Use the method of Laplace transforms, as presented in the lectures, to solve the IVP: y" – 6y' + 12y = 0, y(0) = 4, y'(0) = −6

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A: a) So,  E[V]=0 and Var[V]=415​.  b) Therefore, ∫13​Ws4​dWs​=∫13​4Ws3​dWs​+∫13​6Ws2​ds  The first…

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Q: Need help with these two Intro to Elementary Number Theory Homework Problems.

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Q: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R}…

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A: Step 1: Given:P(E1​)=P(E3​)=P(E5​)=p(say)P(E2​)=P(E4​)=2P(E1​)=2pStep 2: (a)…

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A: Solution are fully explained in below steps Explanation:

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Q: vi. f(x) = centred at x = 0, of order 4

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A: (a) Converges(b) Converges© Converges(d) Inconclusive(e) Converges to e.Explanation:Step 1: Step 2:…

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Q: Find f (t) = L¯¹{F(s)}. a. F(s): = b. F(s): = $3 Se-πs s²+9 c. F(s): 5e-3s = s²(s+5) d. F(s): 2s-1 =…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: 7. Solve the heat equation on the interval (0 ≤ x ≤ 1): Ut = 4uxx u(x, 0) = 1 ur(0,t) = u(1,t) = 0

A: 7) Given PDE is the following :We solve it using Separation of Variables method ,Let,  by…

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Q: 4. For each of the following matrices A Є Mnxn (F), (i) Determine all the eigenvalues of A. (ii) For…

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Q: (b) A = 2 -1 0-2 212 -3 -1 for FR 2 сл 5

A: As asked we shall solve only question 4 part b only. We shall solve only 4(b)

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Q: Use strong induction to show that every positive integer n can be written as a sum of distinct…

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Q: Find the solution y" + 10y' + 125y = y(0) = e y' (0) = 2e 0

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Q: 3. (error) For what values of x can you use sin x ≈ x- with an error less than 5 × 10-4?

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Q: show all th work with correct ans

A: The answer has been provided.Explanation:

Q: 1 8. Let the integral I = = [ f(x) dx = 0 So COS (72) dx be evaluated using the Monte-Carlo method.…

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A: Dear Student  As per our guidelines we can answer only first question.  So kindly resubmit the…

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Q: A DT system is described by the difference equation y[n] + 1/2 y[n - 1] - 1/2 y[n - 2] = x[n] - x[n…

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A: The fibonacci number is defined as 1 , 1 , 2 , 3 , 5 ,8 , 13 , ........ i.e. the next term is the…