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| <span class="aops-font">V</span> | V

6 KB (924 words) - 21:31, 22 February 2024
2015 AMC 8 Problems/Problem 17
For starters, we identify d as distance and v as velocity (speed) ...equation gives us: <math>\frac{d}{v}=\frac{1}{3}</math> and <math>\frac{d}{v+18}=\frac{1}{5}</math>.

4 KB (608 words) - 17:05, 17 January 2024
2016 AMC 12B Problems/Problem 8
...e, we can set up a proportion based on the principle that <math>d=\frac{m}{V}</math>, thus <math>dV=m</math>.

2 KB (325 words) - 14:21, 19 January 2021
Gmaas
231. Gmaas once demanded Epic Games to give him 5,000,000 V-bucks for his 569823rd birthday. EDIT: This is why Gmaas no longer has an E

69 KB (11,805 words) - 20:49, 18 December 2019
2016 USAJMO Problems/Problem 1
pair V = incenter(A,C,P); dot("$I_C$", V, NW);

5 KB (1,004 words) - 15:15, 28 June 2020
2016 USAMO Problems/Problem 3
<math>V</math> is the foot ot perpendicular from <math>O</math> to <math>AI_A.</mat

6 KB (998 words) - 21:36, 17 October 2022
1983 AHSME Problems/Problem 29
...</math> to <math>A, B</math> and <math>C</math>, respectively, be <math>u, v</math> and <math>w</math>. ...est distance that <math>P</math> can be from <math>D</math> if <math>u^2 + v^2 = w^2</math>?

1 KB (255 words) - 01:11, 20 February 2019
Mock AIME 4 Pre 2005/Problems
...<math>\overline{MS}</math> intersects <math>\overline{OP}</math> at <math>V</math> . If <math>AB = 2,</math> <math>BC = 2005,</math> <math>CD = 4,</mat

7 KB (1,094 words) - 15:39, 24 March 2019
Mock AIME 3 2010 Problems
r, s, t, u, v, w, x, y, and z such that n + l + v − y = 0

14 KB (2,904 words) - 18:24, 16 May 2017
2017 AMC 12A Problems/Problem 25
The vertices <math>V</math> of a centrally symmetric hexagon in the complex plane are given by <cmath>V=\left\{ \sqrt{2}i,-\sqrt{2}i, \frac{1}{\sqrt{8}}(1+i),\frac{1}{\sqrt{8}}(

18 KB (2,878 words) - 01:47, 16 December 2023
2017 AMC 12A Problems
...th>1\leq j\leq 12</math>, an element <math>z_j</math> is chosen from <math>V</math> at random, independently of the other choices. Let <math>P={\prod}_{

15 KB (2,418 words) - 16:58, 7 November 2022
2017 AIME I Problems/Problem 4
<cmath>V = Bh/3</cmath> <cmath>V = (192)(25\sqrt{3}/2)/3</cmath>

7 KB (1,177 words) - 15:55, 5 January 2024
2017 USAJMO Problems/Problem 2
<cmath>z \equiv 16 + 0 + v + 0 + w + 0 = 16 + v + w \pmod{32}, </cmath> where <math>v</math> represents <math>15\cdot 2^{2+2k}p^3</math> and <math>w</math> repre

10 KB (1,657 words) - 19:08, 24 April 2023
Walton Math Fest
...ition offered at Walton High School (Walton MathFest was a high school (JV/V) level math tournament until the 2017-2018 school year).

1 KB (158 words) - 20:16, 9 August 2017
Walton MathFest
...ition offered at Walton High School (Walton MathFest was a high school (JV/V) level math tournament until the 2017-2018 school year).

1 KB (158 words) - 20:20, 9 August 2017
2017 JBMO Problems/Problem 1
One could also construct a graph G=(V,E) with the set V of vertices (also called nodes or points) and the set E of edges (also call

5 KB (858 words) - 00:36, 29 November 2023
2020 AMC 12B 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 (2,417 words) - 01:03, 28 April 2022
British Mathematical Olympiad
<cmath>\bar V = \frac {3a^3}{\pi r^2 h} = \frac {3r}{\pi h} \cdot \left( \frac {a}{r} \ri <cmath> \bar V = \frac {3}{\pi f^3} \le \frac {8}{9 \pi} = 0.283.</cmath>

6 KB (1,034 words) - 10:12, 7 June 2023
2018 AMC 10B Problems
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);

15 KB (2,237 words) - 23:08, 15 November 2023
2018 AMC 10B Problems/Problem 10
...>. Using the formula for the volume of a triangular pyramid, we have <math>V = \frac{1}{3} \cdot \frac{1}{2} \cdot 3 = \frac{1}{2}</math>. Also, since t Plugging <math>x</math> and <math>y</math> into the formula <math>V = \dfrac{b \cdot h}{3},</math> we find that the volume is <math>\boxed{2}</

