Solve the equation Ut u(0, t) u(4, t) u(x, 0) - = 2urr 3 -5 = 2

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A: Solution:Now find the outward flux using the divergence theorem.

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Q: Compute using polar coordinates: 1/2 VT-x² Ty√T² + y² dydr. 1.

A: Given IntegralUsing polar coordinates, then And

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Q: The number 42 has the prime factorization 2. 3. 7. Thus, 42 can be written in four ways as a product…

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Q: " [SC₂² [¹ 1 s(s-3)

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Q: f(x) 2. If ƒ(4) = 0, ƒ(-2) = 0, g(4) = 0 and g(5) = 0,then what are the zero(s) of the function y =…

A: We know, the rational functions of the form f(x)/g(x) will define on a domain D whenever..

Q: 2. Find all the values of the constants a and b such that U(x, t) = eaz+bt satisfies the heat…

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Q: Solve the inequality x²-x-2 > 0 O a. x 1 O b. x 2 O c. -1 < x < 2

A: Given inequation

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Q: For which values of x is x²-x-6>5* + 2? a. {x -2.4} c. {x<2.4}

A: To solve for x for the inequationAssume

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Q: Problem 7 Let A = be a 2 x 2-matrix such that det(A) = 0. a) Show that there is a non-zero vector u…

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Q: For a 4×4 matrix whose top three rows are arbitrary and whose bottom row is (0, 0, 0, 1), show that…

A: Suppose our matrix is

Q: 11. If f(x) = 3 and g(x) = x³ + 4, what is y = g(x) − f (x) for x = -2? x

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A: Let, in a particular city represent that day weather .Also let , According to given informations,

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Q: 11) Let f: IR4 → IR³ be defined by : IV f(x₁y₁z₁t) = (2x+y-t, x+8y-92- 2t, x-2y + 3z) (a) show that…

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Q: 2. Determine an inverse Laplace transform. a) I¹ -4s e 2s² +10

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Q: Let ℝ [x]≤ 2 ---> ℝ be a linear transformation such that T(x2)= -3, T(x2+x)=-4, T(x+1)=-1 What is…

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Q: 3) Find the inverse Laplace t 1 {{}}}}}

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Q: Solve the inequality x2 - x - 2 > 0

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Q: (d) Find the net change in position and the total distance traveled in the time interval 0 ≤ t ≤ 6.…

A: Suppose a particle is traveling on a one-dimensional track with a velocity feet per second for .We…

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Q: 3) Use system of equations to work these applied problems. Euro and Pounds: Abigail Henderson has…

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Q: Use the Laplace transform to solve the given initial-value problem. y' + 3y = e4t, y(0) = 2 y(t) =

A: Given initial value problem isWe know that

Q: 1. The graph of y = f(x) = g(x) is shown. Determine the approximate solution to the inequality f(x)…

A: The graph of y = f(x) - g(x) is shown. Determine the approximate solution to the inequality f(x) ≤…

Q: in total? Name: Olivia is making a fruit salad for the entire school. She uses _____blueberries and…

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Q: Find the moment of inertia about the x axis of a plate of constant density o = 1 limited by the…

A: Note: As per the Q&amp;A guidelines, we are supposed to answer only the first question because this…

Q: 4. For any integer n, show that if n³ = 1 (mod 47), then n = 1 (mod 47).

A: To show that if n3≡1(mod47), then n≡1(mod47), it can use proof by contradiction.Assume that…

Q: Prove that the matrix A = product of elementary matrices. 2 1 1 10 0-10 3 1 0 1 -1 is invertible and…

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Q: 3. a) b) For the sequence of functions Find its pointwise limit fn (2) for x = [0, 1]. Justify your…

A: Since you have posted a question with sub-parts greater than three. We will provide the solution…

Q: 2. Let a 0 be such that a+h≤b. Prove that there is € (0,1 such that: 1 f(a+h)-f(x) h = f'(x + 0h)…

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Q: 3. Iff= {(-7, 1), (-5, 8), (3, 11), (5, -1)} and g = {(-6, 4), (-5, 3), (-1, 7), (5,5)}, what is f +…

A: Given that, f={(-7, 1), (-5, 8), (3, 11), (5, -1)} and g={(-6, 4), (-5, 3), (-1, 7), (5, 5)}

Q: 1. Determine the Laplace transform. a) L[tsin(2t)]

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Q: 5. The number of deer in a forest as a function of the number of weeks that have passed can be…

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Q: please could you use Ts and Fs cause i wasnt taught the 0s and 1s format

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Q: dz dt dw dt = = 3ezw + 8 sin(z) = cos(82)

A: We have given system of differential equationsLet, Jacobian matrix is given by

Q: A 1 6 -3 -5 a) The eigenvalues of A are and

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Q: Find the general solution of the given system. dx dt dy dt = x+y-z = бу =y-z (x(t), y(t), z(t)) =

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Q: Find the vector X (in standard coordinates) determined by the given coordinate vector [X] and the…

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Q: The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the…

A: Given system of differential equations:x1′=9x1+3x2+6x3x2′=3x1+12x2+3x3x3′=6x1+3x2+9x3Let X=[x1x2x3]…