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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>

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) - 16:36, 26 July 2024
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 (577 words) - 13:15, 3 September 2024
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) - 15:35, 30 August 2024
Tree (graph theory)
...>u</math> and <math>v</math> in <math>G</math>. Every tree that has <math>|V|=n</math> vertices has exactly <math>n-1</math> edges. ...t union of trees. The number of trees in a forest could be found by <math>|V|-|E|</math>.

2 KB (435 words) - 19:13, 5 July 2024
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 (1,159 words) - 09:15, 30 July 2024
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 (1,494 words) - 18:07, 19 August 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>.

14 KB (2,223 words) - 14:27, 1 September 2024
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 (278 words) - 19:55, 15 September 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) - 08:20, 2 July 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 (2,814 words) - 00:31, 19 September 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));

15 KB (2,406 words) - 21:25, 5 September 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
https://www.youtube.com/watch?v=f-d4mi-AyxQ Plugging in <math>A</math> and <math>B</math> gives <math>u=v=0</math>. Plugging in <math>P</math> gives

7 KB (1,290 words) - 16:16, 15 September 2024
2023 USAMO Problems/Problem 1
Plugging in <math>A</math> and <math>B</math> gives <math>u=v=0</math>. Plugging in <math>P</math> gives

4 KB (684 words) - 03:59, 31 August 2024
Pell's equation (simple solutions)
<cmath>u = 5y - 1, v = 2x - 3y + 1 \implies u^2 - 5 v^2 = - 4 \implies</cmath>

15 KB (2,351 words) - 08:28, 20 April 2023
2023 USAMO Problems/Problem 6
https://youtube.com/watch?v=LAuyU2OuVzE ...and <math>w=\frac{2b^3cx_0z_0}{c^2y_0^2-b^2z_0^2}</math>, so <cmath>\frac{v}{w}=\frac{b^2z_0}{c^2y_0},</cmath> which is the required condition for <mat

14 KB (2,600 words) - 23:37, 10 March 2024
Xosomiennamxsmn
...n có biết tại sao SXMN lại có sức hấp dẫn như vậy hay không, hãy cùng lý giải qua bài XSMN phát triển với mục đích Ích nước lợi nhà<

11 KB (2,230 words) - 23:24, 9 May 2023
Know the Facts: 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

88 KB (14,978 words) - 19:34, 3 September 2024
1997 IMO Problems/Problem 2
...math>AB</math> and <math>AC</math> meet the line <math>AU</math> and <math>V</math> and <math>W</math>, respectively. The lines <math>BV</math> and <ma

736 bytes (124 words) - 23:58, 28 March 2024
1992 IMO Problems/Problem 2
...th>f(u) = f(t^{2}+v) = f^{-1}(v)+f(t)^{2}> f^{-1}(v) = f(f(f^{-1}(v))) = f(v)</math>. Hence f is strictly increasing. It is now clear that since <math>f

1 KB (282 words) - 14:53, 12 March 2024
2023 AMC 10B Problems
...sed as <math>(2u-3w, v+4w)</math> with <math>0\le u\le1</math>, <math>0\le v\le1,</math> and <math>0\le w\le1</math>?

13 KB (1,959 words) - 13:42, 14 June 2024
2024 AIME I Problems/Problem 14
<math>V = \sqrt{(a^2 + b^2 - c^2)(b^2 + c^2 - a^2)(a^2 + c^2 - b^2)/72}</math> ...umes <cmath>[ABCI] + [ABDI] + [ACDI] + [BCDI] = V,</cmath> We have <cmath>V = \frac{4AR}{3}.</cmath> Plugging in and simplifying, we get <math>R = \fra

14 KB (2,198 words) - 22:28, 30 July 2024
2023 AMC 12A Problems/Problem 16
label("$v'$", (0, 2.18), NE); ...eed to find <math>v</math> with the largest imaginary part such that <math>v^2</math> lies on <math>\omega</math>.

