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  • ...'' 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 (619 words) - 12:57, 23 August 2024
  • 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 (859 words) - 15:11, 8 December 2024
  • 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) - 20:13, 20 March 2008
  • 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) - 14:15, 23 March 2020
  • 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) - 12:14, 16 July 2017
  • From the Power of a Point Theorem, we have that ''Back to the [[Power of a Point Theorem]].''
    969 bytes (154 words) - 13:40, 3 July 2006
  • ...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) - 01:14, 26 November 2020
  • #REDIRECT [[Power of a Point Theorem]]
    38 bytes (6 words) - 22:18, 30 June 2006
  • #REDIRECT [[Power of a Point Theorem/Introductory Problem 3]]
    61 bytes (8 words) - 11:07, 10 July 2006
  • #REDIRECT [[Power of a Point Theorem/Introductory Problem 4]]
    61 bytes (8 words) - 17:49, 10 July 2006
  • #REDIRECT [[Power of a Point Theorem/Introductory Problem 1]]
    61 bytes (8 words) - 08:19, 1 July 2006
  • #REDIRECT [[Power of a Point Theorem/Introductory Problem 2]]
    61 bytes (8 words) - 08:25, 1 July 2006
  • #REDIRECT [[Power of a Point Theorem/Introductory Problem 3]]
    61 bytes (8 words) - 08:27, 1 July 2006
  • #REDIRECT [[Power of a Point Theorem/Introductory Problem 4]]
    61 bytes (8 words) - 08:27, 1 July 2006
  • 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) - 10:44, 8 March 2018
  • ...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) - 15:52, 18 August 2013
  • 2 KB (341 words) - 15:57, 16 June 2019
  • ...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) - 22:26, 2 March 2008
  • #REDIRECT [[Power Mean Inequality]]
    35 bytes (4 words) - 20:24, 20 December 2007
  • Besot's Power Series Theorem states that
    735 bytes (146 words) - 20:13, 7 October 2024

Page text matches

  • ...> 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 (885 words) - 22:03, 5 October 2024
  • ...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) - 06:29, 29 September 2021
  • * [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]] * [[Power mean inequality]]
    12 KB (1,806 words) - 05:07, 19 June 2024
  • 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 (709 words) - 14:00, 1 June 2024
  • *A power round, where the questions are proof-oriented and are in a theme
    2 KB (267 words) - 16:06, 7 March 2020
  • ...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
    22 KB (3,532 words) - 10:25, 27 September 2024
  • ...ustification (referring to previous parts is allowed). Groups turn in the Power Round solutions the day of the event.
    2 KB (295 words) - 22:19, 5 January 2019
  • ...'' 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 (619 words) - 12:57, 23 August 2024
  • ...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) - 14:57, 30 August 2024
  • ...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) - 15:40, 17 March 2024
  • ** Power: 33 ** Power: 17
    2 KB (378 words) - 15:34, 5 January 2010
  • .../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 (2,660 words) - 22:42, 28 August 2024
  • ...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) - 23:49, 5 January 2021
  • ...e to be [[positive]] or negative, unlike the [[Power mean inequality|power-mean]] family of inequalities. *[[Power Mean Inequality]]
    5 KB (804 words) - 12:54, 26 January 2023
  • .../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.
    10 KB (1,572 words) - 21:11, 22 September 2024
  • ...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) - 23:59, 28 September 2024
  • ...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 (628 words) - 05:29, 28 November 2024
  • ...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) - 11:54, 7 March 2022
  • 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) - 12:11, 20 February 2024
  • ...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 (1,036 words) - 17:26, 2 September 2024

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