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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
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  • 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>
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  • <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}</
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  • 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>
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  • ..., 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
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  • <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.
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  • ...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>
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  • 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>
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  • 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>
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  • ...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?
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  • <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
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  • 'v'
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  • 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
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  • <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>.
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  • 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);
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  • <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
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  • <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>
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  • Lucky Seven V ARE YOU XPERIENCED? V
    3 KB (452 words) - 10:21, 17 November 2022
  • Suppose that on a parabola with vertex <math>V</math> and a focus <math>F</math> there exists a point <math>A</math> such
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  • Denote <math>u = 1 - x</math>, <math>v = 1 - y</math>, <math>w = 1 - z</math>. \sqrt{(1-u)(1+v)} + \sqrt{(1+u)(1-v)} & = 1 \hspace{1cm} (1) \\
    15 KB (2,208 words) - 01:25, 1 February 2024
  • ...t{10}} , \sqrt{10} \right)</math>, <math>Q = \left( \sqrt{10} , \frac{10 - v}{\sqrt{10}} \right)</math>. We have <math>m_{HP} = \frac{3}{6 - u}</math> and <math>m_{PQ} = - \frac{v}{u}</math>.
    16 KB (2,274 words) - 09:02, 10 December 2022
  • Let <math>O</math> be the center of the base, <math>V</math> be the vertex of the base.
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  • pair A, B, C, D, E, F, G, H, A1, B1, C1, D1, E1, F1, G1, H1, V; V = (3,0);
    24 KB (3,567 words) - 18:14, 30 August 2022
  • Now here comes the smart part. Substitute <math>y = \sqrt[3]{u} - \sqrt[3]{v}</math>. ...<math>u - 3\sqrt[3]{u^2v} + 3\sqrt[3]{uv^2} - v + p\sqrt[3]{u} - p\sqrt[3]{v} + q = 0</math>. Simplification:
    6 KB (1,059 words) - 14:42, 11 December 2020
  • Let <math>u = 10 – y, v = 9 – x.</math> https://www.youtube.com/watch?v=jDP2PErthkg
    5 KB (794 words) - 15:36, 30 August 2022
  • ...3}</math> then we can find a line <math>\ell</math> perpendicular to <math>v</math> such that <math>\ell</math> separates <math>S</math>, and any point Suppose there is no such direction <math>v</math>, then <math>S</math> is contained in a box with side length <math>n^
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  • Suppose that on a parabola with vertex <math>V</math> and a focus <math>F</math> there exists a point <math>A</math> such ...d <math>Y</math> be the orthogonal projections of <math>F</math> and <math>V</math> onto <math>AQ</math>. Because <math>AF < AV</math>, there are two po
    4 KB (796 words) - 17:33, 13 July 2021
  • ...ur squares on the middle of the edges after n moves, and <math>V_n</math> (V for vertex) be the probability that Frieda is on a corner after n moves. Th https://youtube.com/watch?v=kHLR57iP0cU
    17 KB (2,801 words) - 07:29, 4 November 2022
  • ...<math>u</math> and <math>v</math> in <math>G</math>. Every tree on <math>|V|=n</math> vertices has exactly <math>n-1</math> edges.
