Minimize g = 4y1 + 4y2 subject to 70 2y1+3y2 2y1 + y2 ≥ 30 Y₁ ≥ 0, y2 ≥ 0 If no solutions exist enter DNE in all answerboxes. y1 = y2 = 9 || 0

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A: This is the problem of optimization.

Q: 1. Prove that for all positive integers n, n Σj2i = (n − 1)2n+¹ +2 j=1

A: To prove that,              ∑j=1nj2j=n-12n+1+2.

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Q: Consider the matrix A = 0 0 0 0 a = 4 -2 a a 8 a=-4 a € R\{-4,4} A is invertible for any a ER with a…

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Q: 8. Write an equivalent statement that does not use the if... then connective. Use the fact that p→q…

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Q: 4. (3x - y + 6) dx +(6x - 2y - 6) dy = 0 [l Answer: 7x + 14y + 18 ln (21x - 7y - 12) = C.

A: Solution of the differential equation by substitution method

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Q: Noah says, "I worked the problem from left to right and ended up with `20-45x`."

A: NO, I don't agree with Noah. His approach is incorrect.

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Q: 7. Find and classify the stationary points of (a) y = xe * (b) v = ln x - x

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Q: Find the general solution to y′′+ 16y= sec(4θ) using variation of parameters

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Q: 3. Find the general solution to y′′−4y′+ 4y= xe2x using the method of undetermined coefficients.

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Q: Minimize g = 5y1 + 3y2 subject to 4y1 + y2 ≥ 52 y1 + 4y2 88 Y₁ ≥ 0, y2 ≥ 0 If no solutions exist…

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Q: 4. Find the area of the triangle with the vertices: (1,2), (1,5), and (3,2).

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Q: D²y + 2Dy = 4x − 6e-²x -

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A: Demand function: D(p)=-3p+151 Elasticity of demand is given by E(p)=-[pD'(p)]/D(p)

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A: As both the question are different we shall solve one question only as per the company guidelines.…