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  • <math>\delta x'(t)=v(t)</math> <math>v'(t)=a(t)</math>
    9 KB (1,355 words) - 07:29, 29 September 2021
  • 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
  • ...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
  • ...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
  • ...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
  • ...\,\,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
  • ...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
  • ...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
  • ...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
  • ! scope="row" | '''Mock AMC V'''
    51 KB (6,175 words) - 20:58, 6 December 2023
  • 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
  • ...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
  • 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
  • ...>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
  • .... 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
  • ...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
  • ...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
  • ...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
  • ...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 (2,829 words) - 21:21, 21 February 2024
  • ...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
  • ...>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
  • ...(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
  • ...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
  • 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
  • ...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
  • ...<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
  • ...(-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
  • ...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
  • ...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
  • ...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
  • (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
  • ...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
  • ...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
  • ...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
  • ...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
  • 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
  • ...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
  • <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
  • 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
  • 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
  • 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
  • | <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
  • *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
  • ...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
  • ...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
  • ...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
  • \text{(V) } 2007 \quad </math> <math>\text{(V) Ying} \quad
    33 KB (5,177 words) - 21:05, 4 February 2023
  • ...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
  • 5 - '''V''' ''(quinque)''
    865 bytes (140 words) - 13:58, 24 March 2019
  • ..., 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
  • label("V", (2, 6), NE);
    13 KB (1,968 words) - 18:32, 29 February 2024
  • ...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
  • ...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
  • 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
  • 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
  • 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
  • * 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
  • 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
  • ...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
  • 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
  • ...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
  • ...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
  • ...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
  • 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
  • ...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
  • ...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
  • ...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
  • ...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 (321 words) - 02:08, 11 February 2024
  • ...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>
    50 KB (8,763 words) - 16:41, 26 March 2024
  • <math>V = \pi \left(\frac{3}{\pi}\right)^2\cdot 6\sin\theta</math>
    1 KB (166 words) - 16:35, 15 February 2021
  • 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
  • ...>. 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
  • ...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
  • ...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
  • ...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
  • ...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
  • 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
  • ...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
  • *Didion 1870. ''Notice sur la vie et les ouvrages du général J. V. Poncelet''
    2 KB (253 words) - 11:41, 19 December 2018
  • ...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
  • ...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
  • ...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
  • ...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
  • ..., 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
  • ...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
  • ...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
  • <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
  • It is equivalent to <math>\gamma=\dfrac{1}{\sqrt{1-v^2/c^2}}</math>
    226 bytes (34 words) - 11:23, 5 October 2012
  • By another person ^v^
    5 KB (807 words) - 18:37, 25 June 2021
  • ...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
  • 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
  • ...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
  • ...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
  • ...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
  • 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
  • <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
  • ...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
  • ...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
  • V be the foot of the projection of K to AC.
    1 KB (283 words) - 01:15, 19 November 2023
  • 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
  • ...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
  • <cmath>T=32-3k\Rightarrow V=24-4k.</cmath>
    807 bytes (122 words) - 00:08, 5 July 2013
  • 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
  • ...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
  • ...[[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
  • ...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
  • <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
  • <math>\sum_{closed loop} \Delta V = 0</math>
    406 bytes (67 words) - 20:36, 7 March 2014
  • ...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
  • ...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
  • ...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
  • ...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
  • ...[[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
  • :<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
  • 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
  • pair V=(0,0.5); draw(V--O);
    3 KB (544 words) - 20:54, 24 March 2024
  • ...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
  • main(int a, char **v) { int n=atoi(v[1]),
    1 KB (188 words) - 18:08, 21 February 2011
  • 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
  • ...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
  • ...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
  • ...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
  • ...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
  • ...> <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
  • 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
  • ! scope="row" | '''Mock AMC V'''
    18 KB (2,206 words) - 19:41, 24 December 2020
  • 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
  • <cmath> V. x+y = 13, \{49, 58, 67, 76, 85, 94\} = 6 </cmath>
    6 KB (882 words) - 11:45, 12 November 2023
  • ...{v} \rfloor</math> means the greatest integer less than or equal to <math>v</math>.)
