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• Power Mean Inequality
  ...'' is a generalized form of the multi-variable [[Arithmetic Mean-Geometric Mean]] Inequality. ...ights <math>w_i</math> with sum <math>\sum_{i=1}^n w_i=1</math>, the power mean with exponent <math>t</math>, where <math>t\in\mathbb{R}</math>, is defined
  3 KB (606 words) - 23:59, 1 July 2022
• Power of a Point Theorem
  The '''Power of a Point Theorem''' is a relationship that holds between the lengths of t ...ugh <math>P</math> that intersects the circle. This constant is called the power of point <math>P</math>. For example, in the figure below
  5 KB (827 words) - 17:30, 21 February 2024
• Reader's Digest National Word Power Challenge
  The '''Reader's Digest National Word Power Challenge''' is the first nationwide vocabulary competition for middle scho ...dependencies thereof, who have not previously won a scholarship from Word Power, can participate.
  2 KB (293 words) - 21:13, 20 March 2008
• Power of a Point Theorem/Introductory Problem 1
  Applying the [[Power of a Point Theorem]], we get <math> 3\cdot(3+5) = x (x+10) \rightarrow x^2 ''Back to the [[Power of a Point Theorem]].''
  448 bytes (67 words) - 15:15, 23 March 2020
• Power of a Point Theorem/Introductory Problem 2
  Applying the Power of a Point Theorem gives <math> 6\cdot x = 4\cdot 1 </math>, so <math> x = ''Back to the [[Power of a Point Theorem]].''
  289 bytes (45 words) - 13:14, 16 July 2017
• Power of a Point Theorem/Introductory Problem 3
  From the Power of a Point Theorem, we have that ''Back to the [[Power of a Point Theorem]].''
  969 bytes (154 words) - 14:40, 3 July 2006
• Power of a Point Theorem/Introductory Problem 4
  ...3 </math> (or by just knowing your [[Pythagorean Triple]]s). Applying the Power of a Point Theorem gives <math> AE\cdot BE = CE\cdot DE </math>, or <math> ''Back to the [[Power of a Point Theorem]].''
  1 KB (177 words) - 02:14, 26 November 2020
• Power of a point
  #REDIRECT [[Power of a Point Theorem]]
  38 bytes (6 words) - 23:18, 30 June 2006
• Power of a Point Introductory Problem 3
  #REDIRECT [[Power of a Point Theorem/Introductory Problem 3]]
  61 bytes (8 words) - 12:07, 10 July 2006
• Power of a Point Introductory Problem 4
  #REDIRECT [[Power of a Point Theorem/Introductory Problem 4]]
  61 bytes (8 words) - 18:49, 10 July 2006
• Power of a Point Theorem Introductory Problem 1
  #REDIRECT [[Power of a Point Theorem/Introductory Problem 1]]
  61 bytes (8 words) - 09:19, 1 July 2006
• Power of a Point Theorem Introductory Problem 2
  #REDIRECT [[Power of a Point Theorem/Introductory Problem 2]]
  61 bytes (8 words) - 09:25, 1 July 2006
• Power of a Point Theorem Introductory Problem 3
  #REDIRECT [[Power of a Point Theorem/Introductory Problem 3]]
  61 bytes (8 words) - 09:27, 1 July 2006
• Power of a Point Theorem Introductory Problem 4
  #REDIRECT [[Power of a Point Theorem/Introductory Problem 4]]
  61 bytes (8 words) - 09:27, 1 July 2006
• Power set
  The '''power set''' of a given [[set]] <math>S</math> is the set <math>\mathcal{P}(S)</m Similarly, for any [[finite]] set with <math>n</math> elements, the power set has <math>2^n</math> elements.
  4 KB (757 words) - 11:44, 8 March 2018
• Perfect power
  ...math> is a perfect <math>2</math>nd, <math>3</math>rd and <math>6</math>th power. ...h>st power" is a meaningless property: every integer is a <math>1</math>st power of itself.
  870 bytes (148 words) - 16:52, 18 August 2013
• Power's of 2 in pascal's triangle
  2 KB (341 words) - 16:57, 16 June 2019
• Power
  ...oosely defined as the speed something can do [[work]]. The [[SI]] unit for power is the [[Watt]]. ...d of [[time]]. It is also the [[derivative]] of work. If <math>P</math> is power, <math>W</math> is work, and <math>t</math> is time, then:
  467 bytes (77 words) - 23:26, 2 March 2008
• Power mean inequality
  #REDIRECT [[Power Mean Inequality]]
  35 bytes (4 words) - 21:24, 20 December 2007
• Besot Power Series
  Besot's Power Series Theorem states that
  725 bytes (145 words) - 15:51, 17 February 2016

