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• Expression
  ...ally consist of [[number]]s, [[variable]]s, and [[operator]]s, arranged in a sensible way. Thus, <math>3 - \frac x4</math> is an arithmetic expression, ...t an arithmetic expression, this equivalence of logical expressions is not a logical expression. This is amazing. Again please help us by expanding it
  2 KB (239 words) - 14:42, 11 March 2023
• Asymptote: Macros and Packages
  ...+r,b+r)</math>. In addition, you want it to simply return the pair <math>(a,b)</math> if no value of <math>r</math> is specified, so you want <math>r</ real a,b;
  3 KB (515 words) - 00:43, 24 April 2019
• Periodic function
  ...] <math>f</math> is '''periodic''' if for all <math>x</math>, there exists a <math>p</math> such that <math>f(x + p) = f(x)</math>. The smallest positiv
  515 bytes (80 words) - 15:47, 21 August 2011
• 1960 IMO Problems
  For what values of the variable <math>x</math> does the following inequality hold: ...nteger). Let <math>\alpha</math> be the acute angle subtending, from <math>A</math>, that segment which contains the midpoint of the hypotenuse. Let <ma
  3 KB (511 words) - 21:21, 20 August 2020
• 2007 AIME I Problems/Problem 8
  We can see that <math>Q_1</math> and <math>Q_2</math> must have a [[root]] in common for them to both be [[factor]]s of the same cubic. Let this root be <math>a</math>.
  4 KB (728 words) - 00:11, 29 November 2023
• 2007 AIME I Problems/Problem 14
  A [[sequence]] is defined over [[non-negative]] integral indexes in the follo Define a function <math>f(n)</math> on the non-negative integers, as <cmath>f(n) = \
  13 KB (2,185 words) - 23:30, 5 December 2022
• 1989 USAMO Problems
  ...tegers <math>0 < a,\ b,\ c,\ d < 1000000</math> such that <math>T_{1988} = a S_{1989} - b</math> and <math>U_{1988} = c S_{1989} - d</math>. ...laying in at least one game. Prove that within this schedule there must be a set of 6 games with 12 distinct players.
  2 KB (326 words) - 18:52, 18 July 2016
• LaTeX:Commands
  | <math>a^{i+1}_3</math>||a^{i+1}_3||<math>x^{3^2}</math>||x^{3^2} Notice that we can apply both a subscript and a superscript at the same time. For subscripts or superscripts with more than
  12 KB (1,894 words) - 21:24, 7 June 2024
• Imaginary number
  An '''imaginary number''' is a [[complex number]] whose [[real part]] is equal to 0. In the [[complex pla ...math>, which is <math>\sqrt{-1}</math>. <math>i</math> can be treated as a variable with the distinctive property that <math>i^2= -1</math>. Powers of <math>i<
  2 KB (283 words) - 00:18, 8 March 2012
• Zermelo-Fraenkel Axioms
  ...ven property describable by the language of [[set theory]] could be called a [[set]]. As shown by paradoxes such as [[Russell's Paradox]], some restrict The language of set theory consists of a single binary relation <math>\in</math>. As such, all axioms can be written
  4 KB (732 words) - 20:49, 13 October 2019
• Implicit differentiation
  ...e [[dependent variable]] is treated as a [[function]] of the [[independent variable]] and is differentiated with the [[chain rule]].
  757 bytes (125 words) - 01:04, 26 March 2018
• 2007 AMC 12A Problems/Problem 9
  <math>\mathrm{(A)}\ \frac 23\qquad \mathrm{(B)}\ \frac 34\qquad \mathrm{(C)}\ \frac 45\qquad ...r}</math>. If Yan walks directly to the stadium, then assuming he walks at a rate of <math>1</math>, it will take him <math>x-r</math> units of time. Si
  5 KB (804 words) - 14:55, 21 August 2022
• Linear equation
  ...]] of the first [[degree]] - i.e. each term does not have any variables to a power other than one. ...onstants, <math>b_i</math> is a series of variables, and <math>c</math> is a [[constant]].
  1 KB (257 words) - 13:39, 14 July 2021
• 2006 AIME II Problems/Problem 6
  ...d <math> b</math> is not divisible by the square of any prime. Find <math> a+b+c. </math> pair B = (0, 0), C = (1, 0), D = (1, 1), A = (0, 1);
  7 KB (1,067 words) - 12:23, 8 April 2024
• 1989 USAMO Problems/Problem 3
  ...</math> and <math>b</math> such that <math>P(a + bi) = 0</math> and <math>(a^2 + b^2 + 1)^2 < 4 b^2 + 1</math>. ...>\overline{w}</math>, the [[complex conjugate]] of <math>w</math>, is also a root of <math>P</math>.
  2 KB (340 words) - 19:11, 18 July 2016
• 1960 IMO Problems/Problem 2
  For what values of the variable <math>x</math> does the following inequality hold: Set <math>x = -\frac{1}{2} + \frac{a^2}{2}</math>, where <math>a\ge0</math>.
  2 KB (239 words) - 05:51, 7 April 2024
• Excircle
  ...is a [[circle]] [[Tangent line|tangent]] to the extensions of two sides of a [[triangle]] and the third side. pair excenter(pair A, pair B, pair C){
  5 KB (843 words) - 03:02, 1 July 2020
• 2004 AMC 12A Problems/Problem 8
  //Variable Declarations pair A, B, C, D, E;
  5 KB (692 words) - 21:15, 5 April 2024
• Algebraic manipulation
  ...doing opposite operations (undoing) to any equation to solve for a certain variable (often by isolation). Cross multiplication is a common method of solving [[proportions]]. Essentially, one is multiplying
  4 KB (562 words) - 18:49, 8 November 2020
• 2002 AMC 12B Problems/Problem 20
  Let <math>\triangle XOY</math> be a [[right triangle|right-angled triangle]] with <math>m\angle XOY = 90^{\circ <math>\mathrm{(A)}\ 24
  3 KB (447 words) - 15:02, 17 August 2023

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