Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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1. 2. 3. 4. Find the generating function for the number of non-negative integer solutions to 2x+3y+5z = n, where n is a nonnegative integer. Use WolframAlpha to find the number of solutions when n = 30. You will need to use the following command taylor series [insert generating function here] order 30 at x=0 Let n be a nonnegative integer. Find the generating function for the number of solutions to x1+x2+x3 + x4 = n, where x1, x2, x3, x4 are integers and 0x1, 3≤ x2 < ∞0, 2x3 ≤5 1≤ x ≤4. Use WolframAlpha to find the number of solutions when n = = 30. Find the exponential generating function for the number of permutations with repetition of length n of the set {a, b, c}, in which there are an odd number of a's, an odd number of b's, and an even number of c's. Use WolframAlpha to find the number of such permutations when n = 10. Find the generating function for the number of partitions of an integer into distinct even parts. Use Wolfram Alpha to find the number of partitions of 15 into distinct even parts.
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Transcribed Image Text:1. 2. 3. 4. Find the generating function for the number of non-negative integer solutions to 2x+3y+5z = n, where n is a nonnegative integer. Use WolframAlpha to find the number of solutions when n = 30. You will need to use the following command taylor series [insert generating function here] order 30 at x=0 Let n be a nonnegative integer. Find the generating function for the number of solutions to x1+x2+x3 + x4 = n, where x1, x2, x3, x4 are integers and 0x1, 3≤ x2 < ∞0, 2x3 ≤5 1≤ x ≤4. Use WolframAlpha to find the number of solutions when n = = 30. Find the exponential generating function for the number of permutations with repetition of length n of the set {a, b, c}, in which there are an odd number of a's, an odd number of b's, and an even number of c's. Use WolframAlpha to find the number of such permutations when n = 10. Find the generating function for the number of partitions of an integer into distinct even parts. Use Wolfram Alpha to find the number of partitions of 15 into distinct even parts.
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