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• V Olimpiada Iberoamericana de Matemáticas (OIM)
  458 bytes (44 words) - 17:51, 14 December 2023

Page text matches

• Physics
  <math>\delta x'(t)=v(t)</math> <math>v'(t)=a(t)</math>
  9 KB (1,355 words) - 07:29, 29 September 2021
• 2020 CIME II Problems/Problem 10
  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
• Cauchy-Schwarz Inequality
  ...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
• Constructive counting
  ...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
• Base numbers
  ...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
• Vector
  ...\,\,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
• Rational approximation
  ...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
• Algebraic geometry
  ...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
• Euler's Polyhedral Formula
  ...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
• Mock AMC
  ! scope="row" | '''Mock AMC V'''
  51 KB (6,175 words) - 20:58, 6 December 2023
• 2004 AMC 12A Problems
  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
• 2002 AMC 12B Problems
  ...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
• 2004 AIME I Problems/Problem 11
  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
• 1993 AIME Problems
  ...>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
• 1997 AIME Problems
  .... 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
• 2000 AIME I Problems
  ...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
• 2001 AIME II Problems
  ...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
• 1983 AIME Problems/Problem 11
  ...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
• 1985 AIME Problems/Problem 12
  ...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 (2,837 words) - 13:34, 4 April 2024
• 1986 AIME Problems/Problem 14
  ...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

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