Search results

Create the page "V v" on this wiki! See also the search results found.

2009 AIME II Problems/Problem 15
Let <math>V = \overline{NM} \cap \overline{AC}</math> and <math>W = \overline{NM} \cap

11 KB (1,849 words) - 19:43, 2 January 2023
2009 USAMO Problems/Problem 5
...h> intersect <math>\omega</math> at <math>K</math> and another point <math>V</math>, as shown: pair V = IP(L(P, S, 10, 10), circle, 1);

6 KB (973 words) - 19:24, 18 October 2018
1991 AJHSME Problems/Problem 21
<cmath>T=32-3k\Rightarrow V=24-4k.</cmath>

807 bytes (122 words) - 00:08, 5 July 2013
Differentiation Rules
If <math>y(x) = u(x)+v(x)</math> then <math>\frac{dy}{dx} = \frac{du}{dx} + \frac{dv}{dx}</math>. ...x) = u(x) \cdot v(x)</math> then <math>\frac{dy}{dx} = u(x)\frac{dv}{dx} + v(x)\frac{du}{dx}</math>.

2 KB (288 words) - 00:53, 26 March 2018
Tower law
...ath> is a basis for <math>L</math> over <math>K</math>, we can write <math>v = \sum_ia_i\alpha_i</math>, where <math>a_1,a_2,\ldots,a_n\in K</math>. And <cmath>v = \sum_ia_i\alpha_i = \sum_i\left(\sum_jb_{ij}\beta_j\right)\alpha_i = \sum

3 KB (567 words) - 08:42, 21 August 2009
Unit (ring theory)
...[[inverse]] in <math>R</math>, that is, if there is another element <math>v\in R</math> such that <math>uv=vu=1</math>.

446 bytes (86 words) - 20:16, 23 August 2009
2010 AMC 12A Problems/Problem 7
...times more water than Logan's miniature. The volume of a sphere is: <math>V=\dfrac{4}{3}\pi r^3</math>. Since we are comparing the heights (m), we shou

1 KB (198 words) - 18:08, 28 June 2021
2010 AMC 12A Problems/Problem 21
<cmath>= x^6-2ux^5+(u^2+2v)x^4-(2uv+2w)x^3+(2uw+v^2)x^2-2vwx+w^2</cmath> v &= 2\\

5 KB (969 words) - 21:33, 22 June 2022
Kirchhoff's rules
<math>\sum_{closed loop} \Delta V = 0</math>

406 bytes (67 words) - 20:36, 7 March 2014
Characteristic polynomial
...non-zero vector that satisfies the relation <math>A\bold{v} = \lambda\bold{v}</math>, for some scalar <math>\lambda \in K</math>. In other words, applyi ...bold{v} = \lambda \bold{v}</math>, then <math>\lambda I \bold{v} - A \bold{v} = \bold{O}</math>. But then, the column vectors of <math>\lambda I - A</ma

19 KB (3,412 words) - 14:57, 21 September 2022
Eigenvalue
...r constant <math>\lambda</math> such that <math>L \bold{v} = \lambda \bold{v}</math>. Here, <math>\lambda</math> is known as the '''eigenvalue''' associ

821 bytes (138 words) - 19:32, 2 March 2010
Connected set
...h>, there exists a connected open set <math>V</math> such that <math>x \in V \subset C</math>. <math>X</math> is locally connected if it is locally conn ...here exists a path-connected open set <math>V</math> such that <math>x \in V \subset C</math>. <math>X</math> is locally path-connected if it is locally

3 KB (497 words) - 16:27, 15 March 2010
Separation axioms
...el("$y$",(A+C)/2 + shiftfactor,(1.2,-1.2)); label("$U$",B,(1,-1)); label("$V$",B+shiftfactor,(1,-1)); ...sets <math>U, V</math> such that <math>x \in U, y \in V</math> and <math>U,V</math> are [[disjoint]].

