# Search results

• $\sum_{closed loop} \Delta V = 0$
406 bytes (67 words) - 20:36, 7 March 2014
• ...non-zero vector that satisfies the relation $A\bold{v} = \lambda\bold{v}$, for some scalar $\lambda \in K$. In other words, applyi ...bold{v} = \lambda \bold{v}[/itex], then $\lambda I \bold{v} - A \bold{v} = \bold{O}$. But then, the column vectors of $\lambda I - A</ma 20 KB (3,415 words) - 23:26, 9 October 2021 • ...r constant [itex]\lambda$ such that $L \bold{v} = \lambda \bold{v}$. Here, $\lambda$ is known as the '''eigenvalue''' associ
821 bytes (138 words) - 19:32, 2 March 2010
• ...h>, there exists a connected open set $V$ such that $x \in V \subset C$. $X$ is locally connected if it is locally conn ...here exists a path-connected open set $V$ such that $x \in V \subset C$. $X$ 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 $U, V$ such that $x \in U, y \in V$ and $U,V$ are [[disjoint]].
5 KB (672 words) - 13:28, 4 June 2018
• ...[[vector]]s $v_1, v_2, \ldots, v_n$ in a [[vector space]] $V$ over a field $K$ are '''linearly independent''' if there ...ndependent [[iff]] their [[determinant]] $D(\bold{v}_1, \ldots, \bold{v}_n) = 0$.
2 KB (300 words) - 23:35, 16 March 2010
• 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 (543 words) - 19:52, 27 January 2021
• ...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
8 KB (1,400 words) - 02:19, 8 August 2021
• main(int a, char **v) { int n=atoi(v[1]),
1 KB (188 words) - 18:08, 21 February 2011
• A segment through the focus $F$ of a parabola with vertex $V$ is perpendicular to $\overline{FV}$ 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 $v$, $w$, $x$, $y$, and $z label("v",(0.5,2.5)); 5 KB (718 words) - 22:46, 29 June 2021 • ...h>V$ and $W$ are on $\overline{AC}$ with $V$ on $\overline{AW}$, points $X$ and $Y</ma pair[] A, B, C, U, V, W, X, Y, Z; 10 KB (1,638 words) - 21:57, 10 August 2020 • ...h>V$ and $W$ are on $\overline{AC}$ with $V$ on $\overline{AW}$, points $X$ and $Y</ pair[] A, B, C, U, V, W, X, Y, Z; 6 KB (1,077 words) - 21:47, 12 April 2022 • ...math>P(v) = 4$, which will give us the working range $5 \le x < v$. v^2 - 3v - 9 &= 4 \\
8 KB (1,273 words) - 21:25, 30 January 2022
• ...> <cmath>\vec{w} = \vec{CD} + \vec{FA}</cmath> Clearly, $\vec{u}+\vec{v}+\vec{w}=\textbf{0}$. ...th>. Thus, $|\vec{u}|=2p \cos \gamma$. Similarly, $|\vec{v}|=2q \cos \alpha$ and $|\vec{w}| = 2r \cos \beta$.
10 KB (1,923 words) - 16:56, 26 August 2020
• A segment through the focus $F$ of a parabola with vertex $V$ is perpendicular to $\overline{FV}$ and intersects the pa ...e equidistant from $F$ and $l$. Therefore $FV=d(V,l)$. Let this distance be $d$. Now note that $d(F,l)= 4 KB (619 words) - 19:15, 11 May 2021 • ! scope="row" | '''Mock AMC V''' 18 KB (2,206 words) - 19:41, 24 December 2020 • label("V-4\beta",(0,-0.3),red); /* AUTO-GRAPH V-4 beta by PythonNut*/ 17 KB (2,910 words) - 15:01, 2 September 2011 • <cmath> V. x+y = 13, \{49, 58, 67, 76, 85, 94\} = 6 </cmath> 5 KB (805 words) - 15:53, 20 February 2022 • ...{v} \rfloor$ means the greatest integer less than or equal to $v$.)