Page text matches

• Pythagorean Theorem
  ...> and <math>AX = AB + BC </math>. By considering the [[Power of a Point | power of point]] <math>A </math> with respect to <math>\omega </math>, we see
  5 KB (886 words) - 21:12, 22 January 2024
• Physics
  ...the study of movement. [[Kinematics]], mechanical [[force]]s, [[work]], [[power]], [[energy]], and [[matter]] are all part of mechanics. ...defined as <math>P =\int^{v_f}_{v_i} F\,dv</math> where <math>P</math> is power delivered and <math>v</math> is velocity. [[Energy]] is the other basic int
  9 KB (1,355 words) - 07:29, 29 September 2021
• Inequality
  * [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]] * [[Power mean inequality]]
  12 KB (1,798 words) - 16:20, 14 March 2023
• 2015 IMO Problems
  is a power of 2. (<i>A power of 2 is an integer of the form <math>2^n</math> where <math>n</math> is a n
  4 KB (692 words) - 22:33, 15 February 2021
• American Regions Mathematics League
  *A power round, where the questions are proof-oriented and are in a theme
  2 KB (267 words) - 17:06, 7 March 2020
• Joining an ARML team
  ...ractices which are usually composed of individual tests, team tests, and a power round test. ...n Individual Exam, Individual Short Answer Section, Team Questions, a Team Power Question, and 2 sets of relays of 5 each (there are 10 members in each team
  21 KB (3,500 words) - 18:41, 23 April 2024
• Princeton University Mathematics Competition
  ...ustification (referring to previous parts is allowed). Groups turn in the Power Round solutions the day of the event.
  2 KB (295 words) - 23:19, 5 January 2019
• Power Mean Inequality
  ...'' is a generalized form of the multi-variable [[Arithmetic Mean-Geometric Mean]] Inequality. ...ights <math>w_i</math> with sum <math>\sum_{i=1}^n w_i=1</math>, the power mean with exponent <math>t</math>, where <math>t\in\mathbb{R}</math>, is defined
  3 KB (606 words) - 23:59, 1 July 2022
• Polynomial
  ...mation that one can have about a polynomial of one variable is the highest power of the variable which appears in the polynomial. This number is known as t
  6 KB (1,100 words) - 01:44, 17 January 2024
• Factorial
  ...n</math>, and not divisible by any prime <math>p>n</math>. But what is the power of a prime <math>p\le n</math> ...r of <math>p</math>. Those divisible by <math>p^3</math> give yet another power of <math>p</math>. Continuing in this manner gives
  10 KB (809 words) - 16:40, 17 March 2024
• San Diego ARML
  ** Power: 33 ** Power: 17
  2 KB (378 words) - 16:34, 5 January 2010
• Fermat's Little Theorem
  .../math> as a product of cyclic groups of prime order where the set of prime power orders is unique. We can do this because if any two prime powers are not c
  16 KB (2,675 words) - 10:57, 7 March 2024
• Harmonic mean
  ...d of mean (like [[arithmetic mean]] and [[geometric mean]]). The harmonic mean of a [[set]] of <math>n</math> [[positive]] [[real number]]s <math> x_1, x_ ...to avoid division by zero. For instance, if we tried to take the harmonic mean of the set <math>\{-2, 3, 6\}</math> we would be trying to calculate <math>
  1 KB (196 words) - 00:49, 6 January 2021
• Rearrangement Inequality
  ...e to be [[positive]] or negative, unlike the [[Power mean inequality|power-mean]] family of inequalities. *[[Power Mean Inequality]]
  5 KB (804 words) - 13:54, 26 January 2023
• Divisibility rules
  .../math> if and only if the last <math>n</math> digits are divisible by that power of 5. ...zeros that should be at the end of a number for it to be divisible by that power of 10.
  8 KB (1,315 words) - 18:18, 2 March 2024
• Induction
  ...s an emphasis on proof. Induction problems can be found anywhere from the Power Round of the [[American Regions Math League | ARML]] up through the [[Unite ...number of odd binomial coefficients in any row of the Pascal triangle is a power of 2. (1956 Putnam Competition)
  5 KB (768 words) - 20:45, 1 September 2022
• Jensen's Inequality
  ...t examples of Jensen's inequality is the [[quadratic mean]] - [[arithmetic mean]] inequality. Taking <math>F(x)=x^2</math>, which is convex (because <math> Similarly, [[arithmetic mean]]-[[geometric mean]] inequality ([[AM-GM]]) can be obtained from Jensen's inequality by consid
  3 KB (623 words) - 13:10, 20 February 2024
• Generating function
  ...ath>, give the terms of a [[sequence]] which is of interest. Therefore the power series (i.e. the generating function) is <math>c_0 + c_1 x + c_2 x^2 + \cdo ...the result is uninteresting (both the generating function and the desired power series are just <math>1</math>).
  4 KB (659 words) - 12:54, 7 March 2022
• Binomial Theorem
  Since <math>e^{a+b} = e^ae^b</math>, and power series for the same function are termwise equal, the series at <math>x = a
  5 KB (935 words) - 13:11, 20 February 2024
• Prime number
  ...prime, ''n'' must not have any odd divisor larger than 1 and so must be a power of 2. Therefore all Fermat primes have the form <math>2^{2^n}+1</math>. [[
  6 KB (985 words) - 12:38, 25 February 2024

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