5 KB (672 words) - 13:28, 4 June 2018
Linearly independent
...[[vector]]s <math>v_1, v_2, \ldots, v_n</math> in a [[vector space]] <math>V</math> over a field <math>K</math> are '''linearly independent''' if there ...ndependent [[iff]] their [[determinant]] <math>D(\bold{v}_1, \ldots, \bold{v}_n) = 0</math>.

2 KB (300 words) - 23:35, 16 March 2010
2010 IMO Problems/Problem 6
:<math>a_{n} = max_{\text{(T is valid n-type)}} v(t)</math> ...ch n} \not\le \text{s we pick a valid n-type } T_{n} \text{ with } a_{n} = v(T_{n})</math>

4 KB (786 words) - 08:46, 12 March 2024
2013 IMO Problems/Problem 3
V=D("V",circumcenter(Ia,Ib,Ic),SE); D(circumcircle(B,C,V),linetype("2 2")+rgb(0.6,0,1));

3 KB (553 words) - 09:41, 17 January 2016
2010 AMC 10B Problems/Problem 16
pair V=(0,0.5); draw(V--O);

3 KB (544 words) - 20:54, 24 March 2024
2011 AMC 10A Problems/Problem 22
...so we can color it in k ways. We then move on to the vertices adjacent to v, etc, and at the end we multiply all these together. For example, the chrom

14 KB (2,425 words) - 09:13, 5 November 2023
KGS math club/solution 11 2
main(int a, char **v) { int n=atoi(v[1]),

1 KB (188 words) - 18:08, 21 February 2011
2011 AMC 12B Problems
A segment through the focus <math>F</math> of a parabola with vertex <math>V</math> is perpendicular to <math>\overline{FV}</math> and intersects the pa

13 KB (1,978 words) - 16:28, 12 July 2020
2001 AMC 10 Problems/Problem 22
...and diagonal are the same. Five of these numbers are represented by <math> v </math>, <math> w </math>, <math> x </math>, <math> y </math>, and <math> z label("$v$",(0.5,2.5));

5 KB (721 words) - 16:44, 9 August 2022
2011 AIME I Problems
...h>V</math> and <math>W</math> are on <math>\overline{AC}</math> with <math>V</math> on <math>\overline{AW}</math>, points <math>X</math> and <math>Y</ma pair[] A, B, C, U, V, W, X, Y, Z;

10 KB (1,634 words) - 22:21, 28 December 2023
2011 AIME I Problems/Problem 8
...h>V</math> and <math>W</math> are on <math>\overline{AC}</math> with <math>V</math> on <math> \overline{AW} </math>, points <math>X</math> and <math>Y</ pair[] A, B, C, U, V, W, X, Y, Z;

6 KB (1,077 words) - 21:47, 12 April 2022
2011 AIME II Problems/Problem 15
...math>P(v) = 4</math>, which will give us the working range <math>5 \le x < v</math>. v^2 - 3v - 9 &= 4 \\

8 KB (1,273 words) - 14:03, 7 January 2023
2011 USAMO Problems/Problem 3
...> <cmath>\vec{w} = \vec{CD} + \vec{FA}</cmath> Clearly, <math>\vec{u}+\vec{v}+\vec{w}=\textbf{0}</math>. ...th>. Thus, <math>|\vec{u}|=2p \cos \gamma</math>. Similarly, <math>|\vec{v}|=2q \cos \alpha</math> and <math>|\vec{w}| = 2r \cos \beta</math>.

