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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 defined3 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 below5 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 that735 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 see5 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 int9 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 n4 KB (709 words) - 14:00, 1 June 2024
- *A power round, where the questions are proof-oriented and are in a theme2 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 team22 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 defined3 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 t6 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 gives10 KB (809 words) - 15:40, 17 March 2024
- ** Power: 33 ** Power: 172 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 c16 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 consid3 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 = a5 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