 KB (600 words) - 16:42, 5 August 2023
• 2003 AIME II Problems/Problem 5
  ...another identical wedge and sticking it to the existing one). Thus, <math>V=\dfrac{6^2\cdot 12\pi}{2}=216\pi</math>, so <math>n=\boxed{216}</math>. Part 1: https://www.youtube.com/watch?v=EzE53aPGbrQ&list=PLSQl0a2vh4HCtW1EiNlfW_YoNAA38D0l4&index=5
  1 KB (204 words) - 17:41, 30 July 2022
• 2001 AIME II Problems/Problem 15
  triple S=(1,0,0), T=(2,0,2), U=(8,6,8), V=(8,8,6), W=(2,2,0), X=(6,8,8); ...-U--V--W--cycle); draw((0,0,1)--T--U--X--(0,2,2)--cycle); draw((0,1,0)--W--V--X--(0,2,2)--cycle);
  4 KB (518 words) - 15:01, 31 December 2021
• 2001 AIME II Problems/Problem 7
  ...ine{UV}</math> with <math>U</math> on <math>\overline{PQ}</math> and <math>V</math> on <math>\overline{QR}</math> such that <math>\overline{UV}</math> i pair P = (0,0), Q = (90, 0), R = (0, 120), S=(0, 60), T=(45, 60), U = (60,0), V=(60, 40), O1 = (30,30), O2 = (15, 75), O3 = (70, 10);
  7 KB (1,112 words) - 02:15, 26 December 2022
• Integration by parts
  <math>\int u\, dv=uv-\int v\,du</math> ...math>u</math> will show up as <math>du</math> and <math>dv</math> as <math>v</math> in the integral on the RHS, <math>u</math> should be chosen such tha
  1 KB (235 words) - 17:01, 11 March 2022
• Holomorphic function
  Specifically, let <math>u, v : \mathbb{R \times R \to R}</math> be definted <cmath> u(x,y) = \text{Re}\,f(x+iy), \qquad v(x,y) = \text{Im}\,f(x+iy) . </cmath>
  9 KB (1,537 words) - 21:04, 26 July 2017
• Expected value
  https://www.youtube.com/watch?v=BBD66Q3KXuI ...enter connecting the midpoints of the two sides of the small triangle with V as an endpoint. Find, with proof, the expected value of the number of full
  4 KB (719 words) - 19:41, 25 November 2020
• 1977 Canadian MO Problems
  the vertex <math>V</math> to this path? MP("P",(-1,0),W);MP("V",(-.5,2.4),N);
  3 KB (560 words) - 19:23, 10 March 2015
• Derivative/Formulas
  | <math>\left(u(x)\times v(x)\right)'=u(x)v'(x)+u'(x)v(x)</math> | <math>\left(\frac{u(x)}{v(x)}\right)' = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}</math>
  3 KB (506 words) - 16:23, 11 March 2022
• P versus NP
  *Given a weighted, undirected graph <math>G = (V,E)</math> and two vertices <math>s, t \in E</math>, does there exist a path
  6 KB (1,104 words) - 15:11, 25 October 2017
• 2015 IMO Problems/Problem 6
  ...for which <cmath>\left\vert\sum_{j=m+1}^n(a_j-(v+1))\right\vert\le (T-v)\,v \le \left(\frac T 2\right)^2</cmath>for all integers <math>m</math> and <ma ...is:<cmath>\sum_{i=1}^v (T-v+i) - \sum_{i=1}^v i=\sum_{i=1}^v (T-v)=(T-v)\,v\;. \quad \blacksquare</cmath>
  4 KB (833 words) - 01:33, 31 December 2019
• Zero (constant)
  ...s had to make change on a purchase of LXIV dollars with bills marked L, X, V and I when handed XC dollars.
  2 KB (371 words) - 12:55, 21 June 2023
• Free group
  ...group over a set <math>I</math> and <math>uv = vu</math>, then <math>u^m = v^n</math>, for some [[integer]]s <math>m</math> and <math>n</math>.
  2 KB (454 words) - 17:54, 16 March 2012
• 2007 iTest Problems
  \text{(V) } 2007 \quad </math> <math>\text{(V) Ying} \quad
  33 KB (5,177 words) - 21:05, 4 February 2023
• 1981 IMO Problems/Problem 2
  ...ng subset. Hence <cmath>F(n,r)=\frac{1}{\binom{n}{r}} \sum_{v \in B} \deg (v)= \frac{n+1}{r+1}.</cmath>
  5 KB (879 words) - 11:18, 27 June 2020
• Roman numerals
  5 - '''V''' ''(quinque)''
  865 bytes (140 words) - 13:58, 24 March 2019
• 2002 IMO Shortlist Problems/N3
  ..., then the [[greatest common factor]] of <math>2^u + 1 </math> and <math>2^v + 1 </math> is 3. ...ath>t </math>, contradicting our assumption that <math>u </math> and <math>v </math> are relatively prime.
  10 KB (1,739 words) - 06:38, 12 November 2019
• 2020 AMC 10A Problems
  label("V", (2, 6), NE);
  13 KB (1,968 words) - 18:32, 29 February 2024
• 2007 AIME II Problems/Problem 15
  ...ale the triangle with the circumradius by a [[line]]ar scale factor, <math>v</math>. :<math>\frac{65}{8}v=8u</math>
  11 KB (2,099 words) - 17:51, 4 January 2024
• 2007 AMC 12A Problems/Problem 20
  ...cut off corners is a [[pyramid]], whose volume can be calculated by <math>V = \frac 13 Bh</math>. Use the base as one of the three [[congruency (geomet
  2 KB (317 words) - 10:10, 16 September 2022
• 1989 USAMO Problems/Problem 2
  Call it a vertex set <math>V</math>. <math>10</math> vertices remain outside <math>V</math> and each has to be attached to at least one edge.
