Search results

• $\delta x'(t)=v(t)$ $v'(t)=a(t)$
9 KB (1,355 words) - 06:29, 29 September 2021
• Case V) $a+b=5c\Rightarrow (5a-1)(5b-1)=126$ for which there are 2 solu
2 KB (332 words) - 08:37, 30 December 2021
• ...{R} [/itex] be an [[inner product]]. Then for any $\mathbf{a,b} \in V$,
11 KB (1,952 words) - 15:38, 29 December 2021
• ...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) - 16:23, 30 December 2020
• ...\,\,y\,\,z\,\,...)[/itex]. The magnitude of a vector, denoted $\|\vec{v}\|$, is found simply by ...d by them, $\|\vec{v}+\vec{w}\|^2=\|\vec{v}\|^2+\|\vec{w}\|^2+2\|\vec{v}\|\|\vec{w}\|\cos\theta$.
7 KB (1,265 words) - 12:22, 14 July 2021
• ...aQ[/itex] and $|qx-(\tilde\beta P-\tilde\alpha v)|\le\tilde\alpha|ux+v|+\tilde\beta|Qx-P|\le ...\le \frac {6a^2}q$. Thus, setting $p=\tilde\beta P-\tilde\alpha v$, we get $\left|x-\frac pq\right|<\frac {6a^2}{q^2}$.
7 KB (1,290 words) - 11:18, 30 May 2019
• ...and let $I$ be a [[prime ideal]] of $R$. Then $V(I)=\{p\in\mathbb{A}^n\mid f(p)=0\mathrm{\ for\ all\ } f\in I\}$ is ca
2 KB (361 words) - 00:59, 24 January 2020
• ...of [[vertex|vertices]], [[edge]]s, and [[face]]s, respectively. Then $V-E+F=2$.
970 bytes (132 words) - 21:36, 1 February 2021
• ! scope="row" | '''Mock AMC V'''
58 KB (7,011 words) - 21:23, 25 January 2022
• Let $U=2\cdot 2004^{2005}$, $V=2004^{2005}$, $W=2003\cdot 2004^{2004}$, $X=2\cdot 20 [itex]\text{(A) } U-V \qquad \text{(B) } V-W \qquad \text{(C) } W-X \qquad \text{(D) } X-Y \qquad \text{(E) } Y-Z \qqu 13 KB (1,953 words) - 21:24, 22 November 2021 • ...ngles of a pentagon. Suppose that [itex]v < w < x < y < z$ and $v, w, x, y,$ and $z$ form an arithmetic sequence. Find the
10 KB (1,548 words) - 12:06, 19 February 2020
• Our original solid has volume equal to $V = \frac13 \pi r^2 h = \frac13 \pi 3^2\cdot 4 = 12 \pi$ and has [[surf Our original solid $V$ has [[surface area]] $A_v = \pi r^2 + \pi r \ell$, where
5 KB (839 words) - 21:12, 16 December 2015
• ...>P^{}_{}[/itex] pentagonal faces meet. What is the value of $100P+10T+V\,$?
8 KB (1,275 words) - 05:55, 2 September 2021
• .... Let $m/n$ be the probability that $\sqrt{2+\sqrt{3}}\le |v+w|$, where $m$ and $n$ are relatively prime pos
7 KB (1,098 words) - 16:08, 25 June 2020
• ...he area of pentagon $ABCDE$ is $451$. Find $u + v$.
7 KB (1,208 words) - 18:16, 2 January 2022
• ...ine{UV}[/itex] with $U$ on $\overline{PQ}$ and $V$ on $\overline{QR}$ such that $\overline{UV}$ i
8 KB (1,282 words) - 20:12, 19 February 2019
• ...Using the formula for the volume of a regular tetrahedron, which is $V = \frac{\sqrt{2}S^3}{12}$, where S is the side length of the tetrahed $V = \frac{1}{2} \cdot \frac{\sqrt{2} \cdot (12\sqrt{2})^3}{12} = \boxed{288}< 5 KB (865 words) - 09:17, 20 January 2021 • ...rom vertex [itex]V$ and ending at vertex $A,$ where $V\in\{A,B,C,D\}$ and $k$ is a positive integer. We wish to f ...math>V[/itex] to $A$ and the paths from $A$ to $V$ have one-to-one correspondence. So, we must get <cmath>A_k+B_k+C_k+D
12 KB (2,017 words) - 17:17, 26 January 2022
• ...th>h = 15[/itex], $l = 5$, $w = 10$. Therefore $V = 5 \cdot 10 \cdot 15 = \boxed{750}$
2 KB (346 words) - 12:13, 22 July 2020
• ...(x)[/itex] are also roots of $f(x)$. Let these roots be $u,v$. We get the system If we multiply the first equation by $v^{16}$ and the second by $u^{16}$ we get <cmath>\begin{alig
8 KB (1,350 words) - 13:13, 17 September 2021
• ...lies on exactly one vertex of a square/hexagon/octagon, we have that $V = 12 \cdot 4 = 8 \cdot 6 = 6 \cdot 8 = 48$. ...h of its endpoints, the number of edges $E$ is $\frac{3}{2}V = 72$.
5 KB (811 words) - 18:10, 25 January 2021
• Finally, we substitute $h$ into the volume equation to find $V = 6\sqrt{133}\left(\frac{99}{\sqrt{133}}\right) = \boxed{594}$. ...ave the base area as $18\sqrt {133}$. Thus, the volume is $V = \frac {1}{3}\cdot18\sqrt {133}\cdot\frac {99}{\sqrt {133}} = 6\cdot99 = 5 7 KB (1,085 words) - 20:56, 28 December 2021 • ...th>(u,v)$ and $(p,q)$, then $u=2r-p$ and $v=2s-q$. So we start with the point they gave us and work backwards. We
4 KB (611 words) - 10:31, 23 August 2020
• ...$P$ pentagonal faces meet. What is the value of $100P+10T+V$? ...ge). Thus, $E=60$. Finally, using Euler's formula we have $V=E-30=30$.