6 KB (1,055 words) - 21:58, 28 February 2024
2023 AMC 12A Problems/Problem 21
...t, to find the amount of vertices we can use Euler's characteristic, <math>V - E + F = 2</math>, and therefore the amount of vertices is <math>12</math> By Euler's formula, which states that <math>v-e+f=2</math> for all convex polyhedra, we know that there are <math>2-f+e=1

13 KB (2,187 words) - 08:39, 5 September 2024
2023 AMC 10A Problems/Problem 18
...nvex polyhedra, <math>V-E+F=2</math>. In our case, <math>V-24+12=2\implies V=14.</math> We know that <math>A+B</math> is the total number of vertices as Note that Euler's formula is <math>V+F-E=2</math>. We know <math>F=12</math> from the question. We also know <ma

7 KB (1,171 words) - 21:11, 7 September 2024
2023 AMC 12B Problems/Problem 25
pair K, L, M, N, O, P, Q, R, S, T, U, V; pair K, L, M, N, O, P, Q, R, S, T, U, V;

18 KB (2,765 words) - 19:17, 15 August 2024
2023 AMC 10B Problems/Problem 24
...sed as <math>(2u-3w, v+4w)</math> with <math>0\le u\le1</math>, <math>0\le v\le1,</math> and <math>0\le w\le1</math>? ...h <math>x</math> and <math>y</math>. We first fix <math>u</math> and <math>v</math> to <math>0</math>, and graph <math>(-3w,4w)</math> from <math>0\le w

6 KB (983 words) - 12:34, 24 July 2024
2000˙AIME˙II˙Problems/Problem˙3
V

814 bytes (128 words) - 10:36, 11 November 2023
2023 AMC 10B Problems/Problem 14
Denote <math>m = k u</math> and <math>n = k v</math>. Thus, <math>{\rm gcd} \left( u, v \right) = 1</math>.

4 KB (639 words) - 22:31, 9 July 2024
2024 AMC 8 Problems/Problem 20
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);

3 KB (445 words) - 19:58, 28 August 2024
2023 AMC 12B Problems/Problem 12
For complex number <math>u = a+bi</math> and <math>v = c+di</math> (where <math>i=\sqrt{-1}</math>), define the binary operation <math>u \otimes v = ac + bdi</math>

1 KB (205 words) - 02:52, 20 November 2023
2024 AIME I Problems/Problem 7
https://www.youtube.com/watch?v=ejmrAJ9TpvM&ab_channel=MegaMathChannel ...math> is <math>u=v/|v|</math>, so <math>v \cdot u= v\cdot v = |v|^2/|v| = |v|</math>, which here is just <math>\sqrt{3^2+(-4)^2} =5</math>.

12 KB (1,991 words) - 00:24, 19 July 2024
2002 IMO Problems/Problem 5
Given the problem $ (f(x) + f(y))(f(u) + f(v)) = f(xu - yv) + f(xv - yu) $, we aim to find a function that satisfies it We start by considering the case when $ x = y = u = v = 0 $.

2 KB (369 words) - 16:12, 26 March 2024
Bisector
The points <math>U \in AA''</math> and <math>V \in CC''</math> be such points that <math>L \in UV, UV \perp BB''.</math> Similarly points <math>V, M,</math> and <math>D</math> are collinear.

14 KB (2,490 words) - 06:51, 6 June 2024
OIM Problems and Solutions
* [[V Olimpiada Iberoamericana de Matemáticas (OIM) ]] Valladolid, España , 19 * [[X Olimpiada Iberoamericana de Matemáticas (OIM) ]] Región V, Chile , 1995

14 KB (1,323 words) - 12:18, 13 December 2023
1988 OIM Problems/Problem 5
...at if <math>x+yt+zt^2 \ne 0</math>, then there exist <math>u</math>, <math>v</math>, and <math>w</math> as rational numbers such that:

511 bytes (84 words) - 13:28, 13 December 2023
1996 OIM Problems/Problem 1
<math>V=\sum_{i}^{}2^ik_i=13^3</math> where <math>k_i</math> is the quantity of cub

2 KB (387 words) - 10:29, 23 December 2023
2021 OIM Problems/Problem 6
...lar polygon with <math>n</math> sides, <math>n \ge 4</math>, and let <math>V</math> be a subset of <math>r</math> vertices of the polygon. Show that if vertices are in <math>V</math>.

