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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'''
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 (2,009 words) - 13:21, 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

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