11 KB (1,925 words) - 12:07, 31 August 2023
2011 AMC 12B Problems/Problem 14
A segment through the focus <math>F</math> of a parabola with vertex <math>V</math> is perpendicular to <math>\overline{FV}</math> and intersects the pa ...e equidistant from <math>F</math> and <math>l</math>. Therefore <math>FV=d(V,l)</math>. Let this distance be <math>d</math>. Now note that <math>d(F,l)=

4 KB (619 words) - 19:15, 11 May 2021
Mock Amc 12
! scope="row" | '''Mock AMC V'''

18 KB (2,206 words) - 19:41, 24 December 2020
Autograph
label("$V-4\beta$",(0,-0.3),red); /* AUTO-GRAPH V-4 beta by PythonNut*/

17 KB (2,910 words) - 15:01, 2 September 2011
2003 AMC 10B Problems/Problem 25
<cmath> V. x+y = 13, \{49, 58, 67, 76, 85, 94\} = 6 </cmath>

6 KB (882 words) - 11:45, 12 November 2023
1989 AHSME Problems/Problem 20
...{v} \rfloor</math> means the greatest integer less than or equal to <math>v</math>.)

1 KB (155 words) - 07:58, 22 October 2014
1964 AHSME Problems/Problem 3
.../math> and the remainder is <math>v</math>, where <math>u</math> and <math>v</math> are integers. \textbf{(D)}\ v \qquad

2 KB (296 words) - 06:04, 31 December 2023
1992 AJHSME Problems/Problem 16
The volume of a cylinder is given by the formula <math>V=\pi r^2 h</math>. The given cylinder therefore has a volume of <math>\pi (1

2 KB (266 words) - 00:09, 5 July 2013
KGS math club/solution 10 2
...? Because Uberdude supplied a hint that the answer begins with the letter V, and a vole seemed as good as anything else. Vole are small rodents, like m

307 bytes (64 words) - 12:59, 10 September 2012
2010 AMC 8 Problems
...-4), P=(1,-3.8), Q=(1,-3.6), R=(1,-3.4), S=(1,-3.2), T=(1,-3), U=(1,-2.8), V=(1,-2.6), W=(1,-2.4), Z=(1,-2.2), E_1=(1.4,-2.6), F_1=(1.8,-2.6), O_1=(14,- ...th(1pt)); D(S,linewidth(1pt)); D(T,linewidth(1pt)); D(U,linewidth(1pt)); D(V,linewidth(1pt)); D(W,linewidth(1pt)); D(Z,linewidth(1pt)); D(E_1,linewidth(

18 KB (2,768 words) - 21:05, 9 January 2024
2011 AMC 8 Problems
...,-2), M=(0,-6), O=(0,-4), P=(4,-4), Q=(2,-2), R=(2,-6), T=(6,4), U=(10,0), V=(10,4), Z=(10,2), A_1=(8,4), B_1=(8,0), C_1=(6,-2), D_1=(10,-2), E_1=(6,-6) ...--cycle,linewidth(1.6)); draw(M--O--Q--R--cycle,linewidth(1.6)); draw(A_1--V--Z--cycle,linewidth(1.6)); draw(G_1--K_1--J_1--E_1--cycle,linewidth(1.6));

16 KB (2,371 words) - 17:34, 9 January 2024
1973 Canadian MO Problems
<math>\text{(v)}</math> Without the use of logarithm tables evaluate <math>\frac{1}{\log_{

4 KB (540 words) - 18:23, 8 October 2014
1973 Canadian MO Problems/Problem 1
<math>\text{(v)}</math> Without the use of logarithm tables evaluate <math>\frac{1}{\log_{ <math>\text{(v)}</math> <center>

2 KB (286 words) - 15:14, 21 July 2012
2011 AMC 8 Problems/Problem 7
...,-2), M=(0,-6), O=(0,-4), P=(4,-4), Q=(2,-2), R=(2,-6), T=(6,4), U=(10,0), V=(10,4), Z=(10,2), A_1=(8,4), B_1=(8,0), C_1=(6,-2), D_1=(10,-2), E_1=(6,-6) ...--cycle,linewidth(1.6)); draw(M--O--Q--R--cycle,linewidth(1.6)); draw(A_1--V--Z--cycle,linewidth(1.6)); draw(G_1--K_1--J_1--E_1--cycle,linewidth(1.6));

4 KB (557 words) - 00:30, 4 January 2023
1989 AHSME Problems
...{v} \rfloor</math> means the greatest integer less than or equal to <math>v</math>.)

