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• $\delta x'(t)=v(t)$ $v'(t)=a(t)$
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'''
57 KB (6,925 words) - 01:50, 2 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
11 KB (1,885 words) - 03:20, 19 October 2021
• ...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
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 [itex]\lambda I - A</ma
20 KB (3,415 words) - 22:26, 9 October 2021

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