    1 KB (155 words) - 07:58, 22 October 2014
  • .../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
  • 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
  • ...? 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
  • ...-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
  • ...,-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
  • <math>\text{(v)}</math> Without the use of logarithm tables evaluate <math>\frac{1}{\log_{
    4 KB (540 words) - 18:23, 8 October 2014
  • <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
  • ...,-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
  • ...{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
  • ...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
  • ...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
  • ...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
  • ...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
  • ...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
  • 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
  • ...,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
  • ...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
  • ...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
  • ...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
  • ...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
  • ...-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
  • ...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
  • ...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
  • ...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
  • ...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
  • 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
  • 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
  • ...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
  • 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
  • ...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
  • ...(\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
  • ...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
  • ...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
  • ...>. 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
  • ...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
  • 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
  • ...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
  • ...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
  • 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
  • ...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
  • ...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 pair A, B, C, I, M, N, P, E, F, U, V, X, R;
    7 KB (1,273 words) - 18:17, 28 August 2021
  • The volume <math>V = \pi R^2H</math> is to be increased by the same fixed positive amount when
    21 KB (3,242 words) - 21:27, 30 December 2020
  • Of the following five statements, I to V, about the binary operation of averaging (arithmetic mean), <math>\text{V. Averaging has an identity element }</math>
    18 KB (2,788 words) - 13:55, 20 February 2020
  • ...1,1)</math> and <math>C(0,1)</math>. Let <math>u=x^2-y^2</math>, and <math>v=xy</math> be a transformation of the <math>xy</math>-plane into the <math>u ...h>x = \tfrac{v}{2}</math>, <math>u = (\tfrac{v}{2})^2 - 1</math>, so <math>v = 2\sqrt{u+1}</math>, where <math>-1 \le u \le 0</math>. That means some o
    2 KB (377 words) - 17:24, 20 June 2018
  • ...1,1)</math> and <math>C(0,1)</math>. Let <math>u=x^2-y^2</math>, and <math>v=2xy</math> be a transformation of the <math>xy</math>-plane into the <math>
    16 KB (2,662 words) - 14:12, 20 February 2020
  • ...),-sqrt(5)), W=(4+2/sqrt(5),sqrt(5)), T=(4,0), U=(4+2/sqrt(5),-4/sqrt(5)), V=(4+2/sqrt(5),1/sqrt(5)); draw(X--Y--Z--W--X^^T--V--X^^Y--U);
    17 KB (2,535 words) - 13:45, 19 February 2020
  • <math>\{V, W, X, Y, Z\}</math>. Using this correspondence, the cryptographer finds th
    16 KB (2,291 words) - 13:45, 19 February 2020
  • ...</math> to <math>A, B</math> and <math>C</math>, respectively, be <math>u, v</math> and <math>w</math>. ...est distance that <math>P</math> can be from <math>D</math> if <math>u^2 + v^2 = w^2</math>?
    15 KB (2,309 words) - 23:43, 2 December 2021
  • \text{(v) }y+a\ge x </math>
    15 KB (2,432 words) - 01:06, 22 February 2024
  • the vertex <math>V</math> to this path? MP("P",(-1,0),W);MP("V",(-.5,2.4),N);
    889 bytes (136 words) - 15:53, 7 October 2014
  • real t=pi/8;real u=7*pi/12;real v=13*pi/12; draw((ct,st)--(-ct,st)--(cos(v),sin(v)));
    17 KB (2,732 words) - 13:54, 20 February 2020
  • \text{(V) } 2007 \quad </math>
    929 bytes (137 words) - 22:05, 10 January 2019
  • \text{(V) } 21\qquad
    2 KB (270 words) - 14:35, 29 July 2018
  • ...oor</math> (the greatest integer less than or equal to the volume of <math>V</math>).
