Use the convolution theorem to determin 8 f(0) = (²+8²) (a² + b²) c¹[1()](t)=

Q: Using the Convolution Theorem, what is L[h(t)]?

A: In this question, we use the convolution theorem to find the Laplace transform of the given function…

Q: Consider the function f(x) = 8x³ - 6x² + 3x - 8. An antiderivative of f(x) is F(x) = Axª + Bx³ +…

A: We know that integration power rule is - Integration of xn is xn+1/n+1 +C. Here C is integration…

Q: Find f(t). f(t) + 1 7) M(²-[ u t-

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Q: Let f(x) = 5 – Vx² + 1 and g(x) = x -7. Then (f o g)( – 1) = %3D (fo g)(x) = || %3D

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Q: Prove F(x) = x 3 – 2x + 10 is an antiderivative of the function f(x)=x 2 – 2 %3D

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Q: Let f(x, y) = 5x + 9y, r(t) = (r³,1²). Use the Chain Rule to calculate f (r(t)) at the value t = -4.…

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Q: Abstract Algebra: Let p(x) = 2x3 −3x2 + 4x−5 and q(x) = 7x3 + 33x−4 in R[x], where R = Z/3Z.…

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Q: Consider the function f(x) = 8x³ - 2x² + 3x - 6. An antiderivative of f(x) is F(x) = Ax¹ + Bx³ + Cr²…

A: Integrate both side in equation and comparison to given equation

Q: r(0)=, find v(t) and r(t).

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Q: Compute the n x n determinants: X a a 8 a (a) a a a x ⠀⠀ : a a a ... ... 000 000 a X " (b) -t 0 1 -t…

A: As per our guidelines we are supposed to answer only first question, kindly repost other parts in…

Q: Consider the quadratic function f: R3 →R defined by f(X) = xỉ – x1x2 + x – x2x3 + x3 + 1 A: Express…

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Q: Let f(z) =z² – 40, g(z) = 3z – 5. Solve for z exactly: f9(=}) = 0

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Q: Show that V ar(aX + b) = a2V ar(X).  V ar(c) = 0 for any constant c.

A: Solution-:We want to show that.   Where, Var (c) =0  for any constant.

Q: Write f(z) = Im(z - f(z) = u(x, y) + iv(x, y). 3z) zRe(z²) - 5z in the form ○ a. (4y+x³ − xy²) +…

A: Step 1Step 2Step 3 : Step 4