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2020 AMC 10A Problems
label("V", (2, 6), NE);

13 KB (1,968 words) - 18:32, 29 February 2024
2007 AIME II Problems/Problem 15
...ale the triangle with the circumradius by a [[line]]ar scale factor, <math>v</math>. :<math>\frac{65}{8}v=8u</math>

11 KB (2,099 words) - 17:51, 4 January 2024
2007 AMC 12A Problems/Problem 20
...cut off corners is a [[pyramid]], whose volume can be calculated by <math>V = \frac 13 Bh</math>. Use the base as one of the three [[congruency (geomet

2 KB (317 words) - 10:10, 16 September 2022
1989 USAMO Problems/Problem 2
Call it a vertex set <math>V</math>. <math>10</math> vertices remain outside <math>V</math> and each has to be attached to at least one edge.

3 KB (438 words) - 01:19, 27 December 2023
1989 USAMO Problems
Let <math>u</math> and <math>v</math> be real numbers such that (u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8.

2 KB (326 words) - 18:52, 18 July 2016
2007 USAMO Problems/Problem 4
Chose a vertex, <math>v</math>, for which <math>a</math> is minimal (i.e. out of all maximal elemen ...h>. So then in this special case, we have <math>D = 4</math>, and so <math>V = 2006 \times 4+1</math> (a possible configuration of this size that works

10 KB (1,878 words) - 14:56, 30 June 2021
Octahedron
* The volume <math>V</math> of a regular octahedron with side length <math>a</math> is <math>\fr

1 KB (155 words) - 12:19, 21 July 2023
1989 USAMO Problems/Problem 5
Let <math>u</math> and <math>v</math> be real numbers such that <cmath> (u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8. </cmath>

2 KB (300 words) - 19:16, 18 July 2016
2004 AMC 12A Problems/Problem 11
...bstituting yields: <math>20n+25=21(n+1),</math> so <math>n=4</math>, <math>v = 80.</math> Then, we see that the only way Paula can satisfy this rule is

2 KB (310 words) - 17:39, 31 December 2022
2004 AMC 12A Problems/Problem 6
Let <math>U=2\cdot 2004^{2005}</math>, <math>V=2004^{2005}</math>, <math>W=2003\cdot 2004^{2004}</math>, <math>X=2\cdot 20 <math>\mathrm {(A)} U-V \qquad \mathrm {(B)} V-W \qquad \mathrm {(C)} W-X \qquad \mathrm {(D)} X-Y \qquad \mathrm {(E)} Y-

1 KB (139 words) - 02:10, 30 December 2020
Binet's Formula
...d <math>p= \frac{1-\sqrt{5}}{2}.</math> We get that <cmath>F_n = \lambda_1 v^n + \lambda_2 p^n.</cmath>Plugging in our initial conditions, we get <cmath>0 = \lambda_1 + \lambda_2 </cmath> <cmath> 1= \lambda_1 v + \lambda_2 p </cmath>

3 KB (550 words) - 16:12, 24 February 2024
Celsius
...cncn vmnsnfdv jcd vndlfencm savdnm vs,czfvndm ,cxafkvsnsm dvhbfvm c,cdfemw v,dsnekmc xvzmvsdv vndnf cnvdjnf dfnwfd fwe vndkbfwenj sdbfwenj fbhkfenlkjs

4 KB (357 words) - 22:40, 17 April 2024
Mass
...math>, where <math>M</math> is momentum, <math>m</math> is mass, and <math>v</math> is [[velocity]].

1 KB (188 words) - 22:44, 10 October 2013
Graph (graph theory)
...may be defined using ordered pairs from the [[product set]] <math>V \times V</math>. ...ay the edges <math>e</math> and <math>f</math> are ''coincident'' at <math>v</math>.

8 KB (1,428 words) - 10:26, 27 August 2020
2000 AMC 12 Problems/Problem 13
https://www.youtube.com/watch?v=OT42J21ZNC8&feature=youtu.be https://www.youtube.com/watch?v=7QU8OlnljHw ~David

6 KB (996 words) - 18:14, 29 June 2023
1997 PMWC Problems
...uilateral triangle with sides of length three units. <math>U</math>, <math>V</math>, <math>W</math>, <math>X</math>, <math>Y</math>, and <math>Z</math> label("$V$",(-1/3,sqrt(3)/6),NW);

15 KB (2,057 words) - 19:13, 10 March 2015
1951 AHSME Problems
...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

23 KB (3,641 words) - 22:23, 3 November 2023
2002 AMC 12B Problems/Problem 5
...s of a [[pentagon]]. Suppose that <math>v < w < x < y < z</math> and <math>v, w, x, y, </math> and <math>z</math> form an [[arithmetic sequence]]. Find ...ath> triangles) is <math>3 \cdot 180 = 540^{\circ}</math>. If we let <math>v = x - 2d, w = x - d, y = x + d, z = x+2d</math>, it follows that

2 KB (263 words) - 05:58, 8 August 2023
2003 AMC 12B Problems/Problem 17
...that <cmath>2 \cdot \textbf{(2)} + \textbf{(1)} = 5u + 5v = 3 \implies u + v = \frac{3}{5} \implies c = \boxed{\textbf{(D)}~\frac{3}{5}}</cmath>.

