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• 2003 AMC 12B Problems/Problem 18
  ...p + 1}</math> to the fifth root. Similarly, we want to look for the lowest power <math>n</math> of <math>7</math> such that <math>13n - 1 \equiv 0 \pmod{5}<
  6 KB (914 words) - 11:07, 7 September 2023
• Topological space
  ...</math> is a [[set]] and <math>\mathcal{T}</math> is a [[subset]] of the [[power set]] of <math>X</math> satisfying the following relations: ...ts <math>\{ \varnothing, X\}</math>, and <math>\mathfrak{P}(X)</math> (the power set of <math>X</math>) are both topologies. They are the least and greates
  6 KB (1,142 words) - 15:38, 21 June 2008
• Mechanics
  Mechanics is the study of movement. Kinematics, mechanical forces, work, power, energy, and matter are all part of mechanics. ...states respectively. Similarly, mechanical power is defined as where is power delivered and is velocity. Energy is the other basic intrinsic property of
  2 KB (309 words) - 15:41, 1 December 2015
• 1995 AHSME Problems/Problem 27
  ...few rows: <math>0, 2, 6, 14, 30, 62</math>. They are each two less than a power of <math>2</math>, so we try to prove it: ...2S_n-2(n-1)+2(n-1)+2=2S_n+2</math>. If <math>S_n</math> is two less than a power of 2, then it is in the form <math>2^x-2</math>. <math>S_{n+1}=2^{x+1}-4+2=
  5 KB (682 words) - 09:45, 18 February 2022
• 1995 AHSME Problems/Problem 26
  By [[Power of a point]], <math>AE \cdot EB = DE \cdot EF \Rightarrow (r+x)(r-x)=r^2-x^
  2 KB (359 words) - 20:01, 23 January 2017
• 1988 IMO Problems/Problem 1
  Since <math>PB\cdot PC</math> is the power of the point <math>P</math>, it stays constant as <math>A</math> varies. T
  3 KB (545 words) - 11:32, 30 January 2021
• 2003 USAMO Problems/Problem 4
  ...D = \angle MBC</math>. This exact condition can also be visualized through power of M with respect to the circumcircle of triangle <math>BDC</math> and gett
  5 KB (820 words) - 02:39, 10 January 2023
• 1985 IMO Problems/Problem 4
  ...a subset of <math>4</math> elements whose product is the <math>4</math>th power of an integer.
  1 KB (261 words) - 23:56, 29 January 2021
• 1995 IMO Problems/Problem 1
  Think about Radical Axis, Power of a Point and Radical Center. ...ath>, we have <math>PN\cdot PB=PM\cdot PC</math> and so by the converse of Power of a Point, the quadrilateral <math>MNBC</math> is cyclic. Thus, <math>90-
  5 KB (847 words) - 19:03, 12 October 2021
• 2008 iTest Problems
  ...e people will have reasonably inexpensive options for switching to cleaner power sources. Even now most families could switch to biomass for between <math>\ element which is the [[arithmetic mean]] of all the elements in that subset?
  71 KB (11,749 words) - 01:31, 2 November 2023
• Gauss's Lemma (polynomial)
  ...ily commutative) [[ring]]; let <math>A[[X]]</math> be the ring of [[formal power series]] over <math>A</math>. For <math>P \in A[[X]]</math>, let <math>I(P ...t, with <math>A = \mathbb{Z}</math>, and <math>P</math> and <math>Q</math> power series with finitely many nonzero coefficients.
  3 KB (483 words) - 12:23, 30 May 2019
• POP
  #REDIRECT[[Power of a Point Theorem]]
  37 bytes (6 words) - 22:48, 3 November 2008
• Intermediate Math Open
  ...Club participants for 2 and 1/4 hours. Then, lunch is held. Next comes the Power Round, where teams work together on a series of related problems for 45 min
  1 KB (243 words) - 17:53, 1 November 2014
• Binary
  ! Power of two !! Number in base 10 !! Binary representation ...which can be odd, as in any other place the digit will be multiplied by a power of 2 that doesn't equal 1.)
  2 KB (294 words) - 12:55, 3 September 2019
• Float
  *It is an important metric in measuring computational power (in [[FLOPS]]).
  953 bytes (136 words) - 16:08, 10 March 2011
• FLOPS
  It is a commonly used metric for measuring computational power.
  187 bytes (23 words) - 17:51, 18 December 2008
• Decibel
  ...are a logarithmic units that are used to measure intensity of things like power or sound.
  140 bytes (22 words) - 17:16, 31 August 2009
• Horsepower
  '''Horsepower''' ('''hp''' or '''Hp'''), is a measurement of [[power]]. It was developed by James Watt, who wanted to market his steam engines i
  255 bytes (41 words) - 16:14, 24 December 2008
• 1992 USAMO Problems/Problem 4
  <math>m\angle APB= m\angle A'PB'</math> because they are vertical angles. By power of point, <math>(AP)(A'P)=(BP)(B'P)\rightarrow\frac{AP}{B'P}=\frac{BP}{A'P}
  5 KB (807 words) - 18:37, 25 June 2021
• 1972 USAMO Problems/Problem 1
  ...h>\alpha + \beta + \alpha) = -\beta</math>. Since every prime has the same power in both expressions, the expressions are equal. <math>\blacksquare</math>
  5 KB (1,018 words) - 11:14, 6 October 2023

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