1 KB (155 words) - 07:58, 22 October 2014
• .../math> and the remainder is $v$, where $u$ and $v$ are integers. \textbf{(D)}\ v \qquad
2 KB (266 words) - 03:30, 23 July 2019
• The volume of a cylinder is given by the formula $V=\pi r^2 h$. The given cylinder therefore has a volume of $\pi (1 2 KB (266 words) - 00:09, 5 July 2013 • ...? Because Uberdude supplied a hint that the answer begins with the letter V, and a vole seemed as good as anything else. Vole are small rodents, like m 307 bytes (64 words) - 12:59, 10 September 2012 • ...-4), P=(1,-3.8), Q=(1,-3.6), R=(1,-3.4), S=(1,-3.2), T=(1,-3), U=(1,-2.8), V=(1,-2.6), W=(1,-2.4), Z=(1,-2.2), E_1=(1.4,-2.6), F_1=(1.8,-2.6), O_1=(14,- ...th(1pt)); D(S,linewidth(1pt)); D(T,linewidth(1pt)); D(U,linewidth(1pt)); D(V,linewidth(1pt)); D(W,linewidth(1pt)); D(Z,linewidth(1pt)); D(E_1,linewidth( 18 KB (2,742 words) - 20:46, 29 July 2021 • ...,-2), M=(0,-6), O=(0,-4), P=(4,-4), Q=(2,-2), R=(2,-6), T=(6,4), U=(10,0), V=(10,4), Z=(10,2), A_1=(8,4), B_1=(8,0), C_1=(6,-2), D_1=(10,-2), E_1=(6,-6) ...--cycle,linewidth(1.6)); draw(M--O--Q--R--cycle,linewidth(1.6)); draw(A_1--V--Z--cycle,linewidth(1.6)); draw(G_1--K_1--J_1--E_1--cycle,linewidth(1.6)); 16 KB (2,345 words) - 00:46, 16 January 2022 • [itex]\text{(v)}$ Without the use of logarithm tables evaluate $\frac{1}{\log_{ 4 KB (540 words) - 18:23, 8 October 2014 • [itex]\text{(v)}$ Without the use of logarithm tables evaluate $\frac{1}{\log_{ [itex]\text{(v)}$ <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));
3 KB (544 words) - 19:57, 17 August 2021
• ...{v} \rfloor[/itex] means the greatest integer less than or equal to $v$.)
15 KB (2,247 words) - 13:44, 19 February 2020
• ...th>. What is the probability that the square region determined by $T(v)$ 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 $T(v)$ contains exactly two points with integer coefficients in its interi ...math>v=(x,y)[/itex] will create the translation of $S$, $T(v)$ such that it covers both $(0,0)$ and $(1,0)$.
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
• ...of the escalator and $c$ be the speed of Clea. Using $d = v t$, the first statement can be translated to the equation $d = 6 2 KB (291 words) - 22:22, 29 September 2020 • The volume of this pyramid can be found by the equation [itex]V=\frac{1}{3}bh$, where $b$ is the base and $h$ i Finally, $V=\frac{1}{3}bh=\frac{1}{3}(225)(10)=\boxed{750}$.
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 $EF=x$, $XD=u$, and $DF=v$. Then $XE^2-XF^2=EF^2=DE^2-DF^2$, so we get
10 KB (1,790 words) - 17:17, 15 January 2022
• ...ank}(A)=r<4[/itex], prove the existence of two invertible matrices $U,V\in M_4(C)$, such that:
10 KB (1,695 words) - 10:03, 10 May 2012
• ...h>, distance $a$, formula $v=\frac{a}{t}$ or $a=v \cdot t$.
