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• 2018 AMC 10B Problems/Problem 8
  path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); filldraw(shift((j,i))*v,black);
  4 KB (609 words) - 19:49, 27 August 2023
• 1971 IMO Problems/Problem 2
  Now all these nine polyhedrons lie inside <math>2 P_1</math>. Let <math>V</math> be the volume of <math>P_1</math>.
  1 KB (242 words) - 13:55, 29 January 2021
• 1960 AHSME Problems/Problem 23
  The volume <math>V = \pi R^2H</math> is to be increased by the same fixed positive amount when
  1 KB (245 words) - 19:07, 17 May 2018
• 2018 AIME I Problems/Problem 13
  https://www.youtube.com/watch?v=sT-wxV2rYqs ...AC = b, AB = c, x_1 = BX, x_2 = CX, \frac{c+t}{x_1} = u, \frac{b+t}{x_2} = v.</math>
  13 KB (2,200 words) - 21:36, 6 January 2024
• 2018 AIME I Problems/Problem 12
  ..., we can always choose <math>3-r</math> as the remainder for our set <math>V</math>, giving us a total of <math>r + 3 - r \equiv 0 \pmod{3}</math>. The
  26 KB (4,044 words) - 13:58, 24 January 2024
• 2018 AIME I Problems/Problem 11
  <cmath>v_{13}(27^m-1^m)=v_{13}(26)+v(m)=1+v(m), 3m = n</cmath> which clearly implies <math>m=13</math> and <math>39 | n
  10 KB (1,448 words) - 06:30, 21 April 2024
• 2018 AIME II Problems/Problem 1
  ...<math>1800-x</math>. Since Eve is the slowest, we can call her speed <math>v</math>, so that Ina's speed is <math>2v</math> and Paul's speed is <math>4v ...e of <math>1800-x</math> which takes them a time of <math>\frac{1800-x}{4v+v}</math>. Paul must run the same distance back to <math>B</math>, so his tot
  3 KB (516 words) - 03:25, 16 January 2023
• Dot product
  ...ots, v_n), \vec{w} = (w_1, \cdots, w_n)</math> is defined to be <math>\vec{v}\cdot\vec{w} = \sum_{i=1}^n v_i w_i</math>. The dot product is [[linear|bil ...el, from which the identity <math>\vec{v} \cdot \vec{v} = \left \Vert \vec{v} \right \Vert ^2</math> follows.
  1 KB (199 words) - 23:10, 19 February 2022
• 1973 AHSME Problems/Problem 27
  ...B travels half the time at <math>u</math> miles per hour and half at <math>v</math> miles per hour. The average speed of Car A is <math>x</math> miles p <cmath>y = \frac{u+v}{2}</cmath>
  2 KB (396 words) - 19:03, 22 June 2021
• 2004 Indonesia MO Problems/Problem 2
  Let the volume of the trough be <math>V</math> liters. Also, let the rate of the cold water tap be <math>C</math> <cmath>V = 21E</cmath>
  1 KB (268 words) - 16:32, 28 July 2018
• 1973 AHSME Problems/Problem 5
  Of the following five statements, I to V, about the binary operation of averaging (arithmetic mean), <math>\text{V. Averaging has an identity element }</math>
  2 KB (432 words) - 13:57, 20 February 2020
• 1988 IMO Problems
  ...positions of the midpoints <math> U</math> of <math> BA</math> and <math> V</math> of <math> AC</math> as <math> \angle OPA</math> varies?
  3 KB (499 words) - 13:29, 2 August 2021
• 2020 AMC 10B Problems
  <math>\quad\bullet\qquad</math> <math>V,</math> a reflection across the <math>y</math>-axis. ...beled vertices back to their original positions? (For example, <math>R, R, V, H</math> is one sequence of <math>4</math> transformations that will send
  16 KB (2,496 words) - 20:09, 19 May 2024
• 2018 Putnam B Problems
  ...P}\setminus\{\mathbf{v}\}</math> obtained by omitting vector <math>\mathbf{v}</math> from <math>\mathcal{P}</math> can be partitioned into two sets of e
  2 KB (369 words) - 23:35, 21 April 2019
• 2018 Putnam B Problems/Problem 1
  ...P}\setminus\{\mathbf{v}\}</math> obtained by omitting vector <math>\mathbf{v}</math> from <math>\mathcal{P}</math> can be partitioned into two sets of e
  531 bytes (88 words) - 23:37, 21 April 2019
• 2019 AMC 12B Problems/Problem 10
  ...egree of <math>V</math> (i.e. the number of edges coming into/out of <math>V</math>). This is because to visit any of these vertices, we would have to e ...isit each vertex <math>M(V)</math> times, and must traverse <math>2\cdot M(V)</math> edges connected to each vertex. Specifically, we must traverse all
  8 KB (1,306 words) - 22:18, 1 February 2020
• 2019 AIME II Problems/Problem 4
  'v'
  19 KB (2,942 words) - 21:22, 21 January 2024
• 2020 AIME I Problems/Problem 14
  Let <math>P(3)=u</math> and <math>P(4) = v</math>. Substituting <math>x=3</math> and <math>x=4</math> into the above q u &= (3-u)(3-v) = 9 - 3u - 3v + uv\\
  10 KB (1,819 words) - 19:34, 17 September 2023
• Rubiks cube
  ...ngineer Panagiotis Verdes figured out how to make 6×6 and 7×7 cubes. The V-Cube 6 (a 6x6x6 Rubik’s cube) has 157 152 858 401 024 063 281 013 959 519 The 7x7x7 Rubik’s cube (the V-Cube 7) has 19 500 551 183 731 307 835 329 126 754 019 748 794 904 992 692
  5 KB (518 words) - 16:53, 19 February 2024
• Classical Mechanics
  <math>\delta x'(t)=v(t)</math> <math>v'(t)=a(t)</math>
  3 KB (423 words) - 12:58, 8 July 2019
• Height
  ...he base's area, and h is the height's length; for a pyramid, we have <math>V=\frac{1}{3}Bh</math>.