4 KB (623 words) - 19:32, 15 February 2021
• ...(-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) - 15:14, 8 March 2021
• ...as $\vec{u}\cdot \vec{v} = \parallel \vec{u}\parallel \parallel \vec{v}\parallel \cos \theta$, we will be able to solve for $\cos \thet <cmath>\vec{v} = \overrightarrow{OB}\times \overrightarrow{OC} - \left|\begin{array}{ccc} 8 KB (1,172 words) - 13:34, 27 October 2021 • ...c{m}{n}$ be the [[probability]] that $\sqrt{2+\sqrt{3}}\le\left|v+w\right|$, where $m$ and $n$ are [[relatively p Now, let $v$ be the root corresponding to $m\theta=2m\pi/1997$, and le
4 KB (714 words) - 13:22, 14 October 2021
• ...coordinates of the vertex of the resulting pyramid. Call this point $V$. Clearly, the height of the pyramid is $z$. The desired v ...= QC[/itex]. We then use distance formula to find the distances from $V$ to each of the vertices of the medial triangle. We thus arrive at a
5 KB (805 words) - 21:34, 28 May 2021
• (Computational) The volume of a cone can be found by $V = \frac{\pi}{3}r^2h$. In the second container, if we let $h',r'< From the formula [itex]V=\frac{\pi r^2h}{3}$, we can find that the volume of the container is
3 KB (544 words) - 21:20, 30 July 2017
• ...rea of [[pentagon]] $ABCDE$ is $451$. Find $u + v$. 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) - 21:43, 16 May 2021
• ...ath>P[/itex] perpendicular to plane $ABC$ can be found as $V=(A-C)\times(B-C)=\langle 8, 12, 24 \rangle$ ...r each pyramid(base times height divided by 3) we have $\dfrac{rF}{3}=V$. The surface area of the pyramid is $\dfrac{6\cdot{4}+6\cdot{2} 6 KB (937 words) - 16:34, 26 December 2021 • ...line{CA}$ and $\overline{AB}$, respectively. Let $U,V$ be the intersections of line $EF$ with line $MN</mat 3 KB (585 words) - 10:12, 16 March 2016 • ...another identical wedge and sticking it to the existing one). Thus, [itex]V=\dfrac{6^2\cdot 12\pi}{2}=216\pi$, so $n=\boxed{216}$.
941 bytes (159 words) - 02:39, 6 December 2019
• 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) - 14:01, 31 December 2021
• ...ine{UV}[/itex] with $U$ on $\overline{PQ}$ and $V$ on $\overline{QR}$ such that $\overline{UV}$ 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);
6 KB (896 words) - 09:13, 22 May 2020
• $\int u\, dv=uv-\int v\,du$ ...math>u[/itex] will show up as $du$ and $dv$ as $v$ in the integral on the RHS, u should be chosen such that it has an "
1 KB (231 words) - 15:19, 18 May 2021
• Specifically, let $u, v : \mathbb{R \times R \to R}$ 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) - 20:04, 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) - 18:41, 25 November 2020
• the vertex $V$ to this path? MP("P",(-1,0),W);MP("V",(-.5,2.4),N);
3 KB (560 words) - 18:23, 10 March 2015
• | $\left(u(x)\times v(x)\right)'=u(x)v'(x)+u'(x)v(x)$ | $\left(\frac{u(x)}{v(x)}\right)' = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}$
3 KB (504 words) - 18:23, 3 March 2010
• *Given a weighted, undirected graph $G = (V,E)$ and two vertices $s, t \in E$, does there exist a path
6 KB (1,104 words) - 14:11, 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 $m$ 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) - 00:33, 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 (365 words) - 19:42, 20 February 2019
• ...group over a set $I$ and $uv = vu$, then $u^m = v^n$, for some [[integer]]s $m$ and $n$.
2 KB (454 words) - 16:54, 16 March 2012
• \text{(V) } 2007 \quad [/itex] $\text{(V) Ying} \quad 33 KB (5,143 words) - 19:49, 28 December 2021 • ...ng subset. Hence <cmath>F(n,r)=\frac{1}{\binom{n}{r}} \sum_{v \in B} \deg (v)= \frac{n+1}{r+1}.</cmath> 5 KB (879 words) - 10:18, 27 June 2020 • 5 - '''V''' ''(quinque)'' 865 bytes (140 words) - 12:58, 24 March 2019 • ..., then the [[greatest common factor]] of [itex]2^u + 1$ and $2^v + 1$ is 3. ...ath>t [/itex], contradicting our assumption that $u$ and $v$ are relatively prime.
10 KB (1,739 words) - 05:38, 12 November 2019
• label("V", (2, 6), NE);
13 KB (1,968 words) - 14:16, 21 October 2021
• ...ale the triangle with the circumradius by a [[line]]ar scale factor, $v$. :$\frac{65}{8}v=8u$
8 KB (1,321 words) - 11:38, 15 January 2022
• ...cut off corners is a [[pyramid]], whose volume can be calculated by $V = \frac 13 Bh$. Use the base as one of the three [[congruency (geomet
2 KB (319 words) - 13:54, 19 December 2020
• Call it a vertex set $V$. $10$ vertices remain outside $V$ and each has to be attached to at least one edge.
