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  • Proof: <math>\sin</math> is a [[concave function]] from <math>0\le \theta \le \pi</math>. Therefore we may use [[Jensen's in Proof: The distance <math>d</math> from the circumcenter and incenter of a triangle can be expr
    7 KB (1,300 words) - 00:11, 28 October 2024
  • ...ance from a fixed point. The fixed point is called the [[center]] and the distance from the center to a point on the circle is called the [[radius]]. ...dentify is a distance <math>r</math> from <math>(h,k)</math>. Using the [[distance formula]], this gives <math>\sqrt{(x - h)^2 + (y - k)^2} = r</math> which i
    9 KB (1,585 words) - 12:46, 2 September 2024
  • ...anted a function that doesn't have a nice anti-derivative.) Interpret the distance that the object travels between times <math>t=1</math> and <math>t=2</math> ...tween times <math>t=2</math> sec and <math>t=5</math> sec? Interpret this distance geometrically, as an area under a curve.
    11 KB (2,082 words) - 14:23, 2 January 2022
  • ...remove the restriction of <math>x\ge 0</math> from the [[domain]] of the [[function]] <math>f(x)=\sqrt{x}</math> (although some additional considerations are n The [[absolute value]] (or modulus or magnitude) of a complex number is the distance from the complex number to the origin. It is denoted by <math>|z|</math>.
    5 KB (860 words) - 14:36, 10 December 2023
  • ...signed portion of <math>x</math>. Geometrically, <math>|x|</math> is the [[distance]] between <math>x</math> and [[zero]] on the real [[number line]]. The absolute value function exists among other contexts as well, including [[complex numbers]].
    2 KB (368 words) - 09:37, 5 January 2009
  • ...hus we begin with an informal explanation: a limit is the value to which a function grows close when its argument is near (but not at!) a particular value. For ...m_{x\to 2}x^2=4</cmath> because whenever <math>x</math> is close to 2, the function <math>f(x)=x^2</math> grows close to 4.
    7 KB (1,327 words) - 17:39, 28 September 2024
  • ...ing above it. The bottom ring has an outside diameter of 3 cm. What is the distance, in cm, from the top of the top ring to the bottom of the bottom ring? The function <math>f</math> has the property that for each real number <math>x</math> in
    15 KB (2,223 words) - 12:43, 28 December 2020
  • Let <math>f</math> be a function with the following properties: ...zontal plane. A sphere of radius <math>2</math> rests on them. What is the distance from the plane to the top of the larger sphere?
    13 KB (1,953 words) - 23:31, 25 January 2023
  • ...er <math>A</math> at points <math>P</math> and <math>D</math>. What is the distance from <math>P</math> to <math>\overline{AD}</math>? ...\text{a non-horizontal line}\qquad\textbf{(E)}\ \text{the graph of a cubic function} </math>
    13 KB (1,955 words) - 20:06, 19 August 2023
  • ...math>C_{3}</math> the inscribed circle of <math>\triangle{QUV}</math>. The distance between the centers of <math>C_{2}</math> and <math>C_{3}</math> can be wri A certain function <math>f</math> has the properties that <math>f(3x) = 3f(x)</math> for all p
    8 KB (1,282 words) - 20:12, 19 February 2019
  • .../math> are (1) on opposite sides of <math>\ell</math>. and (2) at the same distance from <math>\ell</math>. Notice that the distance <math>OM</math> equals <math>PN + PO \cos \angle AOM = r(1 + \cos \angle AO
    20 KB (3,497 words) - 14:37, 27 May 2024
  • So it is only necessary to find the length of the function at <math>3 \le x \le 4</math> and <math>3 \le y \le 4</math>: ...meter <math>4\sqrt{2}</math>. Now, we make use of the following fact for a function of two variables <math>x</math> and <math>y</math>: Suppose we have <math>f
    7 KB (1,225 words) - 18:56, 4 August 2021
  • The [[function]] <math>f</math> defined by <math>f(x)= \frac{ax+b}{cx+d}</math>, where <ma ...>f(f(x)) = x</math> for all <math>x</math> in the domain. Substituting the function definition, we have <math>\frac {a\frac {ax + b}{cx + d} + b}{c\frac {ax +
    11 KB (2,065 words) - 16:53, 8 September 2024
  • ...here <math>a_{}</math> and <math>b_{}</math> are positive numbers. This [[function]] has the property that the image of each point in the complex plane is [[e ...course, <math>(d^2+c^2)</math> can't be zero because this property of the function holds for all complex <math>z</math>. Therefore, <math>a = \frac{1}{2}</mat
    6 KB (1,010 words) - 18:01, 24 May 2023
  • ...> We can write <math>y = mx</math> as <math>y - mx = 0,</math> so from the distance formula, ...ath> is <math>(9, 6)</math>, we see that this parabola is the graph of the function <cmath>y=\frac{1}{12}(x-9)^2+3=\frac{1}{12}x^2-\frac{3}{2}x+\frac{39}{4}.</
    7 KB (1,188 words) - 16:46, 23 June 2024
  • A '''holomorphic function''' <math>f: \mathbb{C} \to \mathbb{C}</math> is a differentiable [[complex number|complex]] [[function]]. That is, just
    9 KB (1,537 words) - 20:04, 26 July 2017
  • ...h>4</math>. Thus, the original sequence can be generated from a quadratic function. ...ves <math>a = 2</math>, and hence <math>b = 2</math>. Thus, our quadratic function is:
    8 KB (1,221 words) - 10:34, 27 November 2024
  • Suppose that <math>f</math> is a function with the property that for all <math>x</math> and <math>y, f(x + y) = f(x) The minimum value of the function
    14 KB (2,102 words) - 21:03, 26 October 2018
  • ...]]s between [[point]]s. Isometries exist in any space in which a distance function is defined, i.e. an arbitrary abstract [[metric space]]. In the particular
    2 KB (282 words) - 16:17, 23 September 2006
  • ...athbb{R}_{\geq 0}</math>. The metric <math>d</math> represents a distance function between pairs of points of <math>S</math> which has the following propertie ...ons, graphics, or grades). The above properties follow from our notion of distance. Non-negativity stems from the idea that A cannot be closer to B than B is
    2 KB (324 words) - 00:19, 22 December 2012

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