  1 KB (207 words) - 01:39, 15 January 2020
• GMAAS
  231. Almighty Gmaas once demanded Epic Games to give him 5,000,000 V-bucks for his 569823rd birthday. EDIT: This is why Almighty Gmaas no longer
  85 KB (13,971 words) - 18:02, 16 May 2024
• 2020 AMC 10A Problems/Problem 12
  label("V", (2, 6), NE); label("V", (2, 6), NE);
  11 KB (1,770 words) - 08:56, 17 May 2024
• 2020 AMC 10B Problems/Problem 23
  <math>\quad\bullet\qquad</math> <math>V,</math> a reflection across the <math>y</math>-axis. ...beled vertices back to their original positions? (For example, <math>R, R, V, H</math> is one sequence of <math>4</math> transformations that will send
  10 KB (1,653 words) - 23:33, 3 August 2023
• 2020 AMC 10B Problems/Problem 10
  ...of a cone is <math>\frac{1}{3}\pi r^{2}h</math>. Plugging in we find <math>V = 3\pi \sqrt{7} \implies \boxed{\textbf{(C)}}</math>
  3 KB (493 words) - 16:14, 11 September 2023
• 2020 AMC 12B Problems/Problem 7
  ...the origin and select a point on each line to define vectors <math>\mathbf{v}_{i}=(x_{i},y_{i})</math>. <cmath>\mathbf{v}_1\cdot\mathbf{v}_2 = v_{1}v_{2}\cos\theta \quad\mathrm{and}\quad
  5 KB (895 words) - 15:03, 8 June 2023
• 2020 AMC 12B Problems/Problem 13
  <li><math>\log_b{(uv)}=\log_b u + \log_b v.</math></li><p>
  5 KB (680 words) - 16:40, 22 April 2024
• AMC 12C 2020 Problems
  Let <math>V</math> and <math>F</math> be the vertex and focus of the Parabola <math>P(x
  8 KB (1,223 words) - 15:02, 27 November 2022
• 1954 AHSME Problems/Problem 45
  ...an upright V.}\\ \textbf{(D)}\ \text{Two line segments forming an inverted V.}\\ \textbf{(E)}\ \text{None of these.}</math>
  1 KB (193 words) - 10:42, 6 July 2020
• F = MA 2020 (Mock) Problems
  ...d a horizontal circle of radius <math>r</math> with a constant speed <math>v</math>, in a conical pendulum. The center of the circle is vertically below ...ath>16 kg</math> which slides at a speed of <math>v</math>, with <math>u > v</math>. Block A slides east while Block B slides in west. The surface has c
  2 KB (439 words) - 11:52, 1 August 2020
• 2021 AIME I Problems/Problem 13
  ...th>x=PT</math>, where the length <math>O_{1}O_{2}</math> splits as <math>u+v</math>. Because the lines <math>PQ</math> and <math>O_{1}O_{2}</math> are p ...u^{2}+(r+x)^{2}-u(r+x) \\ \triangle O_{1}OT&:(r+R_{1})^{2}=v^{2}+(r+x)^{2}+v(r+x)\end{align*}</cmath>
  17 KB (2,852 words) - 03:59, 7 February 2024
• Wood2009
  Lucky Seven V ARE YOU XPERIENCED? V
  3 KB (452 words) - 10:21, 17 November 2022
• 2021 AMC 12A Problems
  Suppose that on a parabola with vertex <math>V</math> and a focus <math>F</math> there exists a point <math>A</math> such
  15 KB (2,383 words) - 09:49, 25 June 2023
• 2022 AIME I Problems/Problem 15
  Denote <math>u = 1 - x</math>, <math>v = 1 - y</math>, <math>w = 1 - z</math>. \sqrt{(1-u)(1+v)} + \sqrt{(1+u)(1-v)} & = 1 \hspace{1cm} (1) \\
  15 KB (2,208 words) - 01:25, 1 February 2024
• 2021 Fall AMC 10B Problems/Problem 25
  ...t{10}} , \sqrt{10} \right)</math>, <math>Q = \left( \sqrt{10} , \frac{10 - v}{\sqrt{10}} \right)</math>. We have <math>m_{HP} = \frac{3}{6 - u}</math> and <math>m_{PQ} = - \frac{v}{u}</math>.
