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- Find the number of ordered pairs <math>(a, b, c, d)</math> that satisfy these conditions. A tripod has three legs of length 3 feet, 4 feet, and 4 feet. It is set up so that the angle between any two legs is <math>90^{\circ}</math>. The h12 KB (1,917 words) - 12:14, 29 November 2021
- How many ordered pairs of integers <math>(x,y)</math> satisfy the equation <cmath>x^{2020} + ...h its interior. For real <math>r\geq0</math>, let <math>S(r)</math> be the set of points in <math>3</math>-dimensional space that lie within a distance <m16 KB (2,496 words) - 20:09, 19 May 2024
- ...from <math>1^2</math> to <math>36^2</math>, and how many ways they can be ordered ...nce of <math>4</math> numbers whose product is a perfect square. To form a set, we can simply select zero to two groups of size <math>2</math> or <math>3<19 KB (2,941 words) - 16:16, 7 June 2024
- A '''system of equations''' is a set of [[equation]]s which share the same [[variable]]s. An example of a syste Find the ordered pair <math>(x,y)</math> for which35 KB (5,882 words) - 18:08, 28 June 2021
- ...th>f(x)=x^2+ax+b</math> and <math>g(x)=x^2+cx+d.</math> Find the number of ordered triples <math>(a,b,c)</math> of integers with absolute values not exceeding ...> can be anything. However, <math>c</math> can also be anything, as we can set the root of <math>g</math> (not equal to <math>f(2) = f(4)</math>) to any i6 KB (964 words) - 22:33, 18 January 2024
- For a particular positive integer <math>n</math>, the number of ordered sextuples of positive integers <math>(a, b, c, d, e, f)</math> that satisfy ...nd stops as soon as it touches the ground again. What is the volume of the set of points swept out by the larger log as it rolls over the smaller one?13 KB (2,059 words) - 02:59, 21 January 2021
- ...<math>(0,0),(0,a),(a,0),(a,a)</math>. It seems as if the solution to the set involves only <math>0</math> and <math>a</math>. To prove this, we need to ...i+1})^2 = (n+1)a^2</math>. The inductive step holds, so solutions are all ordered pairs <math>(x_1, x_2, \cdots x_n)</math> where <math>x_i = 0</math> or <ma3 KB (629 words) - 00:26, 18 December 2019
- ...ed quadruple of not necessarily distinct integers, each one of them in the set <math>\{0,1,2,3\}.</math> For how many such quadruples is it true that <mat ...actly one term to be odd, one term to be even. Because of symmetry, we can set <math>ad</math> to be odd and <math>bc</math> to be even, then multiply by6 KB (1,044 words) - 13:50, 4 April 2024
- ...e properties that factors are greater than <math>1</math>, and differently ordered products are counted separately. ...ly totaling the number of ways there are to insert a <math>3</math> into a set of numbers that multiply to <math>32</math>.16 KB (2,562 words) - 17:41, 25 May 2024
- How many ordered pairs of integers <math>(x, y)</math> satisfy the equation <cmath>x^{2020}+ ...<math>(0,2)</math> gives a total of <math>\boxed{\textbf{(D) }4}</math> ordered pairs.8 KB (1,221 words) - 16:29, 5 February 2024
- Let <math>S</math> be the set of positive integers <math>N</math> with the property that the last four di ...e numbers are chosen independently and at random with replacement from the set <math>S</math> and labeled <math>a_1,a_2,</math> and <math>a_3</math> in th7 KB (1,257 words) - 17:51, 5 February 2022
- ...y the number of distinct subsets <math>S</math> such of our aforementioned set <math>E_1, E_2, ..., E_n</math> such that the sum of the members in <math>S The only basic ordered pair <math>(E_1, E_2)</math> that offers a nonzero number of legal placemen4 KB (690 words) - 14:32, 6 January 2021
- ...th>(0, 0), (6, 0)</math>, and <math>(0, 5)</math>. Let <math>S</math> be a set of rigid transformations consistsing of rotataions <math>90, 180</math>, an Let there be multiple ordered pairs <math>(n, k)</math> where <math>n</math> and <math>k</math> are posit9 KB (1,450 words) - 18:33, 21 April 2020
- ...math> and <math>b</math> is the ordinal that describes the order type of a set with order type a concatenated with one of order type b. Warning! Ordinal a Every ordinal characterizes the order type of the ordered ordinals less than it. For example, <math>0,1,2,\dotsb,\omega</math> has or5 KB (811 words) - 14:16, 7 June 2020
- ...ordered triple can be identified with a multiset of three elements of the set of <math>2003</math> integers <math>\{17,18,19,\ldots,2019\}</math>, which7 KB (1,186 words) - 15:31, 5 January 2024
- Let <math>S</math> denote the set of all positive integers <math>n</math> that satisfy <math>0 \leq n \leq 10 ...hat he is on <math>(x, y)</math>, he will randomly choose one point in the set <math>\{ (x-1, y-1), (x, y-1), (x+1, y-1) \}</math> to travel to. The proba14 KB (2,267 words) - 12:49, 9 June 2020
- Let <math>S</math> denote the set of all positive integers <math>n</math> that satisfy <math>0 \leq n \leq 10 ...integers (which are ordered accordingly) not including <math>1</math> are ordered based on the placement of the <math>1</math> in the permutation. For instan15 KB (2,388 words) - 13:24, 9 June 2020
- Denote by <math>A</math> the set of all integers <math>a</math> such that <math>1 \le a < p</math>, and both ...value of <math>N</math> over all possible choices of the <math>100</math> ordered pairs.4 KB (614 words) - 13:47, 22 November 2023
- ...th>, we can first choose two different numbers <math>a > b</math> from the set <math>\{0,1,2,\ldots,10\}</math> in <math>\binom{11}{2}=55</math> ways. Thi As indicated by the X-marks, the ordered pairs <math>(a,b)=(10,0),(10,1),(10,2),(10,3),(10,4)</math> generate <math>7 KB (1,174 words) - 08:21, 13 May 2023
- ...uence<cmath>3, 4, 5, a, b, 30, 40, 50</cmath>is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression8 KB (1,205 words) - 22:55, 26 March 2023