1 KB (191 words) - 14:40, 20 April 2014
• ...ind a vertical vector $v$ such that $(A^8+A^6+A^4+A^2+I)v=\left(\begin{matrix}0\\11\end{matrix}\right)$ (where $I </math 4 KB (596 words) - 20:09, 27 May 2012 • ...ind a vertical vector [itex] v$ such that $(A^8+A^6+A^4+A^2+I)v=\left(\begin{matrix}0\\11\end{matrix}\right)$ (where $I </math ...ght)v=\left(\begin{matrix}0\\11\end{matrix}\right)$. Letting $v=\left(\begin{matrix}a\\b\end{matrix}\right)$, 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 (840 words) - 15:22, 15 August 2021
• ...an upright V.}\\ \textbf{(D)}\ \text{Two line segments forming an inverted V.}\\ \textbf{(E)}\ \text{None of these.} [/itex]
23 KB (3,535 words) - 16:29, 24 April 2020
• ...fication/Lemma:}[/itex] The sum of degrees of a connected graph $G = (V,E)$ is $2V -2 + 2R = 2E,$ where $R$ is the circ $\textit{Proof.}$ $2 \times V -2$ is the sum of ranks of the spanning tree created by decircuiting
2 KB (440 words) - 01:58, 27 November 2017
• ...true with equality iff either (1) $p = q$ or (2) three of $v, w, x, y, z$ are $p$ and two are $q$ or vice ve
2 KB (389 words) - 23:08, 27 June 2018
• ...itive integers $s, t, u, v, w, x, y, z$ where $s > t > u > v > w > x > y > z$. Find $2(z + u) + s + t + v + w + x + y$.
15 KB (2,452 words) - 03:03, 4 July 2020
• The volume of the box is given by the equation $V(x, y, z) = xyz$. 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 $F+V=E+2$. We know that there are originally $6$ faces on the
1 KB (169 words) - 21:46, 28 December 2019
• ...t of a radical of a complex number: $\sqrt{u}$, where $u = v+wi = r e^{i\theta}$. ...(\theta/2) = \pm \sqrt{r}\sqrt{\frac{1-\cos\theta}{2}} = \pm \sqrt{\frac{r-v}{2}}[/itex].
4 KB (767 words) - 16:52, 3 April 2020
• label("$V$", (1.7922953932137468,0.6108747864253139), NE * labelscalefactor); label("$V$", (1.7922953932137468,0.6108747864253139), NE * labelscalefactor);
14 KB (1,823 words) - 22:03, 22 October 2021
• ...u-v}{u+v}\right), \frac{2uv}{u+v})[/itex]. Also, $Z\left(\frac{u-v}{u+v}\right), 0)$. 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})[/itex]. Let $\overrightarrow{v}$ be a vector with head $(\frac{1}{16},\frac{1}{8},\frac{1}{13} 1 KB (213 words) - 20:48, 15 February 2015 • ...uv.xy}+\overline{xy.uv} </cmath> is an integer? As an example, if [itex](u,v,x,y)=(0,1,2,3)$, then we have $N = 1.23 + 23.01 = 24.24$
8 KB (1,336 words) - 09:10, 30 May 2020
• ...>. Again, by the observation in the previous paragraph, the points $U,V,T$ 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 $v$ is odd and $u - v = 1$, is $v$. ...ts and v blue ones ($u$ is even, $v$ is odd, $u>v$).
3 KB (638 words) - 04:30, 18 June 2018
• I shall prove a more general statement about the unit distance graph($V=\mathbb{R}^2$, adjacency iff the Euclidean distance between the point ...here $G\times H$ is described as $V(G\times H)=V(G)\times V(H), (v_1,w_1)\leftrightarrow (v_2,w_2) \Leftrightarrow v_1=v_2,w_1\leftrigh 4 KB (749 words) - 14:09, 29 January 2021 • ...h>) that we can find a circle passing through [itex]U,D$ (or $F,V$) which cuts the segments $UV,DF$ in $X,Y$. Our
1 KB (230 words) - 15:35, 29 January 2021
• ...h that the translation with translation vector $k\cdot\overrightarrow{v}_p$ maps the plane $p_i$ to the plane $p_j$. Si
7 KB (1,370 words) - 15:42, 29 January 2021
• ...he area $(A)$ of the sail and the square of the velocity $(V)$ of the wind. The pressure on a square foot is $1$ pound .../math>. Solving for $V$, we get $V^2=1024$, so $V=32$. Hence, the answer is $\boxed{C}$.
