Algebra InputsTrigonometry InputsCalculus InputsMatrix Inputs Basic algebra trigonometry calculus statistics matrices Characters ^ { 5 } C _ { 1 } ( 20 ) ^ { \prime } ( 19 ) ^ { 5 - 1 } + ^ { 5 } C _ { 2 } ( 20 ) ^ { 2 } ( 19 ) ^ { 5 \cdot 2 }Factor 2^{5}\times 5^{3}\times 19^{10}View solution stepsSolution Steps ^ { 5 } C _ { 1 } ( 20 ) ^ { \prime } ( 19 ) ^ { 5 - 1 } + ^ { 5 } C _ { 2 } ( 20 ) ^ { 2 } ( 19 ) ^ { 5 \cdot 2 } Subtract 1 from 5 to get 4. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 19^{4}+combination(5,2)\times 20^{2}\times 19^{5\times 2}) Calculate 19 to the power of 4 and get 130321. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 20^{2}\times 19^{5\times 2}) Calculate 20 to the power of 2 and get 400. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 400\times 19^{5\times 2}) Multiply 5 and 2 to get 10. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 400\times 19^{10}) Calculate 19 to the power of 10 and get 6131066257801. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 400\times 6131066257801) Multiply 400 and 6131066257801 to get 2452426503120400. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 2452426503120400) Factor out 130321. 130321\left(5\frac{\mathrm{d}}{\mathrm{d}x}(20)+188183524000\right) Evaluate 24524265031204000QuizCombinations5 problems similar to: ^ { 5 } C _ { 1 } ( 20 ) ^ { \prime } ( 19 ) ^ { 5 - 1 } + ^ { 5 } C _ { 2 } ( 20 ) ^ { 2 } ( 19 ) ^ { 5 \cdot 2 }
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If \displaystyle{\left({1}+{x}\right)}^{{n}}={c}_{{0}}+{c}_{{1}}{x}+{c}_{{2}}{x}^{{2}}+\cdots+{c}_{{n}}{x}^{{n}} then show that \displaystyle{c}_{{0}}+{3}{c}_{{1}}+{5}{c}_{{2}}+\cdots+{\left({2}{n}+{1}\right)}{c}_{{n}}={\left({n}+{1}\right)}{2}^{{n}} ...https://socratic.org/questions/if-1-x-n-c0-c1x-c2x-2-cnx-n-then-show-that-c0-3c1-5c2-2n-1-cn-n-1-2-n See below. Explanation: Taking now \displaystyle{2}\frac{{d}}{{{\left.{d}{x}\right.}}}{\left({1}+{x}\right)}^{{n}}+{\left({1}+{x}\right)}^{{n}}={2}{n}{\left({1}-{x}\right)}^{{{n}-{1}}}+{\left({1}+{x}\right)}^{{n}}={\left({2}{n}+{\left({1}+{x}\right)}\right)}{\left({1}+{x}\right)}^{{{n}-{1}}} ... On 119^2+120^2=13^4\, and p=239https://math.stackexchange.com/questions/2052632/on-11921202-134-and-p-239 Another relation is: (2\cdot2)^4-2^4-239=1 This implies: 239\cdot13^4 + 13^4 + (2\cdot13)^4 = (2\cdot2\cdot13)^4 which, using the first two relations on your list, gives: (120^2-119^2)(120^2+119^2)+13^4+(2\cdot13)^4=(2\cdot2\cdot13)^4 ... Number of ways of choosing two subsets P and Q such that P\cap Q=\emptysethttps://math.stackexchange.com/q/1604428 For the case n(P)=1, you should have {{n−1}\choose 0}+{{n−1}\choose 1}+\cdots+{{n−1}\choose {n−1}}=2^{n-1} because you are not allowed to include any elements of P (of which there is 1) when ... Question on a set of transpose matrices and linear independencehttps://math.stackexchange.com/questions/918346/question-on-a-set-of-transpose-matrices-and-linear-independence Use linearity of the transposition (A+B)^t=A^t+B^t and (A^t)^t=A: if \sum_{j=1}^ka_j A_j^t=0 for some scalars (a_j)_{j=1}^k then taking the transpose \sum_{j=1}^ka_j (A_j^t)^t=0. The LHS is ... Faces of cones give localizations of affine toric varietieshttps://math.stackexchange.com/questions/718149/faces-of-cones-give-localizations-of-affine-toric-varieties Let R be a commutative ring, and let f be a non-zero element. Write R_f for the localization of R at f. Then Spec(R_f) is naturally contained in Spec(R): it is the locus where f is ... Factorization of Ideals in Dedekind Domains Proofhttps://math.stackexchange.com/questions/269109/factorization-of-ideals-in-dedekind-domains-proof I believe this comes from the correspondence theorem: If you have two ideals P and Q of R that contain J such that under the canonical homomorphism \pi : R \to R/J we have \pi(P) = \pi(Q) ...More Items
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CopyCopied to clipboardfactor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 19^{4}+combination(5,2)\times 20^{2}\times 19^{5\times 2}) Subtract 1 from 5 to get 4.factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 20^{2}\times 19^{5\times 2}) Calculate 19 to the power of 4 and get 130321.factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 400\times 19^{5\times 2}) Calculate 20 to the power of 2 and get 400.factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 400\times 19^{10}) Multiply 5 and 2 to get 10.factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 400\times 6131066257801) Calculate 19 to the power of 10 and get 6131066257801.factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 2452426503120400) Multiply 400 and 6131066257801 to get 2452426503120400.130321\left(5\frac{\mathrm{d}}{\mathrm{d}x}(20)+188183524000\right) Factor out 130321.
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Quadratic equation { x } ^ { 2 } - 4 x - 5 = 0Trigonometry 4 \sin \theta \cos \theta = 2 \sin \thetaLinear equation y = 3x + 4Arithmetic 699 * 533Matrix \left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]Simultaneous equation \left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.Differentiation \frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }Integration \int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d xLimits \lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}Back to top
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View solution stepsSolution Steps ^ { 5 } C _ { 1 } ( 20 ) ^ { \prime } ( 19 ) ^ { 5 - 1 } + ^ { 5 } C _ { 2 } ( 20 ) ^ { 2 } ( 19 ) ^ { 5 \cdot 2 } Subtract 1 from 5 to get 4. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 19^{4}+combination(5,2)\times 20^{2}\times 19^{5\times 2}) Calculate 19 to the power of 4 and get 130321. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 20^{2}\times 19^{5\times 2}) Calculate 20 to the power of 2 and get 400. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 400\times 19^{5\times 2}) Multiply 5 and 2 to get 10. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 400\times 19^{10}) Calculate 19 to the power of 10 and get 6131066257801. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 400\times 6131066257801) Multiply 400 and 6131066257801 to get 2452426503120400. factor(combination(5,1)\frac{\mathrm{d}}{\mathrm{d}x}(20)\times 130321+combination(5,2)\times 2452426503120400) Factor out 130321. 130321\left(5\frac{\mathrm{d}}{\mathrm{d}x}(20)+188183524000\right) Evaluate 24524265031204000
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