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• Tangent (geometry)
  ...math> intersects it in 2 points and the tangent line at <math>\left(\frac{\pi}2, 1\right)</math> intersects it in [[infinite]]ly many points (and is in f ...y. Any two disjoint circles have four tangents in common, two internal and two external.
  2 KB (332 words) - 21:54, 11 March 2024
• Right angle
  ...of every right angle is 90 [[degree (geometry) | degrees]] or <math>\frac \pi 2</math> [[radian]]s. When drawing diagrams, we denote right angles with a
  673 bytes (91 words) - 23:59, 11 June 2022
• Integral
  The '''integral''' is one of the two base concepts of [[calculus]], along with the [[derivative]]. In introductory, high-school level texts, the integral is often presented in two parts, the '''indefinite integral''' and '''definite integral'''. Although
  5 KB (909 words) - 14:16, 31 May 2022
• Angle
  An '''angle''' is the [[union]] of two [[ray]]s with a common [[endpoint]]. The common endpoint of the rays is ca If two angles are [[congruent (geometry)|congruent]], they have the same angle mea
  4 KB (597 words) - 18:39, 9 May 2024
• 2007 iTest Problems
  ...>2</math> greater than <math>p</math>. What is the arithmetic mean of the two primes in the smallest twin prime pair? ...ath>4</math> years older than my youngest grandparent. Each grandfather is two years older than his wife. If Bertha is younger than Dolores, what is the d
  30 KB (4,794 words) - 23:00, 8 May 2024
• Straight angle
  ...e of every straight angle is 180 [[degree (geometry) | degrees]] or <math>\pi</math> [[radian]]s.
  568 bytes (78 words) - 13:50, 12 June 2022
• 2005 AMC 10A Problems
  Three tiles are marked <math>X</math> and two other tiles are marked <math>O</math>. The five tiles are randomly arranged There are two values of <math>a</math> for which the equation <math> 4x^2 + ax + 8x + 9 =
  14 KB (2,026 words) - 11:45, 12 July 2021
• 2003 AMC 10A Problems
  The sum of the two 5-digit numbers <math>AMC10</math> and <math>AMC12</math> is <math>123422</ ...e numbers is <math>20</math>. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three?
  13 KB (1,900 words) - 22:27, 6 January 2021
• 1997 AJHSME Problems/Problem 24
  ...CE</math> is divided at <math>C</math> in the ratio <math>2:3</math>. The two semicircles, <math>ABC</math> and <math>CDE</math>, divide the circular reg ...{2}\pi\cdot3^2 - \frac{1}{2}\pi\cdot2^2 =\frac{\pi}{2}(5^2 + 3^2 - 2^2)=15\pi</math>
  2 KB (394 words) - 17:05, 20 October 2023
• 1985 IMO Problems/Problem 1
  ...es of arcs, <math> \angle DTA = \angle DCO = \frac{\angle DCB}{2} = \frac{\pi}{2} - \frac{\angle DAB}{2} </math>. It follows that <math>AT = AD </math>. ...</math> such that <math>AT = AD </math>. Then <math>\angle DTA = \frac{ \pi - \angle DAB}{2} = \angle DCO</math>, so <math>DCOT </math> is a cyclic qua
  4 KB (684 words) - 07:28, 3 October 2021
• 2004 AMC 10A Problems
  ...hat is the probability that the number of heads obtained from flipping the two fair coins is the same? ...tomato, lettuce, pickles, cheese, and onions. A customer can choose one, two, or three meat patties, and any collection of condiments. How many differe
  15 KB (2,092 words) - 20:32, 15 April 2024
• 1985 AIME Problems
  ...rotated about the other leg, the volume of the cone produced is <math>1920\pi \;\textrm{cm}^3</math>. What is the length (in cm) of the hypotenuse of the ...alpha + \beta </math> radians, respectively, where <math>\alpha + \beta < \pi</math>. If <math>\cos \alpha</math>, which is a positive rational number, i
  7 KB (1,071 words) - 19:24, 23 February 2024
• 1985 AIME Problems/Problem 2
  ...rotated about the other leg, the volume of the cone produced is <math>1920\pi \;\textrm{ cm}^3</math>. What is the length (in cm) of the [[hypotenuse]] o ...}b</math>. Then <math>\frac{1}{3} \pi \left(\frac{12}{5}b\right)b^2 = 800\pi</math> so <math>b^3 = 1000</math> and <math>b = 10</math> so <math>a = 24</
  3 KB (463 words) - 15:10, 4 September 2020
• 2003 AMC 12A Problems/Problem 15
  draw(2*expi(2*pi/6)--2*expi(4*pi/6)); ...}{4}+\frac{1}{24}\pi\qquad \mathrm{(E) \ } \frac{\sqrt{3}}{4}+\frac{1}{12}\pi </math>
  3 KB (393 words) - 19:06, 3 June 2024
• Sector
  A '''sector''' of a [[circle]] is a region bounded by two [[radius|radii]] of the circle and an [[arc]]. If the [[central angle]] of the sector is <math>\pi</math> (or <math>180^{\circ}</math>), then the sector is a [[semicircle]].
  1 KB (178 words) - 21:12, 24 April 2008
• Georgia Tech High School Math Competition
  ...annual [[math tournament]] hosted and run by the School of Mathematics and Pi Mu Epsilon of the Georgia Institute of Technology (better known as Georgia After lunch, there is a two-hour, six-question proof test. These papers are graded by School of Mathema
  3 KB (475 words) - 21:51, 31 December 2013
• Asymptote: Advanced Configuration
  There are two things that Asymptote users commonly would like to do with their figures: m \(\int_0^{\pi}{\sin{x}}\,dx=2\)
  12 KB (1,931 words) - 13:53, 26 January 2020
• Asymptote: Reference
  ...'' is associated with a cartesian coordinate pair in Asymptote. There are two useful functions that allow one to use polar coordinates as well: ...joined smoothly in an curve that can be twisted. Keep in mind that if only two things are connected with <tt>..</tt>, the curve will be a straight line.
  7 KB (1,205 words) - 21:38, 26 March 2024
• Asymptote (geometry)
  .../math>; thus the functions is undefined at <math>x=\frac{\pi}{6} + \frac{n\pi}{3}</math>. ...ymptote is at the quotient of the leading coefficient of <math>P(x)</math> over the leading coefficient of <math>Q(x)</math>.
  4 KB (664 words) - 11:44, 8 May 2020
• Mock AIME 3 Pre 2005 Problems
  ...r centers is <math>84</math>, then the area of the third circle is <math>k\pi</math> for some integer <math>k</math>. Determine <math>k</math>. ...lish if and only if between any two <math>O's</math> there appear at least two consonants. Let <math>N</math> denote the number of <math>10</math>-letter
  7 KB (1,135 words) - 23:53, 24 March 2019

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