1 KB (220 words) - 19:45, 20 November 2014
• ...line{CA}[/itex] and $\overline{AB}$, respectively. Let $U,V$ be the intersections of line $EF$ with line $MN</mat pair A, B, C, I, M, N, P, E, F, U, V, X, R; 7 KB (1,273 words) - 18:17, 28 August 2021 • The volume [itex]V = \pi R^2H$ 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), $\text{V. Averaging has an identity element }$
18 KB (2,788 words) - 13:55, 20 February 2020
• ...1,1)[/itex] and $C(0,1)$. Let $u=x^2-y^2$, and $v=xy$ be a transformation of the $xy$-plane into the $u ...h>x = \tfrac{v}{2}$, $u = (\tfrac{v}{2})^2 - 1$, so $v = 2\sqrt{u+1}$, where $-1 \le u \le 0$. That means some o
2 KB (377 words) - 17:24, 20 June 2018
• ...1,1)[/itex] and $C(0,1)$. Let $u=x^2-y^2$, and $v=2xy$ be a transformation of the $xy$-plane into the $16 KB (2,662 words) - 14:12, 20 February 2020 • . A gateway valve has actually a v-ring packaging establish that secures the shaft that's affixed to the gatew 4 KB (596 words) - 22:28, 25 August 2021 • ...),-sqrt(5)), W=(4+2/sqrt(5),sqrt(5)), T=(4,0), U=(4+2/sqrt(5),-4/sqrt(5)), V=(4+2/sqrt(5),1/sqrt(5)); draw(X--Y--Z--W--X^^T--V--X^^Y--U); 17 KB (2,535 words) - 13:45, 19 February 2020 • [itex]\{V, W, X, Y, Z\}$. Using this correspondence, the cryptographer finds th
16 KB (2,291 words) - 13:45, 19 February 2020
• ...[/itex] to $A, B$ and $C$, respectively, be $u, v$ and $w$. ...est distance that $P$ can be from $D$ if $u^2 + v^2 = w^2$?
15 KB (2,309 words) - 23:43, 2 December 2021
• \text{(v) }y+a\ge x [/itex]
15 KB (2,437 words) - 04:39, 26 November 2021
• the vertex $V$ 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 [/itex]
929 bytes (137 words) - 22:05, 10 January 2019
2 KB (270 words) - 14:35, 29 July 2018
• ...oor[/itex] (the greatest integer less than or equal to the volume of $V$).
510 bytes (87 words) - 23:03, 7 October 2014
• $\text{(V) Ying} \quad 1 KB (202 words) - 16:48, 24 November 2018 • \text{(V) }21 \quad 2 KB (340 words) - 19:49, 30 June 2018 • label("u",T+(-0.1,-0.2), S); label("v", S+(0,-0.2), S); Denote [itex]\angle{HSB}=v$, $\angle{HTD}=u$, $\angle{HSC}=s$, $\angl 6 KB (1,071 words) - 03:58, 8 September 2018 • .../math> and the remainder is [itex]v$, where $u$ and $v$ are integers. \textbf{(D)}\ v \qquad
19 KB (2,907 words) - 14:16, 20 February 2020
• If $V = gt + V_0$ and $S = \frac {1}{2}gt^2 + V_0t$, then $[itex] \textbf{(A)}\ \frac{2S}{V+V_0}\qquad 20 KB (3,039 words) - 22:44, 12 February 2021 • ...),-sqrt(5)), W=(4+2/sqrt(5),sqrt(5)), T=(4,0), U=(4+2/sqrt(5),-4/sqrt(5)), V=(4+2/sqrt(5),1/sqrt(5)); draw(X--Y--Z--W--X^^T--V--X^^Y--U); 2 KB (334 words) - 14:11, 27 February 2018 • ...>T$ is halfway between $Q$ and $R$, then $V$ is halfway between $P$ and $S$. Therefore, <m