    510 bytes (87 words) - 23:03, 7 October 2014
  • <math>\text{(V) Ying} \quad
    1 KB (202 words) - 16:48, 24 November 2018
  • \text{(V) }21 \quad
    2 KB (340 words) - 19:49, 30 June 2018
  • label("$u$",T+(-0.1,-0.2), S); label("$v$", S+(0,-0.2), S); Denote <math>\angle{HSB}=v</math>, <math>\angle{HTD}=u</math>, <math>\angle{HSC}=s</math>, <math>\angl
    6 KB (1,071 words) - 03:58, 8 September 2018
  • .../math> and the remainder is <math>v</math>, where <math>u</math> and <math>v</math> are integers. \textbf{(D)}\ v \qquad
    19 KB (2,907 words) - 14:16, 20 February 2020
  • If <math>V = gt + V_0</math> and <math>S = \frac {1}{2}gt^2 + V_0t</math>, then <math> <math> \textbf{(A)}\ \frac{2S}{V+V_0}\qquad
    20 KB (3,039 words) - 22:44, 12 February 2021
  • ...),-sqrt(5)), W=(4+2/sqrt(5),sqrt(5)), T=(4,0), U=(4+2/sqrt(5),-4/sqrt(5)), V=(4+2/sqrt(5),1/sqrt(5)); draw(X--Y--Z--W--X^^T--V--X^^Y--U);
    2 KB (334 words) - 14:11, 27 February 2018
  • ...>T</math> is halfway between <math>Q</math> and <math>R</math>, then <math>V</math> is halfway between <math>P</math> and <math>S</math>. Therefore, <m
    2 KB (349 words) - 02:41, 23 October 2014
  • <math>\{V, W, X, Y, Z\}</math>. Using this correspondence, the cryptographer finds th ...to <math>0</math>, <math>3</math>, and <math>4</math>), we must have <math>V = 2</math> and <math>Y = 1</math>. Thus <math>XYZ = 413_{5} = 4 \cdot 5^{2}
    2 KB (242 words) - 14:32, 1 March 2018
  • ...pairs (not counting transpositions because this does not affect (<math>u + v</math>), <math>(2, 8), (4, 4), (-2, -8), (-4, -4)</math>, yields <math>a =
    2 KB (372 words) - 00:28, 27 September 2021
  • ...dron and <math>TD</math> as the height. Thus, the desired volume is <cmath>V = \dfrac{1}{3} bh = \dfrac{1}{3}\cdot[ABC]\cdot TD = \dfrac{1}{3} \cdot 6 \ <cmath>V = \dfrac{1}{3} Bh = \dfrac{1}{3} h \cdot BE \cdot \dfrac{6\sqrt{2}}{5} = \d
    4 KB (574 words) - 07:18, 16 August 2023
  • path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); filldraw(shift((j,i))*v,black);
    2 KB (280 words) - 23:07, 26 June 2023
  • ...>a\neq 0</math> (else <math>f</math> is not cubic) where <math>\{q,r,s,t,u,v\}</math> is the same as the set <math>\{1,2,3,5,6,7\}</math>. Subtracting t <cmath>24=a((t+u+v-(q+r+s))x^2-a(tu+uv+tv-(qr+qs+rs))x+a(tuv-qrs)</cmath>
    8 KB (1,474 words) - 10:00, 10 November 2023
  • ...he volume of water thus displaced is <math>v</math> cubic feet. Find <math>v^2</math>.
    8 KB (1,326 words) - 19:15, 13 January 2024
  • ...he volume of water thus displaced is <math>v</math> cubic feet. Find <math>v^2</math>. <cmath>v = \frac{1}{3}(2\sqrt{6})\left(\frac{1}{2} \cdot (2\sqrt{6})^2\right) = \fra
    7 KB (1,074 words) - 01:49, 22 January 2024
  • Let <math>M=(u,v)</math>, then <math>T=(2u+\cos(2A), 2v-\sin(2A))</math>. ...cos(2A))^2+ (2v-\sin(2A))^2=1</math>, namely <math>v\sin(2A)-u\cos(2A)=u^2+v^2</math>. (E2)
    5 KB (902 words) - 09:58, 20 August 2021
  • Let <math>M=(u,v)</math>, then <math>T=(2u+\cos(2A), 2v-\sin(2A))</math>. ...cos(2A))^2+ (2v-\sin(2A))^2=1</math>, namely <math>v\sin(2A)-u\cos(2A)=u^2+v^2</math>. (E2)
    4 KB (760 words) - 16:45, 29 April 2020
  • | <span class="aops-font">V</span> | V
    6 KB (924 words) - 21:31, 22 February 2024
  • For starters, we identify d as distance and v as velocity (speed) ...equation gives us: <math>\frac{d}{v}=\frac{1}{3}</math> and <math>\frac{d}{v+18}=\frac{1}{5}</math>.