3 KB (438 words) - 04:42, 8 March 2018
• Let $u$ and $v$ 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) - 17:52, 18 July 2016
• Chose a vertex, $v$, for which $a$ is minimal (i.e. out of all maximal elemen ...h>. So then in this special case, we have $D = 4$, and so $V = 2006 \times 4+1$ (a possible configuration of this size that works
10 KB (1,878 words) - 13:56, 30 June 2021
• * The volume $V$ of a regular octahedron with side length $a$ is $\fr 1 KB (155 words) - 11:49, 25 August 2019 • Let [itex]u$ and $v$ 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) - 18:16, 18 July 2016
• ...bstituting yields: $20n+25=21(n+1),$ so $n=4$, $v = 80.$ Then, we see that the only way Paula can satisfy this rule is
2 KB (308 words) - 22:21, 27 January 2021
• Let $U=2\cdot 2004^{2005}$, $V=2004^{2005}$, $W=2003\cdot 2004^{2004}$, $X=2\cdot 20 [itex]\mathrm {(A)} U-V \qquad \mathrm {(B)} V-W \qquad \mathrm {(C)} W-X \qquad \mathrm {(D)} X-Y \qquad \mathrm {(E)} Y- 1 KB (139 words) - 01:10, 30 December 2020 • ...math>, where [itex]M$ is momentum, $m$ is mass, and $v$ is [[velocity]].
1 KB (188 words) - 21:44, 10 October 2013
• ...may be defined using ordered pairs from the [[product set]] $V \times V$. ...ay the edges $e$ and $f$ are ''coincident'' at $v$.
8 KB (1,428 words) - 09:26, 27 August 2020
5 KB (840 words) - 18:32, 6 September 2021
• ...uilateral triangle with sides of length three units. $U$, $V$, $W$, $X$, $Y$, and $Z$ label("$V$",(-1/3,sqrt(3)/6),NW);
15 KB (2,057 words) - 18:13, 10 March 2015
• ...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
23 KB (3,641 words) - 12:47, 23 July 2021
• ...s of a [[pentagon]]. Suppose that $v < w < x < y < z$ and $v, w, x, y,$ and $z$ form an [[arithmetic sequence]]. Find ...ath> triangles) is $3 \cdot 180 = 540^{\circ}$. If we let $v = x - 2d, w = x - d, y = x + d, z = x+2d$, it follows that
2 KB (263 words) - 18:15, 20 August 2019
• $V = \pi \left(\frac{3}{\pi}\right)^2\cdot 6\sin\theta$
1 KB (166 words) - 15:35, 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}[/itex]
12 KB (1,670 words) - 16:42, 24 November 2021
• ...>. Y is on $\overline {ST}$, dividing $SY:YT = 2:1$. V is on $\overline {XY}$, dividing $XV:VY = 1:2$. It is
6 KB (909 words) - 00:31, 21 June 2019
• ...le ADB = \angle BDC = \angle CDA = 120^\circ[/itex]. Prove that $x=u+v+w$. label("$v$",(B+D)/2,N);
7 KB (1,221 words) - 17:57, 3 July 2013
• ...math> Substituting in $P$ yields <cmath>-a^2p(1-p)+vp=0\implies v = a^2(1-p).</cmath> Substituting in $B_1$ yields
6 KB (1,117 words) - 00:17, 11 October 2021
• ...me of a pyramid, $V = \frac{1}{3} \cdot B \cdot h$, where $V$ is the volume, $B$ is the area of the base and $h</m 7 KB (1,129 words) - 16:19, 30 January 2016 • ...space]] of all such functions. Define the linear operator [itex]A : V \to V$ as <cmath>(Af)(v) = \sum_{v \sim w} f(v) - f(w)</cmath>
13 KB (2,414 words) - 13:37, 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) - 21:32, 5 December 2020
• ...ing the Hamiltonian, usually of the form $-\frac{\hbar^2}{2m}\Delta + V$ where $\Delta$ is the relevant Laplace(-Beltrami) operato
417 bytes (69 words) - 13:32, 21 April 2018
• *Didion 1870. ''Notice sur la vie et les ouvrages du général J. V. Poncelet''
2 KB (253 words) - 10:41, 19 December 2018
• ...ble positions of the midpoints $U$ of $AB$ and $V$ of $AC$ as $A$ varies?</li> We claim that all points $U,V$ lie on a circle centered at the midpoint of $OP$, $M 3 KB (545 words) - 10:32, 30 January 2021 • ...uilateral triangle with sides of length three units. [itex]U$, $V$, $W$, $X$, $Y$, and $Z$ label("$V$",(-1/3,sqrt(3)/6),NW);
1 KB (188 words) - 13:38, 20 April 2014
• ...nd there is a morphism $U \to V$ if and only if $U \subset V$.
5 KB (792 words) - 18:01, 7 April 2012
• ...each step in the process we remove a number of vertices from the set $V$ if their exists an edge sorrounding it which is labelled. Additiona ...of the vertices not in $V$. Notice that since $v_1,v_n\in V$ the edge connecting $v_0$ and $v_1$ and the ed
4 KB (668 words) - 16:45, 30 January 2021
• ..., there exists a $v\in\{1,2,...,m!\}$ such that $t\equiv f{v}\pmod{m!}$. So, let $t\equiv f(v_t)\pmod{m!}$. Consider
2 KB (416 words) - 10:09, 8 May 2011
• ...h>b = 2\sin u[/itex] and $c = 2\sin v$, where $0^\circ < u,v < 90^\circ$. Then <cmath>a = 2(-\sin u\sin v + \cos u\cos v) = 2\cos (u + v),</cmath>
4 KB (799 words) - 17:28, 1 July 2015
• $\dfrac{t_1}{\sqrt{1-v^2/c^2}}=t_2$ $v$ is the relative velocity the ovject is moving to the observer.