  3 KB (438 words) - 01:19, 27 December 2023
• 1989 USAMO Problems
  Let <math>u</math> and <math>v</math> be real numbers such that (u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8.
  2 KB (326 words) - 18:52, 18 July 2016
• 2007 USAMO Problems/Problem 4
  Chose a vertex, <math>v</math>, for which <math>a</math> is minimal (i.e. out of all maximal elemen ...h>. So then in this special case, we have <math>D = 4</math>, and so <math>V = 2006 \times 4+1</math> (a possible configuration of this size that works
  10 KB (1,878 words) - 14:56, 30 June 2021
• Octahedron
  * The volume <math>V</math> of a regular octahedron with side length <math>a</math> is <math>\fr
  1 KB (155 words) - 12:19, 21 July 2023
• 1989 USAMO Problems/Problem 5
  Let <math>u</math> and <math>v</math> be real numbers such that <cmath> (u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8. </cmath>
  2 KB (300 words) - 19:16, 18 July 2016
• 2004 AMC 12A Problems/Problem 11
  ...bstituting yields: <math>20n+25=21(n+1),</math> so <math>n=4</math>, <math>v = 80.</math> Then, we see that the only way Paula can satisfy this rule is
  2 KB (310 words) - 17:39, 31 December 2022
• 2004 AMC 12A Problems/Problem 6
  Let <math>U=2\cdot 2004^{2005}</math>, <math>V=2004^{2005}</math>, <math>W=2003\cdot 2004^{2004}</math>, <math>X=2\cdot 20 <math>\mathrm {(A)} U-V \qquad \mathrm {(B)} V-W \qquad \mathrm {(C)} W-X \qquad \mathrm {(D)} X-Y \qquad \mathrm {(E)} Y-
  1 KB (139 words) - 02:10, 30 December 2020
• Binet's Formula
  ...d <math>p= \frac{1-\sqrt{5}}{2}.</math> We get that <cmath>F_n = \lambda_1 v^n + \lambda_2 p^n.</cmath>Plugging in our initial conditions, we get <cmath>0 = \lambda_1 + \lambda_2 </cmath> <cmath> 1= \lambda_1 v + \lambda_2 p </cmath>
  3 KB (550 words) - 16:12, 24 February 2024
• Celsius
  ...cncn vmnsnfdv jcd vndlfencm savdnm vs,czfvndm ,cxafkvsnsm dvhbfvm c,cdfemw v,dsnekmc xvzmvsdv vndnf cnvdjnf dfnwfd fwe vndkbfwenj sdbfwenj fbhkfenlkjs
  4 KB (357 words) - 22:40, 17 April 2024
• Mass
  ...math>, where <math>M</math> is momentum, <math>m</math> is mass, and <math>v</math> is [[velocity]].
  1 KB (188 words) - 22:44, 10 October 2013
• Graph (graph theory)
  ...may be defined using ordered pairs from the [[product set]] <math>V \times V</math>. ...ay the edges <math>e</math> and <math>f</math> are ''coincident'' at <math>v</math>.
  8 KB (1,428 words) - 10:26, 27 August 2020
• 2000 AMC 12 Problems/Problem 13
  https://www.youtube.com/watch?v=OT42J21ZNC8&feature=youtu.be https://www.youtube.com/watch?v=7QU8OlnljHw ~David
  6 KB (996 words) - 18:14, 29 June 2023
• 1997 PMWC Problems
  ...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);
  15 KB (2,057 words) - 19:13, 10 March 2015
• 1951 AHSME Problems
  ...he area <math>(A)</math> of the sail and the square of the velocity <math>(V)</math> of the wind. The pressure on a square foot is <math>1</math> pound
  23 KB (3,641 words) - 22:23, 3 November 2023
• 2002 AMC 12B Problems/Problem 5
  ...s of a [[pentagon]]. Suppose that <math>v < w < x < y < z</math> and <math>v, w, x, y, </math> and <math>z</math> form an [[arithmetic sequence]]. Find ...ath> triangles) is <math>3 \cdot 180 = 540^{\circ}</math>. If we let <math>v = x - 2d, w = x - d, y = x + d, z = x+2d</math>, it follows that
  2 KB (263 words) - 05:58, 8 August 2023
• 2003 AMC 12B Problems/Problem 17
  ...that <cmath>2 \cdot \textbf{(2)} + \textbf{(1)} = 5u + 5v = 3 \implies u + v = \frac{3}{5} \implies c = \boxed{\textbf{(D)}~\frac{3}{5}}</cmath>.
  2 KB (329 words) - 13:49, 4 April 2024
• Isogonal conjugate
  ...nes. Let coordinates of images of points be <cmath>X(-a, 0), X'(a,u), Y(-b,v), Y'(b,w).</cmath> ...f a straight line <math>XY</math> is <math>\frac{x + a}{a - b} = \frac {y}{v}.</math>
  54 KB (9,416 words) - 08:40, 18 April 2024
• 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

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