2 KB (329 words) - 13:49, 4 April 2024
Isogonal conjugate
...nes. Let coordinates of images of points be <cmath>X(-a, 0), X'(a,u), Y(-b,v), Y'(b,w).</cmath> ...f a straight line <math>XY</math> is <math>\frac{x + a}{a - b} = \frac {y}{v}.</math>

54 KB (9,416 words) - 08:40, 18 April 2024
2007 AMC 12B Problems/Problem 19
<math>V = \pi \left(\frac{3}{\pi}\right)^2\cdot 6\sin\theta</math>

1 KB (166 words) - 16:35, 15 February 2021
1985 AJHSME Problems
label("V",(1.5,.3),N); ...bf{(A)}\ \text{Z} \qquad \textbf{(B)}\ \text{U} \qquad \textbf{(C)}\ \text{V} \qquad \textbf{(D)}\ \ \text{W} \qquad \textbf{(E)}\ \text{Y}</math>

12 KB (1,670 words) - 17:42, 24 November 2021
Mock AIME 5 Pre 2005 Problems
...>. Y is on <math>\overline {ST}</math>, dividing <math>SY:YT = 2:1</math>. V is on <math>\overline {XY}</math>, dividing <math>XV:VY = 1:2</math>. It is

6 KB (909 words) - 07:27, 12 October 2022
1974 USAMO Problems/Problem 5
...le ADB = \angle BDC = \angle CDA = 120^\circ</math>. Prove that <math>x=u+v+w</math>. label("$v$",(B+D)/2,N);

7 KB (1,221 words) - 18:57, 3 July 2013
2005 USAMO Problems/Problem 3
...math> Substituting in <math>P</math> yields <cmath>-a^2p(1-p)+vp=0\implies v = a^2(1-p).</cmath> Substituting in <math>B_1</math> yields

6 KB (1,117 words) - 01:17, 11 October 2021
Cone
...me of a pyramid, <math>V = \frac{1}{3} \cdot B \cdot h</math>, where <math>V</math> is the volume, <math>B</math> is the area of the base and <math>h</m

7 KB (1,128 words) - 20:12, 27 September 2022
2008 USAMO Problems/Problem 6
...space]] of all such functions. Define the linear operator <math>A : V \to V</math> as <cmath>(Af)(v) = \sum_{v \sim w} f(v) - f(w)</cmath>

13 KB (2,414 words) - 14:37, 11 July 2016
2008 Mock ARML 1 Problems/Problem 3
pair v(int n){ return dir(n * 60); } ...0))--MP("B",v(1),N)--MP("C",v(2),N)--MP("D",v(3),SW)--MP("E",v(4))--MP("F",v(5))--cycle);

3 KB (425 words) - 22:32, 5 December 2020
Schrodinger Equation
...ing the Hamiltonian, usually of the form <math>-\frac{\hbar^2}{2m}\Delta + V</math> where <math>\Delta</math> is the relevant Laplace(-Beltrami) operato

417 bytes (69 words) - 14:32, 21 April 2018
Jean-Victor Poncelet
*Didion 1870. ''Notice sur la vie et les ouvrages du général J. V. Poncelet''

2 KB (253 words) - 11:41, 19 December 2018
1988 IMO Problems/Problem 1
...ble positions of the midpoints <math>U</math> of <math>AB</math> and <math>V</math> of <math>AC</math> as <math>A</math> varies?</li> We claim that all points <math>U,V</math> lie on a circle centered at the midpoint of <math>OP</math>, <math>M

3 KB (545 words) - 11:32, 30 January 2021
1997 PMWC Problems/Problem T1
...uilateral triangle with sides of length three units. <math>U</math>, <math>V</math>, <math>W</math>, <math>X</math>, <math>Y</math>, and <math>Z</math> label("$V$",(-1/3,sqrt(3)/6),NW);

1 KB (188 words) - 14:38, 20 April 2014
Category (category theory)
...nd there is a morphism <math>U \to V</math> if and only if <math>U \subset V</math>.