15 KB (2,247 words) - 13:44, 19 February 2020
2012 AMC 12A Problems
...th>. What is the probability that the square region determined by <math>T(v)</math> contains exactly two points with integer coordinates in its interio

14 KB (2,197 words) - 13:34, 12 August 2020
2012 AMC 12A Problems/Problem 23
...th>. What is the probability that the square region determined by <math>T(v)</math> contains exactly two points with integer coefficients in its interi ...math>v=(x,y)</math> will create the translation of <math>S</math>, <math>T(v)</math> such that it covers both <math>(0,0)</math> and <math>(1,0)</math>.

4 KB (658 words) - 20:37, 19 January 2021
2012 AMC 12A Problems/Problem 25
...ive slope starting at positive 1. The function now looks like the letter V repeated within every square in the first row.

3 KB (584 words) - 02:55, 26 September 2020
2012 AMC 12B Problems/Problem 21
...linewidth(4)); dot("$Z$",Z,W,linewidth(4)); label("$u$", B--X, SE);label("$v$", X--Cp, SE); label("$40$", A--B, S); label("$s$", A--X, NW); label("$s$", ...\theta</math> and <math>\angle CDX = \theta-30^\circ</math>. Let <math>CX=v</math>. In <math>\triangle CDX</math> we have

9 KB (1,451 words) - 10:01, 27 December 2022
2012 AMC 10B Problems/Problem 13
...of the escalator and <math>c</math> be the speed of Clea. Using <math>d = v t</math>, the first statement can be translated to the equation <math>d = 6

2 KB (351 words) - 21:42, 21 August 2023
2012 AIME II Problems/Problem 5
The volume of this pyramid can be found by the equation <math>V=\frac{1}{3}bh</math>, where <math>b</math> is the base and <math>h</math> i Finally, <math>V=\frac{1}{3}bh=\frac{1}{3}(225)(10)=\boxed{750}</math>.

2 KB (362 words) - 16:34, 29 February 2020
2012 AIME II Problems/Problem 15
...,F)); label("$\gamma$",gamma,dir(180)); label("$u$",X--D,dir(60)); label("$v$",D--F,dir(70)); Let <math>EF=x</math>, <math>XD=u</math>, and <math>DF=v</math>. Then <math>XE^2-XF^2=EF^2=DE^2-DF^2</math>, so we get

13 KB (2,298 words) - 12:56, 10 September 2023
2002 Romanian NMO Problems
...ank}(A)=r<4</math>, prove the existence of two invertible matrices <math>U,V\in M_4(C)</math>, such that:

10 KB (1,695 words) - 10:03, 10 May 2012
1997 PMWC Problems/Problem T4
...h>, distance <math>a</math>, formula <math>v=\frac{a}{t}</math> or <math>a=v \cdot t</math>.

1 KB (191 words) - 14:40, 20 April 2014
2006 SMT/Advanced Topics Problems
...ind a vertical vector <math> v </math> such that <math> (A^8+A^6+A^4+A^2+I)v=\left(\begin{matrix}0\\11\end{matrix}\right) </math> (where <math> I </math

4 KB (596 words) - 20:09, 27 May 2012
2006 SMT/Advanced Topics Problems/Problem 2
...ind a vertical vector <math> v </math> such that <math> (A^8+A^6+A^4+A^2+I)v=\left(\begin{matrix}0\\11\end{matrix}\right) </math> (where <math> I </math ...ght)v=\left(\begin{matrix}0\\11\end{matrix}\right) </math>. Letting <math> v=\left(\begin{matrix}a\\b\end{matrix}\right) </math>, we get the system of e