1 KB (261 words) - 23:19, 30 January 2021
• It is equivalent to $\gamma=\dfrac{1}{\sqrt{1-v^2/c^2}}$
226 bytes (34 words) - 10:23, 5 October 2012
• By another person ^v^
5 KB (807 words) - 17:37, 25 June 2021
• ...le ADB = \angle BDC = \angle CDA = 120^\circ[/itex]. Prove that $x=u+v+w$. label("$v$",(B+D)/2,N);
3 KB (427 words) - 17:55, 3 July 2013
• ...and diagonal are the same. Five of these numbers are represented by $v$, $w$, $x$, $y$, and $z label("v",(0.5,2.5)); 14 KB (1,982 words) - 11:59, 24 November 2021 • ...ath>. Let the volume of the tetrahedron be [itex]V$. Therefore $V=\frac{abc}{6}$. ...{6V}[/itex], or $6V\leq \frac{S^3(\sqrt{2}-1)^3}{27}$, or $V\leq \frac{S^3(\sqrt{2}-1)^3}{162}$, with equality only when $a=b 2 KB (358 words) - 22:15, 18 July 2016 • label("V",(1.5,.3),N); ...>\text{(A)}\ \text{Z} \qquad \text{(B)}\ \text{U} \qquad \text{(C)}\ \text{V} \qquad \text{(D)}\ \ \text{W} \qquad \text{(E)}\ \text{Y}$
2 KB (269 words) - 16:05, 3 July 2013
• $v = \frac{200}{b}$ ...gain $b$ more edges. So the total number of new edges is $v*b \Rightarrow \frac{200}{b}*b \Rightarrow 200$. It doesn't matter how
9 KB (1,549 words) - 07:27, 7 September 2021
• ...of sittings is in the form $N*(5!)^3$ because for each $M, V, E$ sequence we have $5!$ 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
3 KB (578 words) - 12:46, 29 November 2021
• ...en $1$ and $167$, inclusive, and for each such $v$ we have exactly one valid $x$. Hence in this case there a
5 KB (845 words) - 14:45, 28 December 2020
• Let $V = \overline{NM} \cap \overline{AC}$ and $W = \overline{NM} \cap 9 KB (1,610 words) - 19:52, 9 August 2020 • ...h> intersect [itex]\omega$ at $K$ and another point $V$, as shown: pair V = IP(L(P, S, 10, 10), circle, 1);
6 KB (973 words) - 18:24, 18 October 2018
• <cmath>T=32-3k\Rightarrow V=24-4k.</cmath>
807 bytes (122 words) - 23:08, 4 July 2013
• If $y(x) = u(x)+v(x)$ then $\frac{dy}{dx} = \frac{du}{dx} + \frac{dv}{dx}$. ...x) = u(x) \cdot v(x)[/itex] then $\frac{dy}{dx} = u(x)\frac{dv}{dx} + v(x)\frac{du}{dx}$.
2 KB (288 words) - 23:53, 25 March 2018
• ...ath> is a basis for $L$ over $K$, we can write $v = \sum_ia_i\alpha_i$, where $a_1,a_2,\ldots,a_n\in K$. And <cmath>v = \sum_ia_i\alpha_i = \sum_i\left(\sum_jb_{ij}\beta_j\right)\alpha_i = \sum
3 KB (567 words) - 07:42, 21 August 2009
• ...[[inverse]] in $R$, that is, if there is another element $v\in R$ such that $uv=vu=1$.
446 bytes (86 words) - 19:16, 23 August 2009
• ...times more water than Logan's miniature. The volume of a sphere is: $V=\dfrac{4}{3}\pi r^3$. Since we are comparing the heights (m), we shou
1 KB (198 words) - 17:08, 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 (835 words) - 14:18, 5 August 2021
• $\sum_{closed loop} \Delta V = 0$
406 bytes (67 words) - 19:36, 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 $\lambda I - A</ma 20 KB (3,415 words) - 22:26, 9 October 2021 • ...r constant [itex]\lambda$ such that $L \bold{v} = \lambda \bold{v}$. Here, $\lambda$ is known as the '''eigenvalue''' associ
821 bytes (138 words) - 18:32, 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) - 15:27, 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) - 12:28, 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) - 22:35, 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) - 08:41, 17 January 2016
• pair V=(0,0.5); draw(V--O);
3 KB (543 words) - 18:52, 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) - 01:19, 8 August 2021
• main(int a, char **v) { int n=atoi(v[1]),
1 KB (188 words) - 17:08, 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) - 15:28, 12 July 2020
• ...and diagonal are the same. Five of these numbers are represented by $v$, $w$, $x$, $y$, and $z label("v",(0.5,2.5)); 5 KB (718 words) - 21:46, 29 June 2021 • ...h>V$ and $W$ are on $\overline{AC}$ with $V$ on $\overline{AW}$, points $X$ and $Y</ma pair[] A, B, C, U, V, W, X, Y, Z; 10 KB (1,638 words) - 20:57, 10 August 2020 • ...h>V$ and $W$ are on $\overline{AC}$ with $V$ on $\overline{AW}$, points $X$ and $Y</ pair[] A, B, C, U, V, W, X, Y, Z; 6 KB (1,077 words) - 11:30, 25 June 2021 • ...math>P(v) = 4$, which will give us the working range $5 \le x < v$. v^2 - 3v - 9 &= 4 \\
8 KB (1,273 words) - 08:32, 12 July 2021
• ...> <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) - 15:56, 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 $d(F,l)= 4 KB (619 words) - 18:15, 11 May 2021 • ! scope="row" | '''Mock AMC V''' 18 KB (2,206 words) - 18:41, 24 December 2020 • label("V-4\beta",(0,-0.3),red); /* AUTO-GRAPH V-4 beta by PythonNut*/ 17 KB (2,910 words) - 14:01, 2 September 2011 • <cmath> V. x+y = 13, \{49, 58, 67, 76, 85, 94\} = 6 </cmath> 5 KB (801 words) - 18:21, 21 December 2021 • ...{v} \rfloor$ means the greatest integer less than or equal to $v$.)
