Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), (a)=x₂ using the following values. A = 5 -1 7-3 ,f(t) = 19e2t 25e2t x(0) = [:] 0 eAt 1 6 7e4t-e-2t - e4t +e-2t 7e4t-7e-2t - e4t + 7e-2t

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A: Given: A graph of a rational function: To Find: The equation of this function.

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Q: n² Determine whether the given series converges or diverges: n=27²4-8°

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Q: 11. Simplify completely: 12. 12. Simplify: √√√√√B¹² 2√3+√27

A:

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Q: 8. Write the equation of the graph below. (-3,9) (-2,5) (-1,3) -5-4-3-2 10 -9 -8 7 ·6 --5 4 3 2 -2…

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A:

Q: 13. One solution to the equation cos0 = 0.9848 is 0 = 10° . Determine another value of 0 to the…

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Q: d₁: [x,y,z]= [0,2,1]+t[3,1,1] And d₂: [x,y,z]= [1,-3,0]+[2,-1,1]

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Q: 13. Show that (a) (b) f x²s+¹e-ax² dx = x²se-ax² dx = s! 2as+1; (s — 1/1 ) ! 2a³+1/2

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Q: [36] Consider r"(t) = −5x(t)+3y(t), y'(t) = x(t) — 2y(t), x(0) = 2, x'(0) = 7, y(0) = −3. (a)…

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Q: For the DE y"+ 3xy' =0 from problem 2, Give the general solution to the DE.

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Q: Problem 34. A matrix A € Mnxn (R) is called orthogonal if AA = In. Prove that if A is orthogonal,…

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Q: 1. Prove (2p+1) = 2 (mod p) when p is any prime.

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Q: Suppose f: (0, ∞) → (0, ∞) is a continuous function, and g: (0, ∞0)→ (0, ∞) is defined by the…

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Q: 6. How many permutations of {0, 1, 2, 3, ..., n,} leave at least two numbers fixed?

A: How many permutations of {0, 1, 2, ...., n} , leaves at least two number fixed ?

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Q: . Write (13)(1245)(13) and (24)(13456)(24) in disjoint c form. Give a simple description of how each…

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Q: [15] (4) GIVEN: z = f(x, y): = x²y, where (x, y) is subject to the constraint: T: x² + xy + 7y² 27,…

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Q: ܠܐ ܐܘ _ {dA_D = {xy) | 0< x<40<y<x 1+ ܐܨ 7.

A:

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