2 KB (297 words) - 20:09, 27 May 2012
2010 AMC 8 Problems/Problem 3
...-4), P=(1,-3.8), Q=(1,-3.6), R=(1,-3.4), S=(1,-3.2), T=(1,-3), U=(1,-2.8), V=(1,-2.6), W=(1,-2.4), Z=(1,-2.2), E_1=(1.4,-2.6), F_1=(1.8,-2.6), O_1=(14,- ...th(1pt)); D(S,linewidth(1pt)); D(T,linewidth(1pt)); D(U,linewidth(1pt)); D(V,linewidth(1pt)); D(W,linewidth(1pt)); D(Z,linewidth(1pt)); D(E_1,linewidth(

5 KB (847 words) - 19:59, 5 February 2023
1954 AHSME Problems
...an upright V.}\\ \textbf{(D)}\ \text{Two line segments forming an inverted V.}\\ \textbf{(E)}\ \text{None of these.} </math>

23 KB (3,535 words) - 16:29, 24 April 2020
1999 USAMO Problems/Problem 1
...fication/Lemma:}</math> The sum of degrees of a connected graph <math>G = (V,E)</math> is <math>2V -2 + 2R = 2E,</math> where <math>R</math> is the circ <math>\textit{Proof.}</math> <math>2 \times V -2</math> is the sum of ranks of the spanning tree created by decircuiting

4 KB (747 words) - 05:23, 13 May 2023
1977 USAMO Problems/Problem 5
...true with equality iff either (1) <math>p = q</math> or (2) three of <math>v, w, x, y, z</math> are <math>p</math> and two are <math>q</math> or vice ve

2 KB (389 words) - 23:08, 27 June 2018
2020 Mock Combo AMC 10
...itive integers <math>s, t, u, v, w, x, y, z</math> where <math>s > t > u > v > w > x > y > z</math>. Find <math>2(z + u) + s + t + v + w + x + y</math>.

15 KB (2,452 words) - 03:03, 4 July 2020
Lagrange Multipliers
The volume of the box is given by the equation <math>V(x, y, z) = xyz</math>. Because the way the box is described, the point that ...<cmath>\dfrac{\partial V}{\partial y} = xz</cmath> <cmath>\dfrac{\partial V}{\partial z} = xy</cmath>

5 KB (791 words) - 21:06, 30 November 2020
2013 AMC 10A Problems/Problem 14
We can use Euler's polyhedron formula that says that <math>F+V=E+2</math>. We know that there are originally <math>6</math> faces on the

1 KB (169 words) - 21:46, 28 December 2019
2013 AMC 12A Problems/Problem 25
...t of a radical of a complex number: <math>\sqrt{u}</math>, where <math>u = v+wi = r e^{i\theta}</math>. ...(\theta/2) = \pm \sqrt{r}\sqrt{\frac{1-\cos\theta}{2}} = \pm \sqrt{\frac{r-v}{2}}</math>.

4 KB (766 words) - 14:22, 8 October 2023
2013 USAMO Problems/Problem 1
label("$V$", (1.7922953932137468,0.6108747864253139), NE * labelscalefactor); label("$V$", (1.7922953932137468,0.6108747864253139), NE * labelscalefactor);

14 KB (1,830 words) - 18:22, 10 May 2023
2013 USAJMO Problems/Problem 5
...u-v}{u+v}\right), \frac{2uv}{u+v})</math>. Also, <math>Z\left(\frac{u-v}{u+v}\right), 0)</math>. It shall be left to the reader to find the slope of <ma

7 KB (1,250 words) - 18:05, 1 October 2021
Mock AIME 3 2006-2007 Problems/Problem 8
...(\frac{1}{16},\frac{1}{8},\frac{1}{13})</math>. Let <math> \overrightarrow{v} </math> be a vector with head <math>(\frac{1}{16},\frac{1}{8},\frac{1}{13}

1 KB (213 words) - 20:48, 15 February 2015
2014 AIME II Problems/Problem 10
...r labeling the complex numbers with <math>W</math> (<math>w</math>), <math>V</math> (<math>-z</math>), and <math>O</math> (<math>0</math>), we can inter