1 KB (155 words) - 06:58, 22 October 2014
• .../math> and the remainder is $v$, where $u$ and $v$ are integers. \textbf{(D)}\ v \qquad
2 KB (266 words) - 02:30, 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 $\pi (1 2 KB (266 words) - 23:09, 4 July 2013 • ...? Because Uberdude supplied a hint that the answer begins with the letter V, and a vole seemed as good as anything else. Vole are small rodents, like m 307 bytes (64 words) - 11:59, 10 September 2012 • ...-4), P=(1,-3.8), Q=(1,-3.6), R=(1,-3.4), S=(1,-3.2), T=(1,-3), U=(1,-2.8), V=(1,-2.6), W=(1,-2.4), Z=(1,-2.2), E_1=(1.4,-2.6), F_1=(1.8,-2.6), O_1=(14,- ...th(1pt)); D(S,linewidth(1pt)); D(T,linewidth(1pt)); D(U,linewidth(1pt)); D(V,linewidth(1pt)); D(W,linewidth(1pt)); D(Z,linewidth(1pt)); D(E_1,linewidth( 18 KB (2,742 words) - 19:46, 29 July 2021 • ...,-2), M=(0,-6), O=(0,-4), P=(4,-4), Q=(2,-2), R=(2,-6), T=(6,4), U=(10,0), V=(10,4), Z=(10,2), A_1=(8,4), B_1=(8,0), C_1=(6,-2), D_1=(10,-2), E_1=(6,-6) ...--cycle,linewidth(1.6)); draw(M--O--Q--R--cycle,linewidth(1.6)); draw(A_1--V--Z--cycle,linewidth(1.6)); draw(G_1--K_1--J_1--E_1--cycle,linewidth(1.6)); 16 KB (2,345 words) - 23:46, 15 January 2022 • [itex]\text{(v)}$ Without the use of logarithm tables evaluate $\frac{1}{\log_{ 4 KB (540 words) - 17:23, 8 October 2014 • [itex]\text{(v)}$ Without the use of logarithm tables evaluate $\frac{1}{\log_{ [itex]\text{(v)}$ <center>
2 KB (286 words) - 14:14, 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) - 18:57, 17 August 2021
• ...{v} \rfloor[/itex] means the greatest integer less than or equal to $v$.)
15 KB (2,247 words) - 12:44, 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) - 12:34, 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) - 19:37, 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) - 01:55, 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 $d = 6 2 KB (291 words) - 21:22, 29 September 2020 • The volume of this pyramid can be found by the equation [itex]V=\frac{1}{3}bh$, 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) - 15:34, 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) - 16:17, 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) - 09:03, 10 May 2012
• ...h>, distance $a$, formula $v=\frac{a}{t}$ or $a=v \cdot t$.
1 KB (191 words) - 13:40, 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 $I </math 4 KB (596 words) - 19:09, 27 May 2012 • ...ind a vertical vector [itex] v$ 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) - 19:09, 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) - 14:22, 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) - 15:29, 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) - 00:58, 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) - 22:08, 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) - 02:03, 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) - 20:06, 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) - 20:46, 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) - 15:52, 3 April 2020
• label("$V$", (1.7922953932137468,0.6108747864253139), NE * labelscalefactor); label("$V$", (1.7922953932137468,0.6108747864253139), NE * labelscalefactor);
14 KB (1,823 words) - 21:03, 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) - 17:05, 1 October 2021
• ...(\frac{1}{16},\frac{1}{8},\frac{1}{13})[/itex]. Let $\overrightarrow{v}$ be a vector with head $(\frac{1}{16},\frac{1}{8},\frac{1}{13} 1 KB (213 words) - 19:48, 15 February 2015 • ...uv.xy}+\overline{xy.uv} </cmath> is an integer? As an example, if [itex](u,v,x,y)=(0,1,2,3)$, then we have $N = 1.23 + 23.01 = 24.24$
8 KB (1,336 words) - 08:10, 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) - 22:40, 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) - 03:30, 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 $V(G\times H)=V(G)\times V(H), (v_1,w_1)\leftrightarrow (v_2,w_2) \Leftrightarrow v_1=v_2,w_1\leftrigh 4 KB (749 words) - 13:09, 29 January 2021 • ...h>) that we can find a circle passing through [itex]U,D$ (or $F,V$) which cuts the segments $UV,DF$ in $X,Y$. Our
1 KB (230 words) - 14:35, 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) - 14:42, 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) - 18:45, 20 November 2014
• ...line{CA}[/itex] and $\overline{AB}$, respectively. Let $U,V$ be the intersections of line $EF$ with line $MN</mat pair A, B, C, I, M, N, P, E, F, U, V, X, R; 7 KB (1,273 words) - 17:17, 28 August 2021 • The volume [itex]V = \pi R^2H$ is to be increased by the same fixed positive amount when
21 KB (3,242 words) - 20:27, 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) - 12:55, 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) - 16:24, 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 $16 KB (2,662 words) - 13:12, 20 February 2020 • . A gateway valve has actually a v-ring packaging establish that secures the shaft that's affixed to the gatew 4 KB (596 words) - 21:28, 25 August 2021 • ...),-sqrt(5)), W=(4+2/sqrt(5),sqrt(5)), T=(4,0), U=(4+2/sqrt(5),-4/sqrt(5)), V=(4+2/sqrt(5),1/sqrt(5)); draw(X--Y--Z--W--X^^T--V--X^^Y--U); 17 KB (2,535 words) - 12:45, 19 February 2020 • [itex]\{V, W, X, Y, Z\}$. Using this correspondence, the cryptographer finds th
16 KB (2,291 words) - 12:45, 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) - 22:43, 2 December 2021
• \text{(v) }y+a\ge x [/itex]
15 KB (2,437 words) - 03:39, 26 November 2021
• the vertex $V$ to this path? MP("P",(-1,0),W);MP("V",(-.5,2.4),N);
889 bytes (136 words) - 14:53, 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) - 12:54, 20 February 2020
• \text{(V) } 2007 \quad [/itex]
929 bytes (137 words) - 21:05, 10 January 2019
• \text{(V) } 21\qquad
2 KB (270 words) - 13:35, 29 July 2018
• ...oor[/itex] (the greatest integer less than or equal to the volume of $V$).