    401 bytes (75 words) - 16:51, 2 November 2020
  • V&=\frac16\cdot AB\cdot AD\cdot BD \\
    3 KB (496 words) - 19:12, 28 October 2022
  • ...tuy + vy^2 + svy + tv</math>, simplifying to <math>y^4 + (s + u)y^3 + (t + v + su)y^2 + (sv + tu)y + tv</math>. [[Equating coefficients]] gives the foll ...begin{cases} s + u = 0 \text{ since the } y^3 \text{ term is 0} \\ p = t + v + su \\ q = sv + tu \\ r = tv \end{cases}</math>
    13 KB (2,376 words) - 16:56, 19 February 2024
  • ...</math> and <math>2</math> along <math>\textbf{u}</math> and <math>\textbf{v}</math> respectively, then find <cmath>\sum_{i=1}^{n}\|\textbf{r}_i\|^2.</c
    7 KB (1,149 words) - 17:16, 15 December 2020
  • ...đến sâu răng, mất răng. Vì vậy, cần phát hiện kịp thời và điều trị đúng cách mòn cổ răng. ...rãnh này, lâu dần tạo mảng bám, gây viêm nhiễm, tụt lợi và ảnh hưởng tới thẩm mỹ. Cổ răng mòn nhiều thậm chí có
    5 KB (1,261 words) - 05:15, 7 January 2021
  • ...math> OV</math> (but not in <math> \vec{OV}</math>) for some vertex <math> V</math> of the polygon. Each two of these lines are obtained one from anothe
    2 KB (284 words) - 11:02, 30 January 2021
  • 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>
    1,023 bytes (167 words) - 15:57, 4 July 2023
  • 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
    737 bytes (129 words) - 22:53, 12 February 2021
  • ...$c$", D--C, N); label("$d$",D--A,W); label("$u$",D--B,2*dir(170)); label("$v$",A--C,S); ...c, d</math>, be the sides, <math>s</math> the semiperimeter, and <math>u, v</math>, the diagonals. Then the area, <math>K</math>, is given by <cmath>K
    10 KB (1,669 words) - 17:33, 12 January 2024
  • Denote <math>D' – A' = 2\vec V.</math> ...\triangle A'C'E'</math> into <math>\triangle D'F'B'</math> is <math>2\vec {V.}</math>
    5 KB (875 words) - 00:26, 23 May 2023
  • ...<math>n=2k+1</math>, just take <math>(u,v)= (k+1,k)</math> which <math>u^2-v^2=n</math>. Thus the only answer is <math>\boxed{f\equiv 1}</math> and we a https://www.youtube.com/watch?v=Q1NUBUYvOJc
    8 KB (1,492 words) - 00:23, 24 February 2024
  • ...th>t</math> is square free and <math>gcd(u,v,w) = 1</math>, find <math>t+u+v+w</math> if <math>x=\cos 20^o</math> and <math>y=\sin 20^o</math>.
    8 KB (1,385 words) - 12:55, 23 June 2021
  • We could assume a variable <math>v</math> which equals to both <math>\log_{20x} (22x)</math> and <math>\log_{2 So that <math>(20x)^v=22x \textcircled{1}</math>
    5 KB (778 words) - 18:14, 30 January 2024
  • ...s, plus the outer region, <math>E</math> is the number of edges, and <math>V</math> is the number of vertices. Temporarily disregarding the intersection <math>V=V_{i}+210=222</math>
    12 KB (2,025 words) - 14:56, 25 January 2024
  • ...\qquad \text{(iii) }x+y\ge a\\ \\ \qquad \text{(iv) }x+a\ge y\qquad \text{(v) }y+a\ge x</math>
    665 bytes (119 words) - 18:31, 28 August 2023
  • ...t,st),E); label("M",(cu,su),N);label("P",(cu,st),S); label("C",(cos(v),sin(v)),W); //Credit to Zimbalono for the diagram </asy>
    864 bytes (169 words) - 16:47, 23 June 2021
  • ...th>C(1) = 0</math> and our recursive rules for <math>C(n)</math> and <math>V(n)</math> as follows: n & V(n) & C(n) \\ \hline
    8 KB (1,309 words) - 00:31, 6 January 2023
  • .../math> bisects the angle between <math>\mathbf{u}</math> and <math>\mathbf{v}</math>.
    16 KB (2,526 words) - 00:53, 6 May 2023
  • ...h>. Hence, <math>B = \left( - 1 , u \right)</math>, <math>D = \left( 0 , - v \right)</math>. The slope of <math>AD</math> is <math>m_{AD} = \frac{v}{3}</math>.
