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• 1974 USAMO Problems/Problem 2
  This means that this inequality is homogeneous since both sides have the same power of <math>k</math> as a factor. Since the inequality is homogeneous, we can Raising <math>2</math> to the power of each side, we get
  9 KB (1,726 words) - 14:01, 1 February 2024
• 1962 IMO Problems/Problem 6
  ...e at <math>P,Q</math>, we see that <math>AI\cdot IL = PI\cdot QI</math> by Power of a Point. Therefore, <math>2r\rho = PI \cdot QI = (PO + OI)(QO - OI) = (r
  2 KB (308 words) - 06:29, 16 December 2023
• 2021 GMC 10B
  Let <math>f(n)</math> be the largest possible power of <math>2</math> that divides <math>n</math>. Find <math>f((3^2-3)(4^2-4)(
  11 KB (1,695 words) - 14:33, 7 March 2022
• 1998 AHSME Problems/Problem 30
  ...r of <math>5</math> that divides <math>a_n</math> is at least equal to the power of <math>2</math> that divides <math>a_n</math>. ...le by <math>5</math>, and at most one of them can be divisible by a higher power of <math>5</math>. As we need <math>y_n\geq x_n\geq 8</math>, one of the in
  3 KB (486 words) - 10:37, 11 August 2020
• Computer simulation
  ...ithmic Botany | plant growth]]. Currently, however, we lack the processing power and understanding of nature to do large-scale cell-level computations, so o
  1 KB (197 words) - 13:19, 26 August 2019
• 2009 AMC 12A Problems/Problem 24
  ...nt a number <math>x</math>, such that when <math>2</math> is raised to the power of <math>x</math>, we get the expression in the <math>\log</math>. So, when ...<math>124986068</math>, what happens when you raise <math>2</math> to the power of that number? We would end up getting another one of these:
  10 KB (1,595 words) - 22:13, 20 September 2021
• 2009 AMC 12A Problems/Problem 18
  ...h>, and therefore <math>5^6 + 1 \equiv 2 \pmod 4</math>. Hence the largest power of <math>2</math> that divides <math>5^6+1</math> is <math>2^1</math>, and
  6 KB (1,012 words) - 19:16, 14 September 2022
• 2009 AMC 10A Problems/Problem 10
  == Solution 3 (Power of a point)== ...ight angle triangle, AC is the diameter of the circumcircle. By applying [[Power of a Point Theorem]], we can have <math>BD=DE</math> and <math>AD\cdot CD=B
  5 KB (879 words) - 18:57, 30 April 2024
• 2002 AMC 12A Problems/Problem 24
  ...s. We know this because we are taking magnitude to the <math>2003</math>rd power, and if the magnitude of <math>a+bi</math> is larger than <math>1</math>, i
  4 KB (743 words) - 19:54, 14 March 2024
• Two Tangent Theorem
  From a simple application of the [[Power of a Point Theorem]], the result follows.
  566 bytes (93 words) - 22:47, 5 December 2023
• MaCh 8
  ...1-hour proof test on a set of related mathematical concepts. Although the Power test does not expect rigorous proofs, a clear and complete explanation is r The top 5 teams receive awards based on their performance in the individual, Power, Team, and Mach rounds. The rounds are weighted appropriately to promote a
  2 KB (350 words) - 10:09, 1 April 2009
• 2009 AIME I Problems/Problem 7
  ...(3n + 2)}</math> an integer. This means that <math>3n + 2</math> must be a power of <math>5</math>. We test <math>25</math>: <cmath>3n + 2 = 25</cmath> <cma
  2 KB (340 words) - 00:26, 9 January 2023
• Polynomial ring
  ...h the terms are written, and indeed often list them in descending order of power. So we would write: .../math>, of which the ring of polynomials is a subring. In general, formal power series are not associated with mappings of <math>R</math> into itself, as i
  12 KB (2,010 words) - 00:10, 3 August 2020
• 2009 AIME II Problems/Problem 2
  ...rocess for the other ones(you have to turn the square root to a fractional power for c), we get <math>343+121+5 = \boxed{469}</math>
  3 KB (396 words) - 15:20, 10 May 2024
• Hilbert's Basis Theorem
  <!-- I am think it doesn't work for rings of formal power
  4 KB (617 words) - 19:59, 23 April 2023
• 2009 AIME II Problems/Problem 7
  To determine <math>a</math>, we need to determine the largest power of <math>2</math> that divides <math>c</math>. ...{2009}</math> and <math>\dbinom{4016}{2008}</math> and you get the minimum power of <math>2</math> in either expression is <math>8</math> so the answer is <
  8 KB (1,312 words) - 16:23, 30 March 2024
• Determinant
  is an element of a (strictly [[power associative]]) <math>n</math>-dimensional
  8 KB (1,345 words) - 00:31, 9 May 2020
• 2004 USAMO Problems/Problem 2
  ...an existing element of the sequence until it does have a length which is a power of 2 - it is apparent that this will not change <math>S</math>.
  3 KB (508 words) - 14:23, 17 July 2014
• 2009 USAMO Problems/Problem 1
  ...essed using circle <math>\omega_2</math> and <math>\omega_3</math> and the power of <math>O_2</math> can be expressed using circle <math>\omega_1</math> and
  2 KB (290 words) - 13:16, 17 April 2021
• Radical axis
  The '''power''' of point <math>P</math> with respect to circle <math>\omega</math> (with Note that the power of a point is negative if the point is inside the circle.
  12 KB (2,125 words) - 08:38, 23 May 2024

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