510 bytes (87 words) - 22:03, 7 October 2014
• $\text{(V) Ying} \quad 1 KB (202 words) - 15:48, 24 November 2018 • \text{(V) }21 \quad 2 KB (340 words) - 18:49, 30 June 2018 • label("u",T+(-0.1,-0.2), S); label("v", S+(0,-0.2), S); Denote [itex]\angle{HSB}=v$, $\angle{HTD}=u$, $\angle{HSC}=s$, $\angl 6 KB (1,071 words) - 02:58, 8 September 2018 • .../math> and the remainder is [itex]v$, where $u$ and $v$ are integers. \textbf{(D)}\ v \qquad
19 KB (2,907 words) - 13:16, 20 February 2020
• If $V = gt + V_0$ and $S = \frac {1}{2}gt^2 + V_0t$, then $[itex] \textbf{(A)}\ \frac{2S}{V+V_0}\qquad 20 KB (3,039 words) - 21:44, 12 February 2021 • ...),-sqrt(5)), W=(4+2/sqrt(5),sqrt(5)), T=(4,0), U=(4+2/sqrt(5),-4/sqrt(5)), V=(4+2/sqrt(5),1/sqrt(5)); draw(X--Y--Z--W--X^^T--V--X^^Y--U); 2 KB (334 words) - 13:11, 27 February 2018 • ...>T$ is halfway between $Q$ and $R$, then $V$ is halfway between $P$ and $S$. Therefore, <m
2 KB (349 words) - 01:41, 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 $XYZ = 413_{5} = 4 \cdot 5^{2} 2 KB (242 words) - 13:32, 1 March 2018 • ...pairs (not counting transpositions because this does not affect ([itex]u + v$), $(2, 8), (4, 4), (-2, -8), (-4, -4)$, yields $a = 2 KB (372 words) - 23:28, 26 September 2021 • ...dron and [itex]TD$ 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) - 08:24, 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) - 17:02, 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>
7 KB (1,255 words) - 11:10, 1 September 2021
• ...he volume of water thus displaced is $v$ cubic feet. Find $v^2$.
8 KB (1,326 words) - 11:19, 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) - 18:22, 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) - 08:58, 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) - 15:45, 29 April 2020
• | <span class="aops-font">V</span> | V
6 KB (920 words) - 15:40, 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 (436 words) - 20:09, 10 January 2022
• ...e, we can set up a proportion based on the principle that $d=\frac{m}{V}$, thus $dV=m$.
2 KB (325 words) - 13:21, 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) - 19:49, 18 December 2019
• pair V = incenter(A,C,P); dot("$I_C$", V, NW);
5 KB (1,004 words) - 14:15, 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) - 00:11, 20 February 2019
• ...$\overline{MS}$ intersects $\overline{OP}$ at $V$ . If $AB = 2,$ $BC = 2005,$ $CD = 4,</mat 7 KB (1,094 words) - 14:39, 24 March 2019 • r, s, t, u, v, w, x, y, and z such that n + l + v − y = 0 14 KB (2,904 words) - 17:24, 16 May 2017 • The vertices [itex]V$ 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) - 08:44, 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 $P={\prod}_{ 15 KB (2,418 words) - 13:43, 12 August 2020 • <cmath>V = Bh/3</cmath> <cmath>V = (192)(25\sqrt{3}/2)/3</cmath> 6 KB (986 words) - 05:59, 28 December 2020 • ...ition offered at Walton High School (Walton MathFest was a high school (JV/V) level math tournament until the 2017-2018 school year). 1 KB (158 words) - 19:16, 9 August 2017 • ...ition offered at Walton High School (Walton MathFest was a high school (JV/V) level math tournament until the 2017-2018 school year). 1 KB (158 words) - 19:20, 9 August 2017 • One could also construct a graph G=(V,E) with the set V of vertices (also called nodes or points) and the set E of edges (also call 4 KB (574 words) - 19:16, 19 September 2018 • [itex]\quad\bullet\qquad$ $V,$ a reflection across the $y$-axis. ...beled vertices back to their original positions? (For example, $R, R, V, H$ is one sequence of $4$ transformations that will send
16 KB (2,416 words) - 09:32, 26 May 2021
• ...aring both sides and solving, we get $u=\frac{11}{2}$ and $v=\frac{11}{2}-3=\frac{5}{2}$. Adding, we get that the answer is $6 KB (888 words) - 08:28, 28 December 2021 • path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); filldraw(shift((j,i))*v,black); 15 KB (2,237 words) - 13:28, 23 October 2021 • ...>. Using the formula for the volume of a triangular pyramid, we have [itex]V = \frac{1}{3} \cdot \frac{1}{2} \cdot 3 = \frac{1}{2}$. Also, since t Plugging $x$ and $y$ into the formula $V = \dfrac{b \cdot h}{3},$ we find that the volume is $\boxed{2}</ 7 KB (1,118 words) - 00:38, 2 January 2021 • path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); filldraw(shift((j,i))*v,black); 4 KB (593 words) - 16:12, 23 October 2021 • Now all these nine polyhedrons lie inside [itex]2 P_1$. Let $V$ be the volume of $P_1$.