    5 KB (756 words) - 03:40, 23 January 2023
  • v v
    2 KB (259 words) - 22:11, 23 March 2024
  • Let <math>G</math> be a graph with the set of vertices <math>V=\{v_1,v_2,v_3,\ldots, v_n\}</math>. We define its adjacency matrix <math>\
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  • ...> the formula for variance if <math>X</math> is a [[population]] is <cmath>V = \frac{1}{n}\sum_{i=1}^n (x_i - \overline{x})^2.</cmath> Additionally, <math>V = \sigma^2</math> where <math>\sigma</math> is the population [[standard de
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  • ...>, (2) <math>\hat{x}\equiv x\pmod{p^{n-k}}</math> and (3) <math>k=v(p'(x))=v(p'(\hat{x}))</math>. <center><cmath>v=u+p^{n-2k}zs\in u+p\mathbb{Z}_p\subset \mathbb{Z}_p^{\times}</cmath></cente
    13 KB (2,298 words) - 23:34, 28 May 2023
  • pair o = (0, 0), u = (1, 0), v = 0.8*dir(40), w = dir(70); draw(o--u--(u+v));
    7 KB (1,154 words) - 12:54, 20 February 2024
  • ...t{R}(\text{T}))</math> where <math>\text{R}(\text{T})=\{\text{T}(x)~|~x\in V\}</math>. In other words, rank is the dimension of the linear transformati ...aim that if <math>\beta=\{v_1,v_2,\ldots, v_n\}</math> is a basis of <math>V</math>, then
    5 KB (893 words) - 22:41, 28 May 2022
  • ...math> In accordance with Claim, <math>\angle BVD = \angle HVE \implies B', V,</math> and <math>B</math> are collinear.
    10 KB (1,751 words) - 15:34, 25 November 2022
  • ...mathbf{n}\,dS,</cmath> where <math>R</math> is a region whose volume <math>V(R)</math> shrinks to <math>0</math> about the point <math>p</math>, <math>\ ...mathbf{n}\,dS,</cmath> where <math>R</math> is a region whose volume <math>V(R)</math> shrinks to <math>0</math> about the point <math>p</math>, <math>\
    7 KB (1,189 words) - 06:00, 21 December 2022
  • ...the three roots of the polynomial. The lengthened prism's volume is <cmath>V = (a+2)(b+2)(c+2) = abc+2ac+2ab+2bc+4a+4b+4c+8 = abc + 2(ab+ac+bc) + 4(a+b+ We can substitute these into the expression, obtaining <cmath>V = \frac{6}{10} + 2\left(\frac{29}{10}\right) + 4\left(\frac{39}{10}\right)
    7 KB (1,111 words) - 21:00, 21 February 2024
  • ...e R.H.S. is a not a perfect square. Thus, the number of positive <math>(u, v)</math> is equal to the number of positive divisors of <math>2 r^2</math>. ...n if <math>(a, b)</math> with <math>a = 2 r - u</math> and <math>b = 2 r - v</math>.
    7 KB (1,271 words) - 12:09, 4 January 2024
  • We denote by <math>\left( u, v \right)</math> the coordinates of circle <math>C_0</math>, and <math>r</mat u^2 + v^2 = \left( 8 - r \right)^2 . \hspace{1cm} (1)
    7 KB (1,202 words) - 01:15, 10 June 2023
  • .../math>, define the binary operation <math>\otimes</math> by<cmath>u\otimes v=ac+bdi.</cmath>Suppose <math>z</math> is a complex number such that <math>z
    13 KB (2,107 words) - 18:42, 27 March 2024
  • pair P,Q,R,S,T,U,V,W; P=(0,30); Q=(30,30); R=(40,40); S=(10,40); T=(10,10); U=(40,10); V=(30,0); W=(0,0);
    20 KB (2,846 words) - 13:22, 25 February 2024
  • <math>V=\pi{r^2}h</math> <math>V=\pi{r^2}(14-2r)</math>
    4 KB (697 words) - 17:07, 24 March 2023
  • path v=(5,-0.5)--(5,0)--(5,1)--(6,1)--(6,2)--(6,3)--(6,4)--(7,4); draw(v,p);
    11 KB (1,834 words) - 22:01, 4 January 2024
  • pair o = (0, 0), u = (1, 0), v = 0.8*dir(40), w = dir(70); draw(o--u--(u+v));
    13 KB (2,130 words) - 01:52, 31 January 2024
  • <cmath> V = \frac{1}{3} \cdot x \cdot (S_1 + \sqrt{S_1S_2} + S_2) = \frac{1}{3} \cdot Let the volume without water be <math>V,</math> volume of the pyramid <math>SCGJ</math> be <math>U.</math>
    10 KB (1,574 words) - 16:42, 8 March 2024
  • ...en so are <math>f(V)</math>, <math>V+W</math>, <math>V-W</math>, and <math>V \cdot W</math>.
