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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
• 2001 AMC 10 Problems/Problem 22
  ...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));
  5 KB (721 words) - 16:44, 9 August 2022
• 2011 AIME I Problems
  ...h>V</math> and <math>W</math> are on <math>\overline{AC}</math> with <math>V</math> on <math>\overline{AW}</math>, points <math>X</math> and <math>Y</ma pair[] A, B, C, U, V, W, X, Y, Z;
  10 KB (1,634 words) - 22:21, 28 December 2023
• 2011 AIME I Problems/Problem 8
  ...h>V</math> and <math>W</math> are on <math>\overline{AC}</math> with <math>V</math> on <math> \overline{AW} </math>, points <math>X</math> and <math>Y</ pair[] A, B, C, U, V, W, X, Y, Z;
  6 KB (1,077 words) - 21:47, 12 April 2022
• 2011 AIME II Problems/Problem 15
  ...math>P(v) = 4</math>, which will give us the working range <math>5 \le x < v</math>. v^2 - 3v - 9 &= 4 \\
  8 KB (1,273 words) - 14:03, 7 January 2023
• 2011 USAMO Problems/Problem 3
  ...> <cmath>\vec{w} = \vec{CD} + \vec{FA}</cmath> Clearly, <math>\vec{u}+\vec{v}+\vec{w}=\textbf{0}</math>. ...th>. Thus, <math>|\vec{u}|=2p \cos \gamma</math>. Similarly, <math>|\vec{v}|=2q \cos \alpha</math> and <math>|\vec{w}| = 2r \cos \beta</math>.
  11 KB (1,925 words) - 12:07, 31 August 2023
• 2011 AMC 12B Problems/Problem 14
  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 ...e equidistant from <math>F</math> and <math>l</math>. Therefore <math>FV=d(V,l)</math>. Let this distance be <math>d</math>. Now note that <math>d(F,l)=
  4 KB (619 words) - 19:15, 11 May 2021
• Mock Amc 12
  ! scope="row" | '''Mock AMC V'''
  18 KB (2,206 words) - 19:41, 24 December 2020
• Autograph
  label("$V-4\beta$",(0,-0.3),red); /* AUTO-GRAPH V-4 beta by PythonNut*/
  17 KB (2,910 words) - 15:01, 2 September 2011
• 2003 AMC 10B Problems/Problem 25
  <cmath> V. x+y = 13, \{49, 58, 67, 76, 85, 94\} = 6 </cmath>
  6 KB (882 words) - 11:45, 12 November 2023
• 1989 AHSME Problems/Problem 20
  ...{v} \rfloor</math> means the greatest integer less than or equal to <math>v</math>.)
  1 KB (155 words) - 07:58, 22 October 2014
• 1964 AHSME Problems/Problem 3
  .../math> and the remainder is <math>v</math>, where <math>u</math> and <math>v</math> are integers. \textbf{(D)}\ v \qquad
  2 KB (296 words) - 06:04, 31 December 2023
• 1992 AJHSME Problems/Problem 16
  The volume of a cylinder is given by the formula <math>V=\pi r^2 h</math>. The given cylinder therefore has a volume of <math>\pi (1
  2 KB (266 words) - 00:09, 5 July 2013
• KGS math club/solution 10 2
  ...? Because Uberdude supplied a hint that the answer begins with the letter V, and a vole seemed as good as anything else. Vole are small rodents, like m
  307 bytes (64 words) - 12:59, 10 September 2012
• 2010 AMC 8 Problems
  ...-4), P=(1,-3.8), Q=(1,-3.6), R=(1,-3.4), S=(1,-3.2), T=(1,-3), U=(1,-2.8), V=(1,-2.6), W=(1,-2.4), Z=(1,-2.2), E_1=(1.4,-2.6), F_1=(1.8,-2.6), O_1=(14,- ...th(1pt)); D(S,linewidth(1pt)); D(T,linewidth(1pt)); D(U,linewidth(1pt)); D(V,linewidth(1pt)); D(W,linewidth(1pt)); D(Z,linewidth(1pt)); D(E_1,linewidth(
  18 KB (2,768 words) - 21:05, 9 January 2024
• 2011 AMC 8 Problems
  ...,-2), M=(0,-6), O=(0,-4), P=(4,-4), Q=(2,-2), R=(2,-6), T=(6,4), U=(10,0), V=(10,4), Z=(10,2), A_1=(8,4), B_1=(8,0), C_1=(6,-2), D_1=(10,-2), E_1=(6,-6) ...--cycle,linewidth(1.6)); draw(M--O--Q--R--cycle,linewidth(1.6)); draw(A_1--V--Z--cycle,linewidth(1.6)); draw(G_1--K_1--J_1--E_1--cycle,linewidth(1.6));
  16 KB (2,371 words) - 17:34, 9 January 2024
• 1973 Canadian MO Problems
  <math>\text{(v)}</math> Without the use of logarithm tables evaluate <math>\frac{1}{\log_{
  4 KB (540 words) - 18:23, 8 October 2014
• 1973 Canadian MO Problems/Problem 1
  <math>\text{(v)}</math> Without the use of logarithm tables evaluate <math>\frac{1}{\log_{ <math>\text{(v)}</math> <center>
  2 KB (286 words) - 15:14, 21 July 2012
• 2011 AMC 8 Problems/Problem 7
  ...,-2), M=(0,-6), O=(0,-4), P=(4,-4), Q=(2,-2), R=(2,-6), T=(6,4), U=(10,0), V=(10,4), Z=(10,2), A_1=(8,4), B_1=(8,0), C_1=(6,-2), D_1=(10,-2), E_1=(6,-6) ...--cycle,linewidth(1.6)); draw(M--O--Q--R--cycle,linewidth(1.6)); draw(A_1--V--Z--cycle,linewidth(1.6)); draw(G_1--K_1--J_1--E_1--cycle,linewidth(1.6));
  4 KB (557 words) - 00:30, 4 January 2023
• 1989 AHSME Problems
  ...{v} \rfloor</math> means the greatest integer less than or equal to <math>v</math>.)