1 KB (242 words) - 12:55, 29 January 2021
• The volume $V = \pi R^2H$ is to be increased by the same fixed positive amount when
1 KB (245 words) - 18:07, 17 May 2018
• ...$1800-x$. Since Eve is the slowest, we can call her speed $v$, so that Ina's speed is $2v$ and Paul's speed is $4v ...e of [itex]1800-x$ which takes them a time of $\frac{1800-x}{4v+v}$. Paul must run the same distance back to $B$, so his tot
3 KB (503 words) - 19:32, 23 August 2020
• ...ots, v_n), \vec{w} = (w_1, \cdots, w_n)[/itex] is defined to be $\vec{v}\cdot\vec{w} = \sum_{i=1}^n v_i w_i$. The dot product is [[linear|bil
276 bytes (51 words) - 21:30, 13 September 2020
• ...B travels half the time at $u$ miles per hour and half at $v$ miles per hour. The average speed of Car A is $x$ miles p <cmath>y = \frac{u+v}{2}</cmath>
2 KB (396 words) - 18:03, 22 June 2021
• Let the volume of the trough be $V$ liters. Also, let the rate of the cold water tap be $C$ <cmath>V = 21E</cmath>
1 KB (268 words) - 15:32, 28 July 2018
• Of the following five statements, I to V, about the binary operation of averaging (arithmetic mean), $\text{V. Averaging has an identity element }$
2 KB (432 words) - 12:57, 20 February 2020
128 bytes (21 words) - 07:25, 3 May 2019
• ...positions of the midpoints $U$ of $BA$ and $V$ of $AC$ as $\angle OPA$ varies?
3 KB (499 words) - 12:29, 2 August 2021
• $\quad\bullet\qquad$ $V,$ a reflection across the $y$-axis. ...beled vertices back to their original positions? (For example, $R, R, V, H$ is one sequence of $4$ transformations that will send
16 KB (2,485 words) - 09:32, 26 May 2021
• ...P}\setminus\{\mathbf{v}\}[/itex] obtained by omitting vector $\mathbf{v}$ from $\mathcal{P}$ can be partitioned into two sets of e
2 KB (369 words) - 22:35, 21 April 2019
• ...P}\setminus\{\mathbf{v}\}[/itex] obtained by omitting vector $\mathbf{v}$ from $\mathcal{P}$ can be partitioned into two sets of e
531 bytes (88 words) - 22:37, 21 April 2019
• ...egree of $V$ (i.e. the number of edges coming into/out of $V$). This is because to visit any of these vertices, we would have to e ...isit each vertex $M(V)$ times, and must traverse $2\cdot M(V)$ edges connected to each vertex. Specifically, we must traverse all
8 KB (1,306 words) - 21:18, 1 February 2020
• Let $P(3)=u$ and $P(4) = v$. Substituting $x=3$ and $x=4$ into the above q u &= (3-u)(3-v) = 9 - 3u - 3v + uv\\
10 KB (1,805 words) - 19:16, 31 August 2021
• ...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
4 KB (501 words) - 18:14, 7 July 2019
• $\delta x'(t)=v(t)$ $v'(t)=a(t)$
3 KB (423 words) - 11:58, 8 July 2019
• ...he base's area, and h is the height's length; for a pyramid, we have $V=\frac{1}{3}Bh$.
1 KB (207 words) - 00:39, 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
83 KB (13,617 words) - 19:20, 11 January 2022
• label("V", (2, 6), NE); label("V", (2, 6), NE);
9 KB (1,347 words) - 22:14, 1 May 2021
• $\quad\bullet\qquad$ $V,$ a reflection across the $y$-axis. ...beled vertices back to their original positions? (For example, $R, R, V, H$ is one sequence of $4$ transformations that will send
12 KB (2,020 words) - 08:33, 28 December 2021
• ...of a cone is $\frac{1}{3}\pi r^{2}h$. Plugging in we find $V = 3\pi \sqrt{7} \implies \boxed{\textbf{(C)}}$
3 KB (476 words) - 20:10, 17 October 2021
• ...the origin and select a point on each line to define vectors $\mathbf{v}_{i}=(x_{i},y_{i})$. <cmath>\mathbf{v}_1\cdot\mathbf{v}_2 = v_{1}v_{2}\cos\theta \quad\mathrm{and}\quad
5 KB (881 words) - 00:04, 29 January 2021
• <li>$\log_b{(uv)}=\log_b u + \log_b v.$</li><p>
5 KB (675 words) - 16:53, 5 December 2021
• Let $V$ and $F$ be the vertex and focus of the Parabola $P(x 8 KB (1,306 words) - 10:29, 4 September 2020 • ...an upright V.}\\ \textbf{(D)}\ \text{Two line segments forming an inverted V.}\\ \textbf{(E)}\ \text{None of these.}$
1 KB (193 words) - 09:42, 6 July 2020
• ...d a horizontal circle of radius $r$ with a constant speed $v$, in a conical pendulum. The center of the circle is vertically below ...ath>16 kg[/itex] which slides at a speed of $v$, with $u > v$. Block A slides east while Block B slides in west. The surface has c
2 KB (439 words) - 10:52, 1 August 2020
• Lucky Seven V ARE YOU XPERIENCED? V
3 KB (452 words) - 09:35, 6 May 2021
• Suppose that on the parabola with vertex $V$ and a focus $F$ there exists a point $A$ such
15 KB (2,382 words) - 16:41, 4 December 2021
• ...th>C(1) = 0[/itex] and our recursive rules for $C(n)$ and $V(n)$ as follows: <cmath>\begin{tabular}{c|c|c} n & V(n) & C(n) \\ \hline
2 KB (363 words) - 16:49, 22 November 2021
• ...t{10}} , \sqrt{10} \right)[/itex], $Q = \left( \sqrt{10} , \frac{10 - v}{\sqrt{10}} \right)$. We have $m_{HP} = \frac{3}{6 - u}$ and $m_{PQ} = - \frac{v}{u}$.