8 KB (1,286 words) - 13:29, 21 April 2024
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 (2,497 words) - 21:14, 12 November 2023
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 (13,954 words) - 17:25, 22 March 2024
2020 AMC 10A Problems/Problem 12
label("V", (2, 6), NE); label("V", (2, 6), NE);

11 KB (1,707 words) - 17:10, 1 April 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
2021 AIME II Problems/Problem 12
...$c$", D--C, N); label("$d$",D--A,W); label("$u$",D--B,2*dir(170)); label("$v$",A--C,S); ...c, d</math>, be the sides, <math>s</math> the semiperimeter, and <math>u, v</math>, the diagonals. Then the area, <math>K</math>, is given by <cmath>K

10 KB (1,669 words) - 17:33, 12 January 2024
2021 USAMO Problems/Problem 6
Denote <math>D' – A' = 2\vec V.</math> ...\triangle A'C'E'</math> into <math>\triangle D'F'B'</math> is <math>2\vec {V.}</math>

5 KB (875 words) - 00:26, 23 May 2023
2021 USAJMO Problems/Problem 1
...<math>n=2k+1</math>, just take <math>(u,v)= (k+1,k)</math> which <math>u^2-v^2=n</math>. Thus the only answer is <math>\boxed{f\equiv 1}</math> and we a https://www.youtube.com/watch?v=Q1NUBUYvOJc

8 KB (1,492 words) - 00:23, 24 February 2024
G285 2021 MC10A
...th>t</math> is square free and <math>gcd(u,v,w) = 1</math>, find <math>t+u+v+w</math> if <math>x=\cos 20^o</math> and <math>y=\sin 20^o</math>.

8 KB (1,385 words) - 12:55, 23 June 2021
2022 AIME II Problems/Problem 4
We could assume a variable <math>v</math> which equals to both <math>\log_{20x} (22x)</math> and <math>\log_{2 So that <math>(20x)^v=22x \textcircled{1}</math>

5 KB (778 words) - 18:14, 30 January 2024
2022 AIME II Problems/Problem 9
...s, plus the outer region, <math>E</math> is the number of edges, and <math>V</math> is the number of vertices. Temporarily disregarding the intersection <math>V=V_{i}+210=222</math>

12 KB (2,025 words) - 14:56, 25 January 2024
1978 AHSME Problems/Problem 25
...\qquad \text{(iii) }x+y\ge a\\ \\ \qquad \text{(iv) }x+a\ge y\qquad \text{(v) }y+a\ge x</math>

665 bytes (119 words) - 18:31, 28 August 2023
1972 AHSME Problems/Problem 26
...t,st),E); label("M",(cu,su),N);label("P",(cu,st),S); label("C",(cos(v),sin(v)),W); //Credit to Zimbalono for the diagram </asy>

864 bytes (169 words) - 16:47, 23 June 2021
2021 Fall AMC 12B Problems/Problem 17
...th>C(1) = 0</math> and our recursive rules for <math>C(n)</math> and <math>V(n)</math> as follows: n & V(n) & C(n) \\ \hline

8 KB (1,309 words) - 00:31, 6 January 2023
2021 Fall AMC 12A Problems/Problem 13
.../math> bisects the angle between <math>\mathbf{u}</math> and <math>\mathbf{v}</math>.

16 KB (2,526 words) - 00:53, 6 May 2023
2021 Fall AMC 12A Problems/Problem 21
...h>. Hence, <math>B = \left( - 1 , u \right)</math>, <math>D = \left( 0 , - v \right)</math>. The slope of <math>AD</math> is <math>m_{AD} = \frac{v}{3}</math>.

5 KB (756 words) - 03:40, 23 January 2023
OrenSH
v v

2 KB (265 words) - 22:25, 15 April 2024
Matrix Tree Theorem
Let <math>G</math> be a graph with the set of vertices <math>V=\{v_1,v_2,v_3,\ldots, v_n\}</math>. We define its adjacency matrix <math>\

1 KB (264 words) - 11:26, 3 March 2022
Variance
...> the formula for variance if <math>X</math> is a [[population]] is <cmath>V = \frac{1}{n}\sum_{i=1}^n (x_i - \overline{x})^2.</cmath> Additionally, <math>V = \sigma^2</math> where <math>\sigma</math> is the population [[standard de

749 bytes (122 words) - 19:16, 3 March 2022
Newton's method
...>, (2) <math>\hat{x}\equiv x\pmod{p^{n-k}}</math> and (3) <math>k=v(p'(x))=v(p'(\hat{x}))</math>. <center><cmath>v=u+p^{n-2k}zs\in u+p\mathbb{Z}_p\subset \mathbb{Z}_p^{\times}</cmath></cente