2 KB (349 words) - 02:41, 23 October 2014
• $\{V, W, X, Y, Z\}$. Using this correspondence, the cryptographer finds th ...to $0$, $3$, and $4$), we must have $V = 2$ and $Y = 1$. Thus $XYZ = 413_{5} = 4 \cdot 5^{2} 2 KB (242 words) - 14:32, 1 March 2018 • ...pairs (not counting transpositions because this does not affect ([itex]u + v$), $(2, 8), (4, 4), (-2, -8), (-4, -4)$, yields $a = 2 KB (372 words) - 00:28, 27 September 2021 • ...dron and [itex]TD$ 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) - 09:24, 28 December 2021
• 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 (266 words) - 18:02, 16 June 2020
• ...>a\neq 0[/itex] (else $f$ is not cubic) where $\{q,r,s,t,u,v\}$ is the same as the set $\{1,2,3,5,6,7\}$. 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 (1,359 words) - 12:04, 24 April 2022
• ...he volume of water thus displaced is $v$ cubic feet. Find $v^2$.
8 KB (1,326 words) - 12:19, 13 March 2020
• ...he volume of water thus displaced is $v$ cubic feet. Find $v^2$. <cmath>v = \frac{1}{3}(2\sqrt{6})\left(\frac{1}{2} \cdot (2\sqrt{6})^2\right) = \fra
3 KB (510 words) - 19:22, 16 March 2021
• Let $M=(u,v)$, then $T=(2u+\cos(2A), 2v-\sin(2A))$. ...cos(2A))^2+ (2v-\sin(2A))^2=1[/itex], namely $v\sin(2A)-u\cos(2A)=u^2+v^2$. (E2)
5 KB (902 words) - 09:58, 20 August 2021
• Let $M=(u,v)$, then $T=(2u+\cos(2A), 2v-\sin(2A))$. ...cos(2A))^2+ (2v-\sin(2A))^2=1[/itex], namely $v\sin(2A)-u\cos(2A)=u^2+v^2$. (E2)
4 KB (760 words) - 16:45, 29 April 2020
• | <span class="aops-font">V</span> | V
6 KB (920 words) - 16:40, 3 March 2021
• https://www.youtube.com/watch?v=TFm1jNgB4QM ...maybe so?) we get $\frac{d}{v}=\frac{1}{3}$ and $\frac{d}{v+18}=\frac{1}{5}$.
3 KB (442 words) - 13:04, 14 April 2022
• ...e, we can set up a proportion based on the principle that $d=\frac{m}{V}$, thus $dV=m$.
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
• ...[/itex] to $A, B$ and $C$, respectively, be $u, v$ and $w$. ...est distance that $P$ can be from $D$ if $u^2 + v^2 = w^2$?
1 KB (255 words) - 01:11, 20 February 2019
• ...$\overline{MS}$ intersects $\overline{OP}$ at $V$ . If $AB = 2,$ $BC = 2005,$ $CD = 4,</mat 7 KB (1,094 words) - 15:39, 24 March 2019 • r, s, t, u, v, w, x, y, and z such that n + l + v − y = 0 14 KB (2,904 words) - 18:24, 16 May 2017 • The vertices [itex]V$ 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}}(
11 KB (1,828 words) - 09:44, 8 November 2021
• ...th>1\leq j\leq 12[/itex], an element $z_j$ is chosen from $V$ at random, independently of the other choices. Let [itex]P={\prod}_{
15 KB (2,418 words) - 14:43, 12 August 2020
• <cmath>V = Bh/3</cmath> <cmath>V = (192)(25\sqrt{3}/2)/3</cmath>
6 KB (986 words) - 06:59, 28 December 2020

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