16 KB (2,247 words) - 15:05, 1 January 2022
• Let $O$ be the center of the base, $V$ be the vertex of the base.
8 KB (1,301 words) - 21:15, 15 January 2022
• pair A, B, C, D, E, F, G, H, A1, B1, C1, D1, E1, F1, G1, H1, V; V = (3,0);
24 KB (3,577 words) - 20:43, 2 January 2022
• Now here comes the smart part. Substitute $y = \sqrt[3]{u} - \sqrt[3]{v}$. ...$u - 3\sqrt[3]{u^2v} + 3\sqrt[3]{uv^2} - v + p\sqrt[3]{u} - p\sqrt[3]{v} + q = 0$. Simplification:
6 KB (1,059 words) - 13:42, 11 December 2020
• ...3}[/itex] then we can find a line $\ell$ perpendicular to $v$ such that $\ell$ separates $S$, and any point Suppose there is no such direction $v$, then $S$ is contained in a box with side length $n^ 3 KB (574 words) - 10:30, 14 May 2021 • Suppose that on a parabola with vertex [itex]V$ and a focus $F$ there exists a point $A$ such ...d $Y$ be the orthogonal projections of $F$ and $V$ onto $AQ$. Because $AF < AV$, there are two po
4 KB (796 words) - 16:33, 13 July 2021
• ...ur squares on the middle of the edges after n moves, and $V_n$ (V for vertex) be the probability that Frieda is on a corner after n moves. Th https://youtube.com/watch?v=kHLR57iP0cU
14 KB (2,224 words) - 03:14, 5 January 2022
• ...$u$ and $v$ in $G$. Every tree on $|V|=n$ vertices has exactly $n-1$ edges.
401 bytes (75 words) - 15:51, 2 November 2020
• V&=\frac16\cdot AB\cdot AD\cdot BD \\
3 KB (493 words) - 18:19, 28 August 2021
• ...tuy + vy^2 + svy + tv[/itex], simplifying to $y^4 + (s + u)y^3 + (t + v + su)y^2 + (sv + tu)y + tv$. [[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}[/itex]
12 KB (2,047 words) - 15:59, 13 April 2021
• ...[/itex] and $2$ along $\textbf{u}$ and $\textbf{v}$ respectively, then find <cmath>\sum_{i=1}^{n}\|\textbf{r}_i\|^2.</c
7 KB (1,149 words) - 16:16, 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) - 04:15, 7 January 2021
• ...math> OV[/itex] (but not in $\vec{OV}$) for some vertex $V$ of the polygon. Each two of these lines are obtained one from anothe
2 KB (284 words) - 10:02, 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}[/itex]
952 bytes (157 words) - 19:50, 31 January 2021
• If $V = gt + V_0$ and $S = \frac {1}{2}gt^2 + V_0t$, then $[itex] \textbf{(A)}\ \frac{2S}{V+V_0}\qquad 737 bytes (129 words) - 21:53, 12 February 2021 • ...c", D--C, N); label("d",D--A,W); label("u",D--B,2*dir(170)); label("v",A--C,S); ...c, d$, be the sides, $s$ the semiperimeter, and $u, v$, the diagonals. Then the area, $K$, is given by <cmath>K
9 KB (1,397 words) - 18:49, 20 December 2021
• ...$n=2k+1$, just take $(u,v)= (k+1,k)$ which $u^2-v^2=n$. Thus the only answer is $\boxed{f\equiv 1}$ and we a https://www.youtube.com/watch?v=Q1NUBUYvOJc
8 KB (1,492 words) - 20:39, 13 January 2022
• ...th>t[/itex] is square free and $gcd(u,v,w) = 1$, find $t+u+v+w$ if $x=\cos 20^o$ and $y=\sin 20^o$.
8 KB (1,385 words) - 11:55, 23 June 2021
• ...\qquad \text{(iii) }x+y\ge a\\ \\ \qquad \text{(iv) }x+a\ge y\qquad \text{(v) }y+a\ge x[/itex]
665 bytes (119 words) - 13:12, 20 June 2021
• ...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) - 15:47, 23 June 2021
• ...th>C(1) = 0[/itex] and our recursive rules for $C(n)$ and $V(n)$ as follows: <cmath>\begin{tabular}{c|c|c} n & V(n) & C(n) \\ \hline
5 KB (756 words) - 02:42, 29 November 2021
• .../math> bisects the angle between $\mathbf{u}$ and $\mathbf{v}$.
12 KB (1,790 words) - 03:19, 1 January 2022
• ...h>. Hence, $B = \left( - 1 , u \right)$, $D = \left( 0 , - v \right)$. The slope of $AD$ is $m_{AD} = \frac{v}{3}$.
5 KB (734 words) - 02:44, 1 January 2022