396 bytes (66 words) - 04:02, 14 December 2023
2001 OIM Problems/Problem 5
...h> by 2000, and <math>y'</math> is the reminder of the division of <math>y+v'</math> by 2001. There are two ships on the board: the Martian one and the

1 KB (256 words) - 04:26, 14 December 2023
2007 OIM Problems/Problem 4
...h> is greater than the ''dragonian distance'' from <math>C</math> to <math>V</math>.

1,015 bytes (177 words) - 16:49, 14 December 2023
V Olimpiada Iberoamericana de Matemáticas (OIM)

458 bytes (44 words) - 17:51, 14 December 2023
X Olimpiada Iberoamericana de Matemáticas (OIM)
X [[Olimpiada Iberoamericana de Matemáticas]] was held in Región V, Chile , 1995

455 bytes (45 words) - 17:53, 14 December 2023
2024 AMC 8 Problems/Problem 14
...here <math>d(v)</math> indicates the distance from <math>A</math> to <math>v</math>. Consider the outgoing edges <math>(A,X)</math> and <math>(A,M)</mat https://www.youtube.com/watch?v=RRTxlduaDs8

6 KB (989 words) - 00:33, 19 September 2024
DVI exam
DVI is an exam in mathematics at the Moscow State University named after M.V. Lomonosov. The first four problems have a standard level. <cmath>\left\{\begin{array}{l} u = \sqrt {2} (x + y),\\v = 3y.\end{array}\right.</cmath>

48 KB (8,214 words) - 08:59, 30 July 2024
Add
https://archifol.io/v/tjqbn89d https://archifol.io/v/brzmkkgh

273 bytes (44 words) - 21:35, 1 April 2024
2023 CMO Problems/Problem 6
...e arc <math>\overset{\frown}{uv}</math>(excluding <math>u</math> and <math>v</math> ) contains only fixed points, and <math>l_i</math> is clockwise and ...\right),\left(w_2, w_3\right), \ldots,\left(w_{t-1}, w_t\right),\left(w_t, v\right),\left(w_{t-1}, w_t\right), \ldots,\left(w_2, w_3\right),\left(w_1, w

8 KB (1,430 words) - 06:01, 25 May 2024
2023 CMO(CHINA) Problems/Problem 6
...e arc <math>\overset{\frown}{uv}</math>(excluding <math>u</math> and <math>v</math> ) contains only fixed points, and <math>l_i</math> is clockwise and ...\right),\left(w_2, w_3\right), \ldots,\left(w_{t-1}, w_t\right),\left(w_t, v\right),\left(w_{t-1}, w_t\right), \ldots,\left(w_2, w_3\right),\left(w_1, w

8 KB (1,430 words) - 06:06, 25 May 2024
A7456321
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 (11,828 words) - 19:26, 3 September 2024
Cubic formula
.../math>, <math>3uv(u+v)</math> matches up with <math>-px</math>, and <math>(v^3+w^3)</math> matches up with <math>-q</math>. Things are about to get exci ...^3}{27}</math>. This may not sound exciting until our substitution <math>w=v^3</math>. We got rid of <math>u</math> and now we have <math>w^2+\left(q\ri

4 KB (775 words) - 23:03, 22 August 2024
Character
A, F, I, V, r, h, 3, 6, ?, <, ., {, etc.

102 bytes (17 words) - 19:20, 25 June 2024
2013 Mock AIME I Problems/Problem 8
...</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 ...>x'</math>-axis, perpendicular to the <math>y'</math>-axis, on which <math>v</math> now lies, as seen in the diagram below. Rotations do not affect the

2 KB (353 words) - 14:20, 30 July 2024
Disphenoid
<cmath>V= \frac {lmn}{3} = \sqrt {\frac {(a^2+b^2-c^2)(a^2-b^2+c^2)(-a^{2}+b^{2}+c^{ <cmath>V= \frac {l \cdot m \cdot n}{3} = \sqrt {\frac {(a^2+b^2-c^2)(a^2-b^2+c^2)(-a

19 KB (3,355 words) - 08:00, 22 August 2024
Cross-polytope
<cmath>\frac{2^n}{n!}v^n~\text{where}~v=\frac{s}{\sqrt{2}}~\text{is the distance from the center of the cross-polyt

1 KB (181 words) - 16:34, 20 August 2024

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