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- ...ean [[line]] for the [[point]]s <math>w_1, w_2, \dots, w_n</math> if <math>L</math> contains points (complex numbers) <math>z_1, z_2, \dots, z_n</math> ...>, <math>w_4 = 1 + 27i</math>, and <math>w_5 = - 14 + 43i</math>, there is a unique mean line with <math>y</math>-intercept 3. Find the [[slope]] of th2 KB (422 words) - 00:22, 6 September 2020
- ...>, and line <math>XP</math> intersects line <math>YZ</math> at point <math>L</math>, then <math>\dfrac{XP}{PL} = \frac{[XPY] + [ZPX]}{[YPZ]}.</math> pair L = y/(y+z)*Y + z/(y+z)*Z;13 KB (2,091 words) - 00:20, 26 October 2023
- ...^{}_{}</math>, and <math>d^{}_{}</math> are positive integers. Find <math>a + b + c + d^{}_{}</math>. ...\cdot 12\sin 45 = 12\sqrt{2}</math> (or notice that the triangle formed is a <math>45 - 45 - 90</math> [[right triangle]]).6 KB (906 words) - 13:23, 5 September 2021
- ...n two hanging columns of three targets each and one column of two targets. A marksman is to break all the targets according to the following rules: 1) The marksman first chooses a column from which a target is to be broken.3 KB (491 words) - 04:24, 4 November 2022
- ...n the Wiki front page--><onlyinclude>Find <math>A^2_{}</math>, where <math>A^{}_{}</math> is the sum of the [[absolute value]]s of all roots of the foll ...19}+\sqrt{383}}{2}\\\\x_2=\frac{\sqrt{19}-\sqrt{383}}{2}\end{array}\right\}A=|x_1|+|x_2|\Rightarrow\sqrt{383}</math>2 KB (285 words) - 05:15, 13 June 2022
- ...smallest positive integer <math>m^{}_{}</math> for which <math>R^{(m)}(l)=l^{}_{}</math>. ...> in <math>l_1</math>, and let <math>l''</math> be the reflection of <math>l'</math> in <math>l_2</math>.2 KB (404 words) - 19:24, 4 July 2013
- ...int, then <math>P_{n + 1}^{}</math> is the midpoint of <math>\overline{P_n L}</math>. Given that <math>P_7 = (14,92)\,</math>, what is <math>k + m\,</m ...right to the left, we have the following information (remembering that if a point must be <math>(0,0)</math>, we can just ignore it!):4 KB (611 words) - 13:59, 15 July 2023
- A beam of light strikes <math>\overline{BC}\,</math> at point <math>C\,</math pair B = MP("B",(0,0),NW), C = MP("C",D((1,0))), A = MP("A",expi(alpha * pi/180),N); path r = C + .4 * expi(beta * pi/180) -- C - 2*ex2 KB (303 words) - 00:03, 28 December 2017
- // projection of point A onto line BC triple projectionofpointontoline(triple A, triple B, triple C)8 KB (1,172 words) - 21:57, 22 September 2022
- ...ing 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, or do ...math>2!</math> ways to determine the order of the remaining two steps, for a total of <math>12</math> sequences that we have to exclude. This gives <mat3 KB (602 words) - 23:15, 16 June 2019
- ...The vertices of its midpoint triangle are the [[midpoint]]s of its sides. A triangular [[pyramid]] is formed by folding the triangle along the sides of ..."\(D\)",foot(A,B,C),NE);label("\(E\)",foot(B,A,C),SW);label("\(F\)",foot(C,A,B),NW);label("\(P\)",P,NW);label("\(Q\)",Q,NE);label("\(R\)",R,SE);</asy><a7 KB (1,169 words) - 15:28, 13 May 2024
- The diagram shows a [[rectangle]] that has been dissected into nine non-overlapping [[square]]s ...engths from smallest to largest <math>a_1,\ldots,a_9</math>, and let <math>l,w</math> represent the dimensions of the rectangle.3 KB (485 words) - 00:31, 19 January 2024
- A [[sphere]] is inscribed in the [[tetrahedron]] whose vertices are <math>A = (6,0,0), B = (0,4,0), C = (0,0,2),</math> and <math>D = (0,0,0).</math> triple A = (6,0,0), B = (0,4,0), C = (0,0,2), D = (0,0,0);6 KB (1,050 words) - 18:44, 27 September 2023
- A fair die is rolled four times. The [[probability]] that each of the final t ...n the diagram below, the lowest <math>y</math>-coordinate at each of <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> corresponds to t11 KB (1,729 words) - 20:50, 28 November 2023
- ...ne of the two vertices where it is not currently located, and crawls along a side of the triangle to that vertex. Given that the probability that the bu ...o return to the original vertex, the net number of clockwise steps must be a multiple of 3, i.e., <math>\#CW - \#CCW \equiv 0 \pmod{3}</math>. Since <m15 KB (2,406 words) - 23:56, 23 November 2023
- ...th>EI = EJ = EK = 2</math>. A solid <math>S</math> is obtained by drilling a tunnel through the cube. The sides of the tunnel are planes parallel to <ma ...ection = orthographic(camera=(1/4,2,3/4)); defaultpen(linewidth(0.7)); pen l = linewidth(0.5) + linetype("10 2");4 KB (518 words) - 15:01, 31 December 2021
- ...ts <math>A</math>, <math>B</math> and <math>C</math> lie on the surface of a [[sphere]] with center <math>O</math> and radius <math>20</math>. It is giv ...eron's Formula]] the area of <math>\triangle ABC</math> is (alternatively, a <math>13-14-15</math> triangle may be split into <math>9-12-15</math> and <3 KB (532 words) - 13:14, 22 August 2020
- The purpose of integration by parts is to replace a difficult [[integral]] with an easier one. The formula is ...an "easy" (or "easier") [[derivative]] and <math>dv</math> so that it has a easy [[antiderivative]].1 KB (235 words) - 17:01, 11 March 2022
- ...used most frequently in [[geometry]], to denote a set of points satisfying a certain geometric condition. ...can be defined as the locus of all points that are a certain distance from a given center.890 bytes (160 words) - 02:58, 22 March 2011
- A '''Platonic solid''' is a [[polyhedron]], or 3 dimensional figure, in which all [[face]]s are [[congr ...(1+5^.5)/2; currentprojection=orthographic(2,-2.2,2); pen d=linewidth(0.7),l=linetype("2 6"); triple P[];8 KB (1,168 words) - 22:48, 19 February 2022