13 KB (2,298 words) - 23:34, 28 May 2023
2023 AIME I Problems
pair o = (0, 0), u = (1, 0), v = 0.8*dir(40), w = dir(70); draw(o--u--(u+v));

7 KB (1,154 words) - 12:54, 20 February 2024
Rank Nullity Theorem
...t{R}(\text{T}))</math> where <math>\text{R}(\text{T})=\{\text{T}(x)~|~x\in V\}</math>. In other words, rank is the dimension of the linear transformati ...aim that if <math>\beta=\{v_1,v_2,\ldots, v_n\}</math> is a basis of <math>V</math>, then

5 KB (893 words) - 22:41, 28 May 2022
Kimberling’s point X(24)
...math> In accordance with Claim, <math>\angle BVD = \angle HVE \implies B', V,</math> and <math>B</math> are collinear.

10 KB (1,751 words) - 15:34, 25 November 2022
Vector analysis
...mathbf{n}\,dS,</cmath> where <math>R</math> is a region whose volume <math>V(R)</math> shrinks to <math>0</math> about the point <math>p</math>, <math>\ ...mathbf{n}\,dS,</cmath> where <math>R</math> is a region whose volume <math>V(R)</math> shrinks to <math>0</math> about the point <math>p</math>, <math>\

7 KB (1,189 words) - 06:00, 21 December 2022
2022 AMC 10A Problems/Problem 16
...the three roots of the polynomial. The lengthened prism's volume is <cmath>V = (a+2)(b+2)(c+2) = abc+2ac+2ab+2bc+4a+4b+4c+8 = abc + 2(ab+ac+bc) + 4(a+b+ We can substitute these into the expression, obtaining <cmath>V = \frac{6}{10} + 2\left(\frac{29}{10}\right) + 4\left(\frac{39}{10}\right)

7 KB (1,111 words) - 21:00, 21 February 2024
2022 AMC 12A Problems/Problem 25
...e R.H.S. is a not a perfect square. Thus, the number of positive <math>(u, v)</math> is equal to the number of positive divisors of <math>2 r^2</math>. ...n if <math>(a, b)</math> with <math>a = 2 r - u</math> and <math>b = 2 r - v</math>.

7 KB (1,271 words) - 12:09, 4 January 2024
2022 AMC 10B Problems/Problem 22
We denote by <math>\left( u, v \right)</math> the coordinates of circle <math>C_0</math>, and <math>r</mat u^2 + v^2 = \left( 8 - r \right)^2 . \hspace{1cm} (1)

7 KB (1,202 words) - 01:15, 10 June 2023
2023 AMC 12B Problems
.../math>, define the binary operation <math>\otimes</math> by<cmath>u\otimes v=ac+bdi.</cmath>Suppose <math>z</math> is a complex number such that <math>z

13 KB (2,107 words) - 22:19, 20 April 2024
2024 AMC 8 Problems
pair P,Q,R,S,T,U,V,W; P=(0,30); Q=(30,30); R=(40,40); S=(10,40); T=(10,10); U=(40,10); V=(30,0); W=(0,0);

20 KB (2,846 words) - 12:06, 20 April 2024
Random Problem
<math>V=\pi{r^2}h</math> <math>V=\pi{r^2}(14-2r)</math>

4 KB (697 words) - 17:07, 24 March 2023
2023 AIME I Problems/Problem 14
path v=(5,-0.5)--(5,0)--(5,1)--(6,1)--(6,2)--(6,3)--(6,4)--(7,4); draw(v,p);

11 KB (1,834 words) - 22:01, 4 January 2024
2023 AIME I Problems/Problem 13
pair o = (0, 0), u = (1, 0), v = 0.8*dir(40), w = dir(70); draw(o--u--(u+v));

13 KB (2,130 words) - 01:52, 31 January 2024
2023 AIME II Problems/Problem 14
<cmath> V = \frac{1}{3} \cdot x \cdot (S_1 + \sqrt{S_1S_2} + S_2) = \frac{1}{3} \cdot Let the volume without water be <math>V,</math> volume of the pyramid <math>SCGJ</math> be <math>U.</math>

10 KB (1,574 words) - 16:42, 8 March 2024
2019 ELMO Problems
...en so are <math>f(V)</math>, <math>V+W</math>, <math>V-W</math>, and <math>V \cdot W</math>.

5 KB (772 words) - 08:50, 23 February 2023
2023 USAJMO Problems/Problem 2
Plugging in <math>A</math> and <math>B</math> gives <math>u=v=0</math>. Plugging in <math>P</math> gives Since it passes through <math>A</math>, for some <math>v, w</math>, the equation of circle <math>(ABP)</math> is,

7 KB (1,280 words) - 01:22, 6 February 2024

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