6 KB (1,045 words) - 13:08, 21 January 2024
Northeastern WOOTers Mock AIME I Problems
...uv.xy}+\overline{xy.uv} </cmath> is an integer? As an example, if <math>(u,v,x,y)=(0,1,2,3)</math>, then we have <math> N = 1.23 + 23.01 = 24.24 </math>

8 KB (1,336 words) - 09:10, 30 May 2020
1983 IMO Problems/Problem 4
...>. Again, by the observation in the previous paragraph, the points <math>U,V,T</math> must have different colors if we are to have no monochromatic righ

2 KB (373 words) - 23:40, 29 January 2021
2013 IMO Problems/Problem 2
...th> is even and <math>v</math> is odd and <math>u - v = 1</math>, is <math>v</math>. ...ts and v blue ones (<math>u</math> is even, <math>v</math> is odd, <math>u>v</math>).

3 KB (643 words) - 01:31, 19 November 2023
1971 IMO Problems/Problem 5
I shall prove a more general statement about the unit distance graph(<math>V=\mathbb{R}^2</math>, adjacency iff the Euclidean distance between the point ...here <math>G\times H</math> is described as <math>V(G\times H)=V(G)\times V(H), (v_1,w_1)\leftrightarrow (v_2,w_2) \Leftrightarrow v_1=v_2,w_1\leftrigh

4 KB (749 words) - 14:09, 29 January 2021
1972 IMO Problems/Problem 2
...h>) that we can find a circle passing through <math>U,D</math> (or <math>F,V</math>) which cuts the segments <math>UV,DF</math> in <math>X,Y</math>. Our

1 KB (224 words) - 18:15, 7 December 2022
1972 IMO Problems/Problem 6
...h that the translation with translation vector <math>k\cdot\overrightarrow{v}_p</math> maps the plane <math>p_i</math> to the plane <math>p_j</math>. Si

7 KB (1,370 words) - 15:42, 29 January 2021
1973 IMO Problems/Problem 2
Let <math>V</math> be a solid cube or right angled parallelepiped Let <math>M_{v}</math> be the set of all 8 vertices of <math>V</math>

4 KB (663 words) - 21:33, 21 November 2023
1951 AHSME Problems/Problem 28
...he area <math>(A)</math> of the sail and the square of the velocity <math>(V)</math> of the wind. The pressure on a square foot is <math>1</math> pound .../math>. Solving for <math>V</math>, we get <math>V^2=1024</math>, so <math>V=32</math>. Hence, the answer is <math>\boxed{C}</math>.

1 KB (220 words) - 19:45, 20 November 2014
2014 USAJMO Problems/Problem 6
...line{CA}</math> and <math>\overline{AB}</math>, respectively. Let <math>U,V</math> be the intersections of line <math>EF</math> with line <math>MN</mat pair A, B, C, I, M, N, P, E, F, U, V, X, R;

7 KB (1,273 words) - 18:17, 28 August 2021
1960 AHSME Problems
The volume <math>V = \pi R^2H</math> is to be increased by the same fixed positive amount when

21 KB (3,242 words) - 21:27, 30 December 2020
1973 AHSME Problems
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>

18 KB (2,788 words) - 13:55, 20 February 2020
1969 AHSME Problems/Problem 31
...1,1)</math> and <math>C(0,1)</math>. Let <math>u=x^2-y^2</math>, and <math>v=xy</math> be a transformation of the <math>xy</math>-plane into the <math>u ...h>x = \tfrac{v}{2}</math>, <math>u = (\tfrac{v}{2})^2 - 1</math>, so <math>v = 2\sqrt{u+1}</math>, where <math>-1 \le u \le 0</math>. That means some o