    5 KB (772 words) - 08:50, 23 February 2023
  • Plugging in <math>A</math> and <math>B</math> gives <math>u=v=0</math>. Plugging in <math>P</math> gives Since it passes through <math>A</math>, for some <math>v, w</math>, the equation of circle <math>(ABP)</math> is,
    7 KB (1,280 words) - 01:22, 6 February 2024
  • Plugging in <math>A</math> and <math>B</math> gives <math>u=v=0</math>. Plugging in <math>P</math> gives
    4 KB (684 words) - 01:55, 6 February 2024
  • <cmath>u = 5y - 1, v = 2x - 3y + 1 \implies u^2 - 5 v^2 = - 4 \implies</cmath>
    15 KB (2,351 words) - 08:28, 20 April 2023
  • https://youtube.com/watch?v=LAuyU2OuVzE ...and <math>w=\frac{2b^3cx_0z_0}{c^2y_0^2-b^2z_0^2}</math>, so <cmath>\frac{v}{w}=\frac{b^2z_0}{c^2y_0},</cmath> which is the required condition for <mat
    14 KB (2,600 words) - 23:37, 10 March 2024
  • ...n c&oacute; biết tại sao SXMN lại c&oacute; sức hấp dẫn như vậy hay kh&ocirc;ng, h&atilde;y c&ugrave;ng l&yacute; giải qua b&agrave;i <p><strong><span style="color: #000000;">XSMN ph&aacute;t triển với mục đ&iacute;ch &Iacute;ch nước lợi nh&agrave;</span></strong><
    11 KB (2,230 words) - 23:24, 9 May 2023
  • 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
    87 KB (14,763 words) - 14:11, 11 January 2024
  • ...math>AB</math> and <math>AC</math> meet the line <math>AU</math> and <math>V</math> and <math>W</math>, respectively. The lines <math>BV</math> and <ma
    737 bytes (124 words) - 01:00, 17 November 2023
  • ...th>f(u) = f(t^{2}+v) = f^{-1}(v)+f(t)^{2}> f^{-1}(v) = f(f(f^{-1}(v))) = f(v)</math>. Hence f is strictly increasing. It is now clear that since <math>f
    1 KB (282 words) - 14:53, 12 March 2024
  • ...sed as <math>(2u-3w, v+4w)</math> with <math>0\le u\le1</math>, <math>0\le v\le1,</math> and <math>0\le w\le1</math>?
    13 KB (1,959 words) - 05:52, 6 January 2024
  • <math>V = \sqrt{(a^2 + b^2 - c^2)(b^2 + c^2 - a^2)(a^2 + c^2 - b^2)/72}</math> ...umes <cmath>[ABCI] + [ABDI] + [ACDI] + [BCDI] = V,</cmath> We have <cmath>V = \frac{4AR}{3}.</cmath> Plugging in and simplifying, we get <math>R = \fra
    13 KB (1,978 words) - 15:49, 12 March 2024
  • label("$v'$", (0, 2.18), NE); ...eed to find <math>v</math> with the largest imaginary part such that <math>v^2</math> lies on <math>\omega</math>.
