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• 2010 AMC 8 Problems/Problem 3
  ...-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(
  5 KB (847 words) - 19:59, 5 February 2023
• 1954 AHSME Problems
  ...an upright V.}\\ \textbf{(D)}\ \text{Two line segments forming an inverted V.}\\ \textbf{(E)}\ \text{None of these.} </math>
  23 KB (3,535 words) - 16:29, 24 April 2020
• 1999 USAMO Problems/Problem 1
  ...fication/Lemma:}</math> The sum of degrees of a connected graph <math>G = (V,E)</math> is <math>2V -2 + 2R = 2E,</math> where <math>R</math> is the circ <math>\textit{Proof.}</math> <math>2 \times V -2</math> is the sum of ranks of the spanning tree created by decircuiting
  4 KB (747 words) - 05:23, 13 May 2023
• 1977 USAMO Problems/Problem 5
  ...true with equality iff either (1) <math>p = q</math> or (2) three of <math>v, w, x, y, z</math> are <math>p</math> and two are <math>q</math> or vice ve
  2 KB (389 words) - 23:08, 27 June 2018
• 2020 Mock Combo AMC 10
  ...itive integers <math>s, t, u, v, w, x, y, z</math> where <math>s > t > u > v > w > x > y > z</math>. Find <math>2(z + u) + s + t + v + w + x + y</math>.
  15 KB (2,452 words) - 03:03, 4 July 2020
• Lagrange Multipliers
  The volume of the box is given by the equation <math>V(x, y, z) = xyz</math>. Because the way the box is described, the point that ...<cmath>\dfrac{\partial V}{\partial y} = xz</cmath> <cmath>\dfrac{\partial V}{\partial z} = xy</cmath>
  5 KB (791 words) - 21:06, 30 November 2020
• 2013 AMC 10A Problems/Problem 14
  We can use Euler's polyhedron formula that says that <math>F+V=E+2</math>. We know that there are originally <math>6</math> faces on the
  1 KB (169 words) - 21:46, 28 December 2019
• 2013 AMC 12A Problems/Problem 25
  ...t of a radical of a complex number: <math>\sqrt{u}</math>, where <math>u = v+wi = r e^{i\theta}</math>. ...(\theta/2) = \pm \sqrt{r}\sqrt{\frac{1-\cos\theta}{2}} = \pm \sqrt{\frac{r-v}{2}}</math>.
  4 KB (766 words) - 14:22, 8 October 2023
• 2013 USAMO Problems/Problem 1
  label("$V$", (1.7922953932137468,0.6108747864253139), NE * labelscalefactor); label("$V$", (1.7922953932137468,0.6108747864253139), NE * labelscalefactor);
  14 KB (1,830 words) - 18:22, 10 May 2023
• 2013 USAJMO Problems/Problem 5
  ...u-v}{u+v}\right), \frac{2uv}{u+v})</math>. Also, <math>Z\left(\frac{u-v}{u+v}\right), 0)</math>. It shall be left to the reader to find the slope of <ma
  7 KB (1,250 words) - 18:05, 1 October 2021
• Mock AIME 3 2006-2007 Problems/Problem 8
  ...(\frac{1}{16},\frac{1}{8},\frac{1}{13})</math>. Let <math> \overrightarrow{v} </math> be a vector with head <math>(\frac{1}{16},\frac{1}{8},\frac{1}{13}
  1 KB (213 words) - 20:48, 15 February 2015
• 2014 AIME II Problems/Problem 10
  ...r labeling the complex numbers with <math>W</math> (<math>w</math>), <math>V</math> (<math>-z</math>), and <math>O</math> (<math>0</math>), we can inter
  6 KB (1,045 words) - 13:08, 21 January 2024
• Northeastern WOOTers Mock AIME I Problems
  ...uv.xy}+\overline{xy.uv} </cmath> is an integer? As an example, if <math>(u,v,x,y)=(0,1,2,3)</math>, then we have <math> N = 1.23 + 23.01 = 24.24 </math>
  8 KB (1,336 words) - 09:10, 30 May 2020
• 1983 IMO Problems/Problem 4
  ...>. Again, by the observation in the previous paragraph, the points <math>U,V,T</math> must have different colors if we are to have no monochromatic righ
  2 KB (373 words) - 23:40, 29 January 2021
• 2013 IMO Problems/Problem 2
  ...th> is even and <math>v</math> is odd and <math>u - v = 1</math>, is <math>v</math>. ...ts and v blue ones (<math>u</math> is even, <math>v</math> is odd, <math>u>v</math>).
  3 KB (643 words) - 01:31, 19 November 2023
• 1971 IMO Problems/Problem 5
  I shall prove a more general statement about the unit distance graph(<math>V=\mathbb{R}^2</math>, adjacency iff the Euclidean distance between the point ...here <math>G\times H</math> is described as <math>V(G\times H)=V(G)\times V(H), (v_1,w_1)\leftrightarrow (v_2,w_2) \Leftrightarrow v_1=v_2,w_1\leftrigh
  4 KB (749 words) - 14:09, 29 January 2021
• 1972 IMO Problems/Problem 2
  ...h>) that we can find a circle passing through <math>U,D</math> (or <math>F,V</math>) which cuts the segments <math>UV,DF</math> in <math>X,Y</math>. Our
  1 KB (224 words) - 18:15, 7 December 2022
• 1972 IMO Problems/Problem 6
  ...h that the translation with translation vector <math>k\cdot\overrightarrow{v}_p</math> maps the plane <math>p_i</math> to the plane <math>p_j</math>. Si
  7 KB (1,370 words) - 15:42, 29 January 2021
• 1973 IMO Problems/Problem 2
  Let <math>V</math> be a solid cube or right angled parallelepiped Let <math>M_{v}</math> be the set of all 8 vertices of <math>V</math>
  4 KB (663 words) - 21:33, 21 November 2023
• 1951 AHSME Problems/Problem 28
  ...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 .../math>. Solving for <math>V</math>, we get <math>V^2=1024</math>, so <math>V=32</math>. Hence, the answer is <math>\boxed{C}</math>.
  1 KB (220 words) - 19:45, 20 November 2014

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