    4 KB (608 words) - 17:05, 17 January 2024
  • ...e, we can set up a proportion based on the principle that <math>d=\frac{m}{V}</math>, thus <math>dV=m</math>.
    2 KB (325 words) - 14:21, 19 January 2021
  • 231. Gmaas once demanded Epic Games to give him 5,000,000 V-bucks for his 569823rd birthday. EDIT: This is why Gmaas no longer has an E
    69 KB (11,805 words) - 20:49, 18 December 2019
  • pair V = incenter(A,C,P); dot("$I_C$", V, NW);
    5 KB (1,004 words) - 15:15, 28 June 2020
  • <math>V</math> is the foot ot perpendicular from <math>O</math> to <math>AI_A.</mat
    6 KB (998 words) - 21:36, 17 October 2022
  • ...</math> to <math>A, B</math> and <math>C</math>, respectively, be <math>u, v</math> and <math>w</math>. ...est distance that <math>P</math> can be from <math>D</math> if <math>u^2 + v^2 = w^2</math>?
    1 KB (255 words) - 01:11, 20 February 2019
  • ...<math>\overline{MS}</math> intersects <math>\overline{OP}</math> at <math>V</math> . If <math>AB = 2,</math> <math>BC = 2005,</math> <math>CD = 4,</mat
    7 KB (1,094 words) - 15:39, 24 March 2019
  • r, s, t, u, v, w, x, y, and z such that n + l + v − y = 0
    14 KB (2,904 words) - 18:24, 16 May 2017
  • The vertices <math>V</math> of a centrally symmetric hexagon in the complex plane are given by <cmath>V=\left\{ \sqrt{2}i,-\sqrt{2}i, \frac{1}{\sqrt{8}}(1+i),\frac{1}{\sqrt{8}}(
    18 KB (2,878 words) - 01:47, 16 December 2023
  • ...th>1\leq j\leq 12</math>, an element <math>z_j</math> is chosen from <math>V</math> at random, independently of the other choices. Let <math>P={\prod}_{
    15 KB (2,418 words) - 16:58, 7 November 2022
  • <cmath>V = Bh/3</cmath> <cmath>V = (192)(25\sqrt{3}/2)/3</cmath>
    7 KB (1,177 words) - 15:55, 5 January 2024
  • <cmath>z \equiv 16 + 0 + v + 0 + w + 0 = 16 + v + w \pmod{32}, </cmath> where <math>v</math> represents <math>15\cdot 2^{2+2k}p^3</math> and <math>w</math> repre
    10 KB (1,657 words) - 19:08, 24 April 2023
  • ...ition offered at Walton High School (Walton MathFest was a high school (JV/V) level math tournament until the 2017-2018 school year).
    1 KB (158 words) - 20:16, 9 August 2017
  • ...ition offered at Walton High School (Walton MathFest was a high school (JV/V) level math tournament until the 2017-2018 school year).
    1 KB (158 words) - 20:20, 9 August 2017
  • One could also construct a graph G=(V,E) with the set V of vertices (also called nodes or points) and the set E of edges (also call
    5 KB (858 words) - 00:36, 29 November 2023
  • <math>\quad\bullet\qquad</math> <math>V,</math> a reflection across the <math>y</math>-axis. ...beled vertices back to their original positions? (For example, <math>R, R, V, H</math> is one sequence of <math>4</math> transformations that will send
    16 KB (2,417 words) - 01:03, 28 April 2022
  • <cmath>\bar V = \frac {3a^3}{\pi r^2 h} = \frac {3r}{\pi h} \cdot \left( \frac {a}{r} \ri <cmath> \bar V = \frac {3}{\pi f^3} \le \frac {8}{9 \pi} = 0.283.</cmath>
    6 KB (1,034 words) - 10:12, 7 June 2023
  • path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); filldraw(shift((j,i))*v,black);
    15 KB (2,237 words) - 23:08, 15 November 2023
  • ...>. Using the formula for the volume of a triangular pyramid, we have <math>V = \frac{1}{3} \cdot \frac{1}{2} \cdot 3 = \frac{1}{2}</math>. Also, since t Plugging <math>x</math> and <math>y</math> into the formula <math>V = \dfrac{b \cdot h}{3},</math> we find that the volume is <math>\boxed{2}</
    8 KB (1,287 words) - 01:13, 16 January 2024
  • path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); filldraw(shift((j,i))*v,black);
    4 KB (609 words) - 19:49, 27 August 2023
  • Now all these nine polyhedrons lie inside <math>2 P_1</math>. Let <math>V</math> be the volume of <math>P_1</math>.
