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  • Notice that we can graph this on the coordinate plane. ...\frac{15}{2}) - 2(6) = 40 - 15 - 12 = 13</math>. Since the desired area is half the shaded region, our area is <math>\boxed{\textbf{(D)}\ 6\frac{1}{2}}</ma
    8 KB (1,016 words) - 23:17, 30 December 2023
  • Let <math>A,B,C,D</math> be four points in the Euclidean plane. Taking an inversion centered at <math>D</math> (the point doesn't matter, Solution: Consider half of the circle, with the quadrilateral <math>ABCD</math>, <math>AD</math> be
    6 KB (922 words) - 16:34, 13 January 2025
  • Denote by <math>\mathcal{H}</math> the upper half plane (those complex numbers with positive imaginary part). Then there are functi
    5 KB (849 words) - 15:14, 18 May 2021
  • A circle is defined as the or [[locus]] of [[point]]s in a [[plane]] with an equal distance from a fixed point called the [[center]]. This dis We can find the general form of the equation of a circle on the [[coordinate plane]] given its radius, <math>r</math>, and center <math>(h,k)</math>. We know
    9 KB (1,510 words) - 18:56, 16 January 2025
  • ...tions of trigonometric functions from the real numbers to the full complex plane. The Taylor series for sine and cosine are shown below: <cmath>\sin (x) = \ * [[Half angle identities]]
    8 KB (1,228 words) - 14:40, 10 January 2025
  • ...an additional cost of <math>2</math> dollars for putting anchovies on one half. Dave ate all the slices of anchovy pizza and one plain slice. Doug ate the ...es}\qquad\mathrm{(D)}\ \text{a circle}\qquad\mathrm{(E)}\ \text{the entire plane}</math>
    15 KB (2,223 words) - 12:43, 28 December 2020
  • ...ickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets? ...congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest to
    13 KB (1,957 words) - 11:53, 24 January 2024
  • Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles int ...and three times as much area as Carlos’ lawn. Carlos’ lawn mower cuts half as fast as Beth’s mower and one third as fast as Andy’s mower. If they
    10 KB (1,547 words) - 03:20, 9 October 2022
  • One possibility is to use the [[coordinate plane]], setting <math>B</math> at the origin. Point <math>A</math> will be <math ...inating answer choice (A). <math>r</math> is only a little bit bigger than half of <math>s</math>, so we can reasonably assume that their ratio is less tha
    6 KB (958 words) - 22:29, 28 September 2023
  • ...and there was an additional cost of 2 dollars for putting anchovies on one half. Dave ate all of the slices of anchovy pizza and one plain slice. Doug at ...es}\qquad\mathrm{(D)}\ \text{a circle}\qquad\mathrm{(E)}\ \text{the entire plane}</math>
    13 KB (2,028 words) - 15:32, 22 March 2022
  • ...break the octahedron into two [[square pyramid]]s by cutting it along a [[plane]] [[perpendicular]] to one of its internal diagonals. We also know that the height of the pyramid is half the height of the cube, so it is <math>\frac{1}{2}</math>. The volume of a
    2 KB (292 words) - 19:53, 1 October 2024
  • to some [[open set | open]] domain <math>E</math> containing the closed half-plane <math>F_T</math> is defined and analytic on the entire complex plane <math>\mathbb C</math>.
    6 KB (1,034 words) - 06:55, 12 August 2019
  • ...i\ge 1,</math> the lengths of the sides of square <math>S_{i+1}</math> are half the lengths of the sides of square <math>S_{i},</math> two adjacent sides o Starting at <math>(0,0),</math> an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is left, right, up,
    6 KB (1,000 words) - 23:25, 26 March 2024
  • The graph of <math> y^2 + 2xy + 40|x|= 400</math> partitions the plane into several regions. What is the area of the bounded region? Eight [[sphere]]s of [[radius]] 100 are placed on a flat [[plane|surface]] so that each sphere is [[tangent]] to two others and their [[cent
    7 KB (1,084 words) - 01:01, 28 November 2023
  • ...ssible by drawing the lines and observing that the intersection of the two half-planes does not share any point with the circle.)
    20 KB (3,497 words) - 14:37, 27 May 2024
  • ...g a circle with a center as that given point will always cut the circle in half, so we can re-phrase the problem: Consider the region of the plane between <math>x=16</math> and <math>x=17</math>. The parts of the circles c
    6 KB (1,022 words) - 18:29, 22 January 2024
  • ...{ar^{n}}</math> converges for <math>\mid r \mid <1</math>. In the complex plane, this makes a circle of radius 1 centered at (0,0). This is often referred
    1 KB (180 words) - 19:12, 19 August 2015
  • ...which simplifies things quite nicely. Continue as in solution 2, computing half-angle sines instead of nested radicals, to obtain <math>\boxed{720}</math>. Plotting this regular <math>12</math>-gon on the complex plane with center as origin, and a vertex on the <math>x</math>-axis. We have tha
    6 KB (906 words) - 12:23, 5 September 2021
  • ...lope of <math>PR</math> is <math>-\frac{4}{3}</math>. Thus, in the complex plane, they are equivalent to <math>\tan(\alpha)=\frac{24}{7}</math> and <math>\t By the [[Trigonometric identities#Half-angle identities|Half-Angle Identities]], <math>\tan\left(\frac{\alpha}{2}\right)=\pm\sqrt{\frac{
    8 KB (1,319 words) - 10:34, 22 November 2023
  • // calculate intersection of line and plane // q = point in plane
    8 KB (1,172 words) - 20:57, 22 September 2022

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