  16 KB (2,274 words) - 09:02, 10 December 2022
• 2021 Fall AMC 10A Problems/Problem 22
  Let <math>O</math> be the center of the base, <math>V</math> be the vertex of the base.
  8 KB (1,314 words) - 03:54, 5 July 2022
• 2021 Fall AMC 10A Problems/Problem 24
  pair A, B, C, D, E, F, G, H, A1, B1, C1, D1, E1, F1, G1, H1, V; V = (3,0);
  24 KB (3,567 words) - 18:14, 30 August 2022
• Cubic Equation
  Now here comes the smart part. Substitute <math>y = \sqrt[3]{u} - \sqrt[3]{v}</math>. ...<math>u - 3\sqrt[3]{u^2v} + 3\sqrt[3]{uv^2} - v + p\sqrt[3]{u} - p\sqrt[3]{v} + q = 0</math>. Simplification:
  6 KB (1,059 words) - 14:42, 11 December 2020
• 2021 AIME II Problems/Problem 1
  Let <math>u = 10 – y, v = 9 – x.</math> https://www.youtube.com/watch?v=jDP2PErthkg
  5 KB (794 words) - 15:36, 30 August 2022
• 2020 IMO Problems/Problem 6
  ...3}</math> then we can find a line <math>\ell</math> perpendicular to <math>v</math> such that <math>\ell</math> separates <math>S</math>, and any point Suppose there is no such direction <math>v</math>, then <math>S</math> is contained in a box with side length <math>n^
  3 KB (574 words) - 11:30, 14 May 2021
• 2021 AMC 12A Problems/Problem 20
  Suppose that on a parabola with vertex <math>V</math> and a focus <math>F</math> there exists a point <math>A</math> such ...d <math>Y</math> be the orthogonal projections of <math>F</math> and <math>V</math> onto <math>AQ</math>. Because <math>AF < AV</math>, there are two po
  4 KB (796 words) - 17:33, 13 July 2021
• 2021 AMC 12A Problems/Problem 23
  ...ur squares on the middle of the edges after n moves, and <math>V_n</math> (V for vertex) be the probability that Frieda is on a corner after n moves. Th https://youtube.com/watch?v=kHLR57iP0cU
  17 KB (2,801 words) - 07:29, 4 November 2022
• Tree (graph theory)
  ...<math>u</math> and <math>v</math> in <math>G</math>. Every tree on <math>|V|=n</math> vertices has exactly <math>n-1</math> edges.
  401 bytes (75 words) - 16:51, 2 November 2020
• 2021 AMC 10A Problems/Problem 13
  V&=\frac16\cdot AB\cdot AD\cdot BD \\
  3 KB (496 words) - 19:12, 28 October 2022
• Quartic Equation
  ...tuy + vy^2 + svy + tv</math>, simplifying to <math>y^4 + (s + u)y^3 + (t + v + su)y^2 + (sv + tu)y + tv</math>. [[Equating coefficients]] gives the foll ...begin{cases} s + u = 0 \text{ since the } y^3 \text{ term is 0} \\ p = t + v + su \\ q = sv + tu \\ r = tv \end{cases}</math>
  13 KB (2,376 words) - 16:56, 19 February 2024
• 2013 Mock AIME I Problems
  ...</math> and <math>2</math> along <math>\textbf{u}</math> and <math>\textbf{v}</math> respectively, then find <cmath>\sum_{i=1}^{n}\|\textbf{r}_i\|^2.</c
  7 KB (1,149 words) - 17:16, 15 December 2020
• Nhakhoaparis
  ...đến sâu răng, mất răng. Vì vậy, cần phát hiện kịp thời và điều trị đúng cách mòn cổ răng. ...rãnh này, lâu dần tạo mảng bám, gây viêm nhiễm, tụt lợi và ảnh hưởng tới thẩm mỹ. Cổ răng mòn nhiều thậm chí có
  5 KB (1,261 words) - 05:15, 7 January 2021
• 1986 IMO Problems/Problem 4
  ...math> OV</math> (but not in <math> \vec{OV}</math>) for some vertex <math> V</math> of the polygon. Each two of these lines are obtained one from anothe
  2 KB (284 words) - 11:02, 30 January 2021
• 1985 AJHSME Problem 11
  label("V",(1.5,.3),N); ...>\text{(A)}\ \text{Z} \qquad \text{(B)}\ \text{U} \qquad \text{(C)}\ \text{V} \qquad \text{(D)}\ \ \text{W} \qquad \text{(E)}\ \text{Y}</math>
  1,023 bytes (167 words) - 15:57, 4 July 2023
• 1956 AHSME Problems/Problem 40
  If <math>V = gt + V_0</math> and <math>S = \frac {1}{2}gt^2 + V_0t</math>, then <math> <math> \textbf{(A)}\ \frac{2S}{V+V_0}\qquad
  737 bytes (129 words) - 22:53, 12 February 2021

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