Search results

  • Case II) <math>a+b=2c\Rightarrow 2+c=ab\Rightarrow4+a+b=2ab\Rightarrow(2a-1)(2b-1)=9</math> Case V) <math>a+b=5c\Rightarrow (5a-1)(5b-1)=126</math> for which there are 2 solu
    2 KB (332 words) - 09:37, 30 December 2021
  • ...ly if there exists a scalar <math>t</math> such that <math>\overrightarrow{v} = t \overrightarrow{w}</math>, or if one of the vectors is zero. This form ...is equal to <math> \left( ||\mathbf{a}|| * ||\mathbf{b}|| \right)^2 = a^2b^2</math>. The inequality then follows from <math> |\cos\theta | \le 1 </ma
    13 KB (2,048 words) - 15:28, 22 February 2024
  • 3a+2b &= 0. 3a+2b &= -1, \\
    10 KB (1,585 words) - 03:58, 1 May 2023
  • ..., then the [[greatest common factor]] of <math>2^u + 1 </math> and <math>2^v + 1 </math> is 3. ...ath>t </math>, contradicting our assumption that <math>u </math> and <math>v </math> are relatively prime.
    10 KB (1,739 words) - 06:38, 12 November 2019
  • ...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
  • ...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 ...c{k-\sqrt{k^2+4b^2c^2q(1-q)}}{2c^2}, z'=\frac{-k-\sqrt{k^2+4b^2c^2q(1-q)}}{2b^2}</cmath>
    6 KB (1,117 words) - 01:17, 11 October 2021
  • ...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
  • ...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
  • ...> <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
  • ...>, <math>c</math>, and <math>d</math> be positive integers with <math> a < 2b</math>, <math>b < 3c </math>, and <math>c<4d</math>. If <math>d<100</math>, ...{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
  • ...an upright V.}\\ \textbf{(D)}\ \text{Two line segments forming an inverted V.}\\ \textbf{(E)}\ \text{None of these.} </math> ...le by <math>8</math>. If <math>a>b</math>, and <math>2a+1</math> and <math>2b+1</math> are the odd numbers,
    23 KB (3,535 words) - 16:29, 24 April 2020
  • \text{(B) if a }\neq\text{2b}\qquad 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
  • <math>\frac{bx(a^2x^2 + 2a^2y^2 + b^2y^2) + ay(a^2x^2 + 2b^2x^2 + b^2y^2)}{bx + ay}</math> ...),-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));
    17 KB (2,535 words) - 13:45, 19 February 2020
  • .../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
  • ...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>16A^2 = 2a^2 b^2 + 2b^2 c^2 + 2c^2 a^2 - a^4 - b^4 - c^4 = -(a^2 + b^2 - c^2)^2 + 4a^2 b^2.</cmat
    4 KB (574 words) - 07:18, 16 August 2023
  • <math>5a,2b</math> ...</math> be the number of elements <math>2 \pmod{3}</math>. Then, <math>a + 2b \equiv 0 \pmod{3} \implies a - b \equiv 0 \pmod{3}</math>. Since <math>0 \l
    26 KB (4,044 words) - 13:58, 24 January 2024
  • ...equation <math>\frac{6b}{a}=\frac{a+b}{a-b}\implies a^2-5ab+6b^2=(a-3b)(a-2b)=0</math> and this gives our answer to be <math>\mathbf{(C)} \frac{3}{2}</m ...the origin and select a point on each line to define vectors <math>\mathbf{v}_{i}=(x_{i},y_{i})</math>.
    5 KB (895 words) - 15:03, 8 June 2023
  • and solve for <math>m/n = (abc)^2 = a^2b^2c^2</math> Since <math>a^2=b^2+c^2-2bc=\frac{1}{2}</math>, <math>m/n = a^2b^2c^2 = a^2(bc)^2 = \frac{1}{2}\left(\frac{1}{4}\right)^2=\frac{1}{32}</math
    15 KB (2,208 words) - 01:25, 1 February 2024
  • ...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
  • ...\left(\frac{b^3}{27a^3}\right) + \left(\frac{b}{a}\right)y^2 - \left(\frac{2b^2}{3a^2}\right)y + \left(\frac{b^3}{9a^3}\right) + \left(\frac{c}{a}\right) <math>y^3 + \left(\frac{3ac - b^2}{3a^2}\right)y + \left(\frac{2b^3 - 9abc + 27a^2d}{27a^3}\right) = 0</math>.
    6 KB (1,059 words) - 14:42, 11 December 2020

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)