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• 1984 AIME Problems/Problem 4
  Let <math>S</math> be a list of positive integers--not necessarily distinct--in which the number <m == Solution 2 (One Variable) ==
  2 KB (319 words) - 03:38, 16 January 2023
• 1985 AIME Problems/Problem 12
  ...= \frac{n}{729}</math> be the probability that the bug is at vertex <math>A</math> when it has crawled exactly <math>7</math> meters. Find the value of == Solution 1 (Single Variable Recursion) ==
  17 KB (2,837 words) - 13:34, 4 April 2024
• 1986 AIME Problems/Problem 9
  pair C=(0,0),A=(510,0),B=IP(circle(C,450),circle(A,425)); pair Da=IP(Circle(A,289),A--B),E=IP(Circle(C,324),B--C),Ea=IP(Circle(B,270),B--C);
  11 KB (1,850 words) - 18:07, 11 October 2023
• 1988 AIME Problems/Problem 6
  ...od will be to use the given numbers to set up equations to solve for <math>a</math> and <math>b</math>, and then calculate <math>(*)</math>. \hline a & & 103 & & \\
  5 KB (878 words) - 23:06, 20 November 2023
• 1995 AIME Problems/Problem 7
  ...+ \cos t) = \frac{3}{2}</math>. Completing the square on the left in the variable <math>(\sin t + \cos t)</math> gives <math>\sin t + \cos t = -1 \pm \sqrt{\ {{AIME box|year=1995|num-b=6|num-a=8}}
  3 KB (427 words) - 09:23, 13 December 2023
• 1997 AIME Problems/Problem 4
  NOTE: It can be seen that there is no apparent need to use the variable x as a 5,12,13 right triangle has been formed. ...2+k_2k_3+k_3k_1}</math> where each of <math>k_i</math> is the curvature of a circle with radius <math>r_i</math>, and the curvature is defined as <math>
  2 KB (354 words) - 22:33, 2 February 2021
• 2003 AIME II Problems/Problem 13
  ...ne of the two vertices where it is not currently located, and crawls along a side of the triangle to that vertex. Given that the probability that the bu ...o return to the original vertex, the net number of clockwise steps must be a multiple of 3, i.e., <math>\#CW - \#CCW \equiv 0 \pmod{3}</math>. Since <m
  15 KB (2,406 words) - 23:56, 23 November 2023
• Equation
  An '''equation''' is a [[relation]] which states that two [[expression]]s are equal, identical, or A unique aspect to equations is the ability to modify an original equation by
  5 KB (932 words) - 12:57, 26 July 2023
• Identity
  ...x^2+2x+1</math> is an identity, since it holds regardless of the choice of variable. Therefore, it is sometimes written <math>(x+1)^2\equiv x^2+2x+1</math>. ...</math>. If we instead took <math>G</math> to be addition (<math>G(a, b) = a + b</math>), <math>0</math> would be the identity.
  1 KB (238 words) - 13:38, 14 July 2021
• Mock AIME 1 2006-2007 Problems/Problem 9
  Let <math>a_{n}</math> be a [[geometric sequence]] of [[complex number]]s with <math>a_{0}=1024</math> Let <math>a_{n}</math> be a geometric sequence for <math>n\in\mathbb{Z}</math> with <math>a_{0}=1024</m
  5 KB (744 words) - 19:46, 20 October 2020
• Mock AIME 1 2006-2007 Problems/Problem 14
  ...ath>n</math> are positive integers. Construct circle <math>O</math> with a variable radius that is tangent to <math>AB</math> at <math>T</math>. Let <math>P</ ...ee below an attempted solution to understand why this problem doesn't have a solution:
  3 KB (541 words) - 17:32, 22 November 2023
• Mock AIME 1 2006-2007/Problems
  Let <math>\star (x)</math> be the sum of the digits of a positive integer <math>x</math>. <math>\mathcal{S}</math> is the set of pos ...\sqrt{7}</math>, <math>CA=1</math>, and <math>AB=3</math>. If <math>\angle A=\frac{\pi}{n}</math> where <math>n</math> is an integer, find the remainder
  8 KB (1,355 words) - 14:54, 21 August 2020
• Expected value
  Given an event with a variety of different possible outcomes, the '''expected value''' is what on A video that goes over the type of Expected value, practical examples, and pr
  5 KB (789 words) - 20:56, 10 May 2024
• 2006 Romanian NMO Problems
  ...<math>2 \cdot \frac{CN}{BC} = \frac{AM}{AB}</math>. Let <math>P</math> be a point on the line <math>AC</math>. Prove that the lines <math>MN</math> and ...nimal <math>n</math>, such that for each coloring, there exists a line and a column with at least 3 unit squares of the same color (on the same line or
  11 KB (1,779 words) - 14:57, 7 May 2012
• Derivative
  ...ith respect to one of the [[variable]]s. Note that not every function has a derivative.
  509 bytes (64 words) - 19:26, 3 March 2010
• Navier-Stokes Equation
  ...ate how sticky (viscous) a fluid is. Thus, the Navier-Stokes equations are a dynamical statement of the balance of forces acting at any given region of ...odel weather, ocean currents, water flow in a pipe, motion of stars inside a galaxy, and flow around an airfoil (wing). They are also used in the design
  3 KB (553 words) - 22:08, 2 May 2022
• System of equations
  ...[[equation]]s which share the same [[variable]]s. Below is an example of a system of equations. <cmath>\left\{\begin{array}{l}a^2 + b^2 = 25\\a+b=7\end{array}\right.</cmath>
  5 KB (784 words) - 23:27, 30 July 2020
• Linear congruence
  A '''Linear Congruence''' is a [[congruence]] [[modular arithmetic|mod]] p of the form ...c</math>, and <math>p</math> are [[constant]]s and <math>x</math> is the [[variable]] to be solved for.
  1 KB (225 words) - 15:52, 3 August 2022
• Asymptote: Basics
  ...nded with the "[/asy]" tag. Each command in Asymptote must be separated by a semicolon (;), similar to programming languages like C and Java. This conve To write comments (Lines that are not interpreted by Asymptote), start a line with two forward slashes.
  5 KB (801 words) - 20:44, 6 May 2024
• Coefficient
  ...]] of a specified object. The object can be a [[variable]], a [[vector]], a [[function]], or anything else that might be subject to multiplication. ...ficients of: 5 also has a coefficient in <math>5a + b</math>, namely <math>a</math>.
  1 KB (227 words) - 22:38, 6 October 2020

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