    1 KB (242 words) - 13:55, 29 January 2021
  • The volume <math>V = \pi R^2H</math> is to be increased by the same fixed positive amount when
    1 KB (245 words) - 19:07, 17 May 2018
  • https://www.youtube.com/watch?v=sT-wxV2rYqs ...AC = b, AB = c, x_1 = BX, x_2 = CX, \frac{c+t}{x_1} = u, \frac{b+t}{x_2} = v.</math>
    13 KB (2,200 words) - 21:36, 6 January 2024
  • ..., we can always choose <math>3-r</math> as the remainder for our set <math>V</math>, giving us a total of <math>r + 3 - r \equiv 0 \pmod{3}</math>. The
    26 KB (4,044 words) - 13:58, 24 January 2024
  • <cmath>v_{13}(27^m-1^m)=v_{13}(26)+v(m)=1+v(m), 3m = n</cmath> which clearly implies <math>m=13</math> and <math>39 | n
    10 KB (1,448 words) - 19:22, 4 January 2024
  • ...<math>1800-x</math>. Since Eve is the slowest, we can call her speed <math>v</math>, so that Ina's speed is <math>2v</math> and Paul's speed is <math>4v ...e of <math>1800-x</math> which takes them a time of <math>\frac{1800-x}{4v+v}</math>. Paul must run the same distance back to <math>B</math>, so his tot
    3 KB (516 words) - 03:25, 16 January 2023
  • ...ots, v_n), \vec{w} = (w_1, \cdots, w_n)</math> is defined to be <math>\vec{v}\cdot\vec{w} = \sum_{i=1}^n v_i w_i</math>. The dot product is [[linear|bil ...el, from which the identity <math>\vec{v} \cdot \vec{v} = \left \Vert \vec{v} \right \Vert ^2</math> follows.
    1 KB (199 words) - 23:10, 19 February 2022
  • ...B travels half the time at <math>u</math> miles per hour and half at <math>v</math> miles per hour. The average speed of Car A is <math>x</math> miles p <cmath>y = \frac{u+v}{2}</cmath>
    2 KB (396 words) - 19:03, 22 June 2021
  • Let the volume of the trough be <math>V</math> liters. Also, let the rate of the cold water tap be <math>C</math> <cmath>V = 21E</cmath>
    1 KB (268 words) - 16:32, 28 July 2018
  • Of the following five statements, I to V, about the binary operation of averaging (arithmetic mean), <math>\text{V. Averaging has an identity element }</math>
    2 KB (432 words) - 13:57, 20 February 2020
  • ...positions of the midpoints <math> U</math> of <math> BA</math> and <math> V</math> of <math> AC</math> as <math> \angle OPA</math> varies?