  15 KB (2,247 words) - 13:44, 19 February 2020
• 2012 AMC 12A Problems
  ...th>. What is the probability that the square region determined by <math>T(v)</math> contains exactly two points with integer coordinates in its interio
  14 KB (2,197 words) - 13:34, 12 August 2020
• 2012 AMC 12A Problems/Problem 23
  ...th>. What is the probability that the square region determined by <math>T(v)</math> contains exactly two points with integer coefficients in its interi ...math>v=(x,y)</math> will create the translation of <math>S</math>, <math>T(v)</math> such that it covers both <math>(0,0)</math> and <math>(1,0)</math>.
  4 KB (658 words) - 20:37, 19 January 2021
• 2012 AMC 12A Problems/Problem 25
  ...ive slope starting at positive 1. The function now looks like the letter V repeated within every square in the first row.
  3 KB (584 words) - 02:55, 26 September 2020
• 2012 AMC 12B Problems/Problem 21
  ...linewidth(4)); dot("$Z$",Z,W,linewidth(4)); label("$u$", B--X, SE);label("$v$", X--Cp, SE); label("$40$", A--B, S); label("$s$", A--X, NW); label("$s$", ...\theta</math> and <math>\angle CDX = \theta-30^\circ</math>. Let <math>CX=v</math>. In <math>\triangle CDX</math> we have
  9 KB (1,451 words) - 10:01, 27 December 2022
• 2012 AMC 10B Problems/Problem 13
  ...of the escalator and <math>c</math> be the speed of Clea. Using <math>d = v t</math>, the first statement can be translated to the equation <math>d = 6
  2 KB (351 words) - 21:42, 21 August 2023
• 2012 AIME II Problems/Problem 5
  The volume of this pyramid can be found by the equation <math>V=\frac{1}{3}bh</math>, where <math>b</math> is the base and <math>h</math> i Finally, <math>V=\frac{1}{3}bh=\frac{1}{3}(225)(10)=\boxed{750}</math>.
  2 KB (362 words) - 16:34, 29 February 2020
• 2012 AIME II Problems/Problem 15
  ...,F)); label("$\gamma$",gamma,dir(180)); label("$u$",X--D,dir(60)); label("$v$",D--F,dir(70)); Let <math>EF=x</math>, <math>XD=u</math>, and <math>DF=v</math>. Then <math>XE^2-XF^2=EF^2=DE^2-DF^2</math>, so we get
  13 KB (2,298 words) - 12:56, 10 September 2023
• 2002 Romanian NMO Problems
  ...ank}(A)=r<4</math>, prove the existence of two invertible matrices <math>U,V\in M_4(C)</math>, such that:
  10 KB (1,695 words) - 10:03, 10 May 2012
• 1997 PMWC Problems/Problem T4
  ...h>, distance <math>a</math>, formula <math>v=\frac{a}{t}</math> or <math>a=v \cdot t</math>.
  1 KB (191 words) - 14:40, 20 April 2014
• 2006 SMT/Advanced Topics Problems
  ...ind a vertical vector <math> v </math> such that <math> (A^8+A^6+A^4+A^2+I)v=\left(\begin{matrix}0\\11\end{matrix}\right) </math> (where <math> I </math
  4 KB (596 words) - 20:09, 27 May 2012
• 2006 SMT/Advanced Topics Problems/Problem 2
  ...ind a vertical vector <math> v </math> such that <math> (A^8+A^6+A^4+A^2+I)v=\left(\begin{matrix}0\\11\end{matrix}\right) </math> (where <math> I </math ...ght)v=\left(\begin{matrix}0\\11\end{matrix}\right) </math>. Letting <math> v=\left(\begin{matrix}a\\b\end{matrix}\right) </math>, we get the system of e
  2 KB (297 words) - 20:09, 27 May 2012

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