2 KB (377 words) - 17:24, 20 June 2018
1969 AHSME Problems
...1,1)</math> and <math>C(0,1)</math>. Let <math>u=x^2-y^2</math>, and <math>v=2xy</math> be a transformation of the <math>xy</math>-plane into the <math>

16 KB (2,662 words) - 14:12, 20 February 2020
1988 AHSME Problems
...),-sqrt(5)), W=(4+2/sqrt(5),sqrt(5)), T=(4,0), U=(4+2/sqrt(5),-4/sqrt(5)), V=(4+2/sqrt(5),1/sqrt(5)); draw(X--Y--Z--W--X^^T--V--X^^Y--U);

17 KB (2,535 words) - 13:45, 19 February 2020
1987 AHSME Problems
<math>\{V, W, X, Y, Z\}</math>. Using this correspondence, the cryptographer finds th

16 KB (2,291 words) - 13:45, 19 February 2020
1983 AHSME Problems
...</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>?

15 KB (2,309 words) - 23:43, 2 December 2021
1978 AHSME Problems
\text{(v) }y+a\ge x </math>

15 KB (2,432 words) - 01:06, 22 February 2024
1977 Canadian MO Problems/Problem 5
the vertex <math>V</math> to this path? MP("P",(-1,0),W);MP("V",(-.5,2.4),N);

889 bytes (136 words) - 15:53, 7 October 2014
1972 AHSME Problems
real t=pi/8;real u=7*pi/12;real v=13*pi/12; draw((ct,st)--(-ct,st)--(cos(v),sin(v)));

17 KB (2,732 words) - 13:54, 20 February 2020
2007 iTest Problems/Problem 22
\text{(V) } 2007 \quad </math>

929 bytes (137 words) - 22:05, 10 January 2019
2007 iTest Problems/Problem 25
\text{(V) } 21\qquad

2 KB (270 words) - 14:35, 29 July 2018
2007 iTest Problems/Problem 50
...oor</math> (the greatest integer less than or equal to the volume of <math>V</math>).

570 bytes (94 words) - 12:27, 6 April 2024
2007 iTest Problems/Problem 23
<math>\text{(V) Ying} \quad

1 KB (202 words) - 16:48, 24 November 2018
2007 iTest Problems/Problem 24
\text{(V) }21 \quad

2 KB (340 words) - 19:49, 30 June 2018
2014 IMO Problems/Problem 3
label("$u$",T+(-0.1,-0.2), S); label("$v$", S+(0,-0.2), S); Denote <math>\angle{HSB}=v</math>, <math>\angle{HTD}=u</math>, <math>\angle{HSC}=s</math>, <math>\angl

6 KB (1,071 words) - 03:58, 8 September 2018
1964 AHSME Problems
.../math> and the remainder is <math>v</math>, where <math>u</math> and <math>v</math> are integers. \textbf{(D)}\ v \qquad

19 KB (2,907 words) - 14:16, 20 February 2020
1956 AHSME Problems
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

20 KB (3,039 words) - 22:44, 12 February 2021
1988 AHSME Problems/Problem 20
...),-sqrt(5)), W=(4+2/sqrt(5),sqrt(5)), T=(4,0), U=(4+2/sqrt(5),-4/sqrt(5)), V=(4+2/sqrt(5),1/sqrt(5)); draw(X--Y--Z--W--X^^T--V--X^^Y--U);

2 KB (334 words) - 14:11, 27 February 2018
2005 CEMC Gauss (Grade 7) Problems/Problem 15
...>T</math> is halfway between <math>Q</math> and <math>R</math>, then <math>V</math> is halfway between <math>P</math> and <math>S</math>. Therefore, <m

2 KB (349 words) - 02:41, 23 October 2014
1987 AHSME Problems/Problem 16
<math>\{V, W, X, Y, Z\}</math>. Using this correspondence, the cryptographer finds th ...to <math>0</math>, <math>3</math>, and <math>4</math>), we must have <math>V = 2</math> and <math>Y = 1</math>. Thus <math>XYZ = 413_{5} = 4 \cdot 5^{2}