    3 KB (499 words) - 13:29, 2 August 2021
  • <math>\quad\bullet\qquad</math> <math>V,</math> a reflection across the <math>y</math>-axis. ...beled vertices back to their original positions? (For example, <math>R, R, V, H</math> is one sequence of <math>4</math> transformations that will send
    16 KB (2,497 words) - 21:14, 12 November 2023
  • ...P}\setminus\{\mathbf{v}\}</math> obtained by omitting vector <math>\mathbf{v}</math> from <math>\mathcal{P}</math> can be partitioned into two sets of e
    2 KB (369 words) - 23:35, 21 April 2019
  • ...P}\setminus\{\mathbf{v}\}</math> obtained by omitting vector <math>\mathbf{v}</math> from <math>\mathcal{P}</math> can be partitioned into two sets of e
    531 bytes (88 words) - 23:37, 21 April 2019
  • ...egree of <math>V</math> (i.e. the number of edges coming into/out of <math>V</math>). This is because to visit any of these vertices, we would have to e ...isit each vertex <math>M(V)</math> times, and must traverse <math>2\cdot M(V)</math> edges connected to each vertex. Specifically, we must traverse all
    8 KB (1,306 words) - 22:18, 1 February 2020
  • 'v'
    19 KB (2,942 words) - 21:22, 21 January 2024
  • Let <math>P(3)=u</math> and <math>P(4) = v</math>. Substituting <math>x=3</math> and <math>x=4</math> into the above q u &= (3-u)(3-v) = 9 - 3u - 3v + uv\\
    10 KB (1,819 words) - 19:34, 17 September 2023
  • ...ngineer Panagiotis Verdes figured out how to make 6×6 and 7×7 cubes. The V-Cube 6 (a 6x6x6 Rubik’s cube) has 157 152 858 401 024 063 281 013 959 519 The 7x7x7 Rubik’s cube (the V-Cube 7) has 19 500 551 183 731 307 835 329 126 754 019 748 794 904 992 692
    5 KB (518 words) - 16:53, 19 February 2024
  • <math>\delta x'(t)=v(t)</math> <math>v'(t)=a(t)</math>
    3 KB (423 words) - 12:58, 8 July 2019
  • ...he base's area, and h is the height's length; for a pyramid, we have <math>V=\frac{1}{3}Bh</math>.
    1 KB (207 words) - 01:39, 15 January 2020
  • 231. Almighty Gmaas once demanded Epic Games to give him 5,000,000 V-bucks for his 569823rd birthday. EDIT: This is why Almighty Gmaas no longer
    85 KB (13,954 words) - 17:25, 22 March 2024
  • label("V", (2, 6), NE); label("V", (2, 6), NE);
    11 KB (1,707 words) - 17:05, 12 November 2023
  • <math>\quad\bullet\qquad</math> <math>V,</math> a reflection across the <math>y</math>-axis. ...beled vertices back to their original positions? (For example, <math>R, R, V, H</math> is one sequence of <math>4</math> transformations that will send
    10 KB (1,653 words) - 23:33, 3 August 2023
  • ...of a cone is <math>\frac{1}{3}\pi r^{2}h</math>. Plugging in we find <math>V = 3\pi \sqrt{7} \implies \boxed{\textbf{(C)}}</math>
    3 KB (493 words) - 16:14, 11 September 2023
  • ...the origin and select a point on each line to define vectors <math>\mathbf{v}_{i}=(x_{i},y_{i})</math>. <cmath>\mathbf{v}_1\cdot\mathbf{v}_2 = v_{1}v_{2}\cos\theta \quad\mathrm{and}\quad
    5 KB (895 words) - 15:03, 8 June 2023
  • <li><math>\log_b{(uv)}=\log_b u + \log_b v.</math></li><p>
    5 KB (701 words) - 10:24, 1 December 2023
  • Let <math>V</math> and <math>F</math> be the vertex and focus of the Parabola <math>P(x
    8 KB (1,223 words) - 15:02, 27 November 2022
  • ...an upright V.}\\ \textbf{(D)}\ \text{Two line segments forming an inverted V.}\\ \textbf{(E)}\ \text{None of these.}</math>
    1 KB (193 words) - 10:42, 6 July 2020
  • ...d a horizontal circle of radius <math>r</math> with a constant speed <math>v</math>, in a conical pendulum. The center of the circle is vertically below ...ath>16 kg</math> which slides at a speed of <math>v</math>, with <math>u > v</math>. Block A slides east while Block B slides in west. The surface has c
    2 KB (439 words) - 11:52, 1 August 2020
  • ...th>x=PT</math>, where the length <math>O_{1}O_{2}</math> splits as <math>u+v</math>. Because the lines <math>PQ</math> and <math>O_{1}O_{2}</math> are p ...u^{2}+(r+x)^{2}-u(r+x) \\ \triangle O_{1}OT&:(r+R_{1})^{2}=v^{2}+(r+x)^{2}+v(r+x)\end{align*}</cmath>
    17 KB (2,852 words) - 03:59, 7 February 2024

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