    6 KB (1,055 words) - 21:58, 28 February 2024
  • https://www.youtube.com/watch?v=dxYw1wYHid4&t=12s ...t, to find the amount of vertices we can use Euler's characteristic, <math>V - E + F = 2</math>, and therefore the amount of vertices is <math>12</math>
    12 KB (2,101 words) - 21:56, 25 February 2024
  • ...nvex polyhedra, <math>V-E+F=2</math>. In our case, <math>V-24+12=2\implies V=14.</math> We know that <math>A+B</math> is the total number of vertices as Note that Euler's formula is <math>V+F-E=2</math>. We know <math>F=12</math> from the question. We also know <ma
    7 KB (1,175 words) - 16:45, 28 January 2024
  • pair K, L, M, N, O, P, Q, R, S, T, U, V; pair K, L, M, N, O, P, Q, R, S, T, U, V;
    19 KB (2,967 words) - 16:56, 24 February 2024
  • ...sed as <math>(2u-3w, v+4w)</math> with <math>0\le u\le1</math>, <math>0\le v\le1,</math> and <math>0\le w\le1</math>? ...h <math>x</math> and <math>y</math>. We first fix <math>u</math> and <math>v</math> to <math>0</math>, and graph <math>(-3w,4w)</math> from <math>0\le w
    4 KB (584 words) - 16:13, 26 November 2023
  • V
    814 bytes (128 words) - 10:36, 11 November 2023
  • Denote <math>m = k u</math> and <math>n = k v</math>. Thus, <math>{\rm gcd} \left( u, v \right) = 1</math>.
    4 KB (612 words) - 22:25, 22 March 2024
  • pair P,Q,R,S,T,U,V,W; P=(0,30); Q=(30,30); R=(40,40); S=(10,40); T=(10,10); U=(40,10); V=(30,0); W=(0,0);
    3 KB (428 words) - 00:13, 26 March 2024
  • For complex number <math>u = a+bi</math> and <math>v = c+di</math> (where <math>i=\sqrt{-1}</math>), define the binary operation <math>u \otimes v = ac + bdi</math>
    1 KB (205 words) - 02:52, 20 November 2023
  • Given the problem \( (f(x) + f(y))(f(u) + f(v)) = f(xu - yv) + f(xv - yu) \), we aim to find a function that satisfies it We start by considering the case when \( x = y = u = v = 0 \).
    2 KB (369 words) - 16:12, 26 March 2024
  • * [[V Olimpiada Iberoamericana de Matemáticas (OIM) ]] Valladolid, España , 19 * [[X Olimpiada Iberoamericana de Matemáticas (OIM) ]] Región V, Chile , 1995
    14 KB (1,323 words) - 12:18, 13 December 2023
  • ...at if <math>x+yt+zt^2 \ne 0</math>, then there exist <math>u</math>, <math>v</math>, and <math>w</math> as rational numbers such that:
    511 bytes (84 words) - 13:28, 13 December 2023
  • <math>V=\sum_{i}^{}2^ik_i=13^3</math> where <math>k_i</math> is the quantity of cub
    2 KB (387 words) - 10:29, 23 December 2023
  • ...lar polygon with <math>n</math> sides, <math>n \ge 4</math>, and let <math>V</math> be a subset of <math>r</math> vertices of the polygon. Show that if vertices are in <math>V</math>.
    396 bytes (66 words) - 04:02, 14 December 2023
  • ...h> by 2000, and <math>y'</math> is the reminder of the division of <math>y+v'</math> by 2001. There are two ships on the board: the Martian one and the
    1 KB (256 words) - 04:26, 14 December 2023
  • ...h> is greater than the ''dragonian distance'' from <math>C</math> to <math>V</math>.
    1,015 bytes (177 words) - 16:49, 14 December 2023
  • 458 bytes (44 words) - 17:51, 14 December 2023
  • X [[Olimpiada Iberoamericana de Matemáticas]] was held in Región V, Chile , 1995
    455 bytes (45 words) - 17:53, 14 December 2023
  • ...here <math>d(v)</math> indicates the distance from <math>A</math> to <math>v</math>. Consider the outgoing edges <math>(A,X)</math> and <math>(A,M)</mat https://www.youtube.com/watch?v=RRTxlduaDs8
    5 KB (809 words) - 03:31, 6 February 2024
  • Let <math>DD' = x, FF'= y, DH = u, FH = v \implies HH' = \frac{yu + vx}{u+v }= \frac {7}{16}.</math> <cmath>V = \frac{d}{6} \cdot \left(A_1 + A_2 + 4 A_0 \right).</cmath>
    13 KB (2,069 words) - 07:40, 1 February 2024