Let there be set of a, b, c. Prove A×(B∩C) = (A∩B)×(B∩C)

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Q: 1. Using the definition of Laplace transforms, prove that L {sin(t) = 95² +4} a.

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Q: 22 J 2x2 winx(0) 2 and ₂(0) = -2. (e) x₁ = -6x₁ +9x2 - 4x3, x2 = -6x₁+11x2 - 6x3, x3 = -10x1 +21x2 -…

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A: We solve this by first operating multiplication then subtraction and then we combine like terms.

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A: We eliminate the parameters.

Q: a) Solve y" -6y' +9y=0. b) Find the particular solution of y"-6y' +9y=3-t c) Use the Laplace…

A: THE SOLUTION IS GIVEN BE

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Q: Let A = {x ∈ R| x≠0}, and then define f: A->R by:           f(x) = 6x+10/2x         is f…

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Q: Find the Inverse Laplace Transform. 14s² +70s +134 (2s +1)(s² + 6s +13)

A: Find the Inverse Laplace transformation

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Q: If f(x, y) = 3x² + 4y², find the curve through which the function increases most rapidly.

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Q: 10. Show that among 7 randomly chosen integers, there must be 2 whose difference is divisible by 6.

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Q: Find a function f such that F(x, y, z) = evaluate F. dr along the curve C given by r(t) = (t² +1,2…

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Q: Solve the equation subject to the given conditions. d'y dy dx² dx -6y-0, y(0)-2, y'(0)-4

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Q: Hello, can you please answer the following problem and show all your work. Thank you.

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Q: 1. Show that Led edx + (xe" + sinz)dy + ycoszdz is independent of the path and evaluate the integral…

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A: yt=4cost-7t-43 The domain is -2≤t≤3 Step length h=0.001

Q: Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 1 1 1 2√2 + 3√3+ 4√4…

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Q: Consider the vectors = ,= , and 11 19 w = . What value of k will cause the set {u, v, w} to be…

A: three vectors u→,v→,w→ will be linearly dependent when for some non zero constant a,b,c…

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Q: Let W be the set of all 3 x 3 matrices of the Го X 0 form y 0 X 0 0 I where y < 0. Then: Select one:…

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Q: 9. Second order ODE a) Consider the following nonhomogeneous ODEs, find their homogeneous solution,…

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Q: Explain in your own words wh equations. 2 3 6 1 2 3 0.000 1 0

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