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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
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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