2 KB (242 words) - 14:32, 1 March 2018
2015 AMC 10A Problems/Problem 23
...pairs (not counting transpositions because this does not affect (<math>u + v</math>), <math>(2, 8), (4, 4), (-2, -8), (-4, -4)</math>, yields <math>a =

2 KB (372 words) - 00:28, 27 September 2021
2015 AMC 10A Problems/Problem 21
...dron and <math>TD</math> as the height. Thus, the desired volume is <cmath>V = \dfrac{1}{3} bh = \dfrac{1}{3}\cdot[ABC]\cdot TD = \dfrac{1}{3} \cdot 6 \ <cmath>V = \dfrac{1}{3} Bh = \dfrac{1}{3} h \cdot BE \cdot \dfrac{6\sqrt{2}}{5} = \d

4 KB (574 words) - 07:18, 16 August 2023
2015 AMC 10A Problems/Problem 3
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);

2 KB (280 words) - 23:07, 26 June 2023
2015 AIME I Problems/Problem 10
...>a\neq 0</math> (else <math>f</math> is not cubic) where <math>\{q,r,s,t,u,v\}</math> is the same as the set <math>\{1,2,3,5,6,7\}</math>. Subtracting t <cmath>24=a((t+u+v-(q+r+s))x^2-a(tu+uv+tv-(qr+qs+rs))x+a(tuv-qrs)</cmath>

8 KB (1,474 words) - 10:00, 10 November 2023
2015 AIME II Problems
...he volume of water thus displaced is <math>v</math> cubic feet. Find <math>v^2</math>.

8 KB (1,326 words) - 19:15, 13 January 2024
2015 AIME II Problems/Problem 9
...he volume of water thus displaced is <math>v</math> cubic feet. Find <math>v^2</math>. <cmath>v = \frac{1}{3}(2\sqrt{6})\left(\frac{1}{2} \cdot (2\sqrt{6})^2\right) = \fra

7 KB (1,074 words) - 01:49, 22 January 2024
2015 USAMO Problems/Problem 2
Let <math>M=(u,v)</math>, then <math>T=(2u+\cos(2A), 2v-\sin(2A))</math>. ...cos(2A))^2+ (2v-\sin(2A))^2=1</math>, namely <math>v\sin(2A)-u\cos(2A)=u^2+v^2</math>. (E2)

5 KB (902 words) - 09:58, 20 August 2021
2015 USAJMO Problems/Problem 3
Let <math>M=(u,v)</math>, then <math>T=(2u+\cos(2A), 2v-\sin(2A))</math>. ...cos(2A))^2+ (2v-\sin(2A))^2=1</math>, namely <math>v\sin(2A)-u\cos(2A)=u^2+v^2</math>. (E2)

4 KB (760 words) - 16:45, 29 April 2020
Aops font
| V | 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>

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
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) - 01:55, 6 February 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 (14,927 words) - 01:36, 16 April 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) - 10:29, 4 April 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

13 KB (2,042 words) - 09:34, 3 April 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
https://www.youtube.com/watch?v=dxYw1wYHid4&t=12s ...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>

12 KB (2,101 words) - 10:08, 31 March 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 (1,175 words) - 16:45, 28 January 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;

19 KB (2,967 words) - 16:56, 24 February 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) - 13:53, 4 April 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 (616 words) - 14:14, 29 March 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 (426 words) - 01:50, 18 April 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
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
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

5 KB (887 words) - 14:09, 3 April 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. Let <math>DD' = x, FF'= y, DH = u, FH = v \implies HH' = \frac{yu + vx}{u+v }= \frac {7}{16}.</math>

19 KB (3,295 words) - 04:11, 12 April 2024
Add
https://archifol.io/v/tjqbn89d https://archifol.io/v/brzmkkgh

273 bytes (44 words) - 21:35, 1 April 2024

Page

Toolbox

Search

Search results