What is coefficient of x31y4 in the expansion of ((x + y)8 + y)7 ???
please help with discrete math HW. please write clearly and dont make up an answer.............i will rate for the best answer thank you.

What is coefficient of x31y4 in the expansion of ((x + y)8 + y)7 ??? please help...
please help with discrete math HW. please write clearly and dont
make up an answer.............i will rate for the best answer thank
you. will appreciate if you can answer all 5 parts.
(L,) complete lattice and f L >L an order-preserving function (i) Let a, bE L with a b. Define a, b]= {z € L | a b} Show that (a, b], 3) is a complete lattice (ii) Consider X = {x € L \ f(x) = x}. The...
need help with discrete math HW, please write solutions clearly,
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Let G be the set of 4 x 4 invertible real matrices and let - be matrix...
This is Math Differential Equation. Please Show Your Full Work.
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8. (7 pts) Solve y"-10'+25y Se In x by variation of parameters.
8. (7 pts) Solve y"-10'+25y Se In x by variation of parameters.
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8) [8] Given: E is the solid that lies below z = Vx² + y2 and inside x² + y2 + z2 = 5z. First describe what each surface represents, and sketch the solid. Then SET UP a triple integral using spherical coordinates to describe the volume of the solid. Explain clearly how you found the bounds for the spherical coordinates. DO NOT evaluate the integral.
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Detween twO strips: Let X~Gamma(a, A), where a, A > 0. Find E(X), and Var(X) 7 Let X, Y, Z be discrete random variables, a, b E R. Assuming all the 8
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Let A and be B be sets and let f:A B be a function. Define C Ax A by r~y if and only if f(x)f(y). Prove thatis an equivalence relation on A. Let X be the set of~-equivalence classes of A. L.e. Define g : X->B by g(x) Prove that g is a function. Prove that g is injective. Since g...
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(i) Prove that every complete lattice has a unique maximal element. (ii) Give an example of an infinite chain complete poset with no unique maximal 1 element (iii) Prove that any closed interval on R ([a, b) with the usual order (<) is a complete lattice (you may assume the properties of R that you assume in Calculus class) (iv) Say that...
The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make sure you derive expressions for the cdf in the regions • x < 0 or y < 0; • 0 ≤ x ≤ 1, 0 ≤ y ≤ 1; • x > 1, 0 ≤ y ≤...
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5) [8] Evaluate ds , where C is the curve y=-x4 1<x<2. 7 X
This is a question for Advanced Linear Algebra. Please answer
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(5) §5.11. Suppose X,y are subspaces of an inner-product space V. Show directly (do not use the fact (X1)1x) that (XnX+
(5) §5.11. Suppose X,y are subspaces...