5 KB (792 words) - 19:01, 7 April 2012
1991 IMO Problems/Problem 4
...each step in the process we remove a number of vertices from the set <math>V</math> if their exists an edge sorrounding it which is labelled. Additiona ...of the vertices not in <math>V</math>. Notice that since <math>v_1,v_n\in V</math> the edge connecting <math>v_0</math> and <math>v_1</math> and the ed

4 KB (668 words) - 17:45, 30 January 2021
2001 IMO Problems/Problem 4
..., there exists a <math>v\in\{1,2,...,m!\}</math> such that <math>t\equiv f(v)\pmod{m!}</math>. So, let <math>t\equiv f(v_t)\pmod{m!}</math>. Consider

2 KB (416 words) - 20:01, 19 May 2023
Acceleration
...known to be constant, then <cmath>\textbf{a} = \frac{\textbf{v}_2 -\textbf{v}_1 }{t_2 - t_1}</cmath> Note that velocity is a vector, so the magnitudes c ...instance, <cmath>\textbf{a} = \lim_{h\to 0} \frac{v(t+h)-v(t)}{(t+h)-t} = v'(t)</cmath>

2 KB (277 words) - 14:04, 24 April 2022
2001 USAMO Problems/Problem 3
...h>b = 2\sin u</math> and <math>c = 2\sin v</math>, where <math>0^\circ < u,v < 90^\circ</math>. Then <cmath>a = 2(-\sin u\sin v + \cos u\cos v) = 2\cos (u + v),</cmath>

4 KB (807 words) - 10:45, 9 April 2023
Time dilation
<math>\dfrac{t_1}{\sqrt{1-v^2/c^2}}=t_2</math> <math>v</math> is the relative velocity the ovject is moving to the observer.

1 KB (261 words) - 00:19, 31 January 2021
Lorentz Factor
It is equivalent to <math>\gamma=\dfrac{1}{\sqrt{1-v^2/c^2}}</math>

226 bytes (34 words) - 11:23, 5 October 2012
1992 USAMO Problems/Problem 4
By another person ^v^

5 KB (807 words) - 18:37, 25 June 2021
1974 USAMO Problems
...le ADB = \angle BDC = \angle CDA = 120^\circ</math>. Prove that <math>x=u+v+w</math>. label("$v$",(B+D)/2,N);

3 KB (427 words) - 18:55, 3 July 2013
1962 IMO Problems/Problem 3
Answer: the rhombus CUVW, where U is the center of ABCD, V is the center of ABB'A, and W is the center of BCC'B'. ...x/2 + 1/2, x/2, 1/2) = x (1, 1/2, 1/2) + (1-x) (1/2, 0, 1/2) = x W + (1-x) V, so M traces out the line VW.

3 KB (581 words) - 02:00, 6 May 2023
1962 IMO Problems/Problem 7
...n the direction of <math>V{i}</math> to <math>V{j}</math> and beyond <math>V{j}</math> for <math>i=1,2,3,4</math>; <math>j=1,2,3,4</math>; and <math>i \ ...trahedron opposite of vertex <math>V_{4}</math> below <math>\Delta V{1}V{2}V{3}</math>

11 KB (1,928 words) - 20:52, 21 November 2023
2001 AMC 10 Problems
...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));

14 KB (1,983 words) - 16:25, 2 June 2022
1976 USAMO Problems/Problem 4
...ath>. Let the volume of the tetrahedron be <math>V</math>. Therefore <math>V=\frac{abc}{6}</math>. ...{6V}</math>, or <math>6V\leq \frac{S^3(\sqrt{2}-1)^3}{27}</math>, or <math>V\leq \frac{S^3(\sqrt{2}-1)^3}{162}</math>, with equality only when <math>a=b

2 KB (358 words) - 23:15, 18 July 2016
1985 AJHSME Problems/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>

2 KB (279 words) - 09:25, 10 January 2023
2009 AMC 12B Problems/Problem 20
<math>v = \frac{200}{b}</math> ...gain <math>b</math> more edges. So the total number of new edges is <math>v*b \Rightarrow \frac{200}{b}*b \Rightarrow 200</math>. It doesn't matter how

9 KB (1,567 words) - 13:43, 19 August 2023
2009 AIME I Problems/Problem 10
...of sittings is in the form <math>N*(5!)^3</math> because for each <math>M, V, E</math> sequence we have <math>5!</math> arrangements within the Ms, Vs, ...members must sit in cycles of M, V, E, but not necessarily with one M, one V, and one E in each cycle(for example, MMVVVE, MVVVEEE, MMMVVVEE all count a

4 KB (590 words) - 16:49, 27 September 2023
2009 AIME II Problems/Problem 9
...en <math>1</math> and <math>167</math>, inclusive, and for each such <math>v</math> we have exactly one valid <math>x</math>. Hence in this case there a

5 KB (845 words) - 15:45, 28 December 2020
2008 IMO Problems/Problem 6
V be the foot of the projection of K to AC.

1 KB (283 words) - 01:15, 19 November 2023
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

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