Use the Divergence Theorem to find the flux of F(x, y, z) = 3x³i + 3x²yj + 24xyk across the surface of the solid bounded by z = 4 – x², y + z = 5, 0, and y = 0 with outward orientation. NOTE: Enter the exact answer. Φ =

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A: For the solution of the problem follow the next steps.

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A: We have to find the slope of surface z=xy2  in x direction and y direction at point (2,3).

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Q: 5. Consider a one-dimensional control system given by that minimizes zu, with r(0) = 1. Find a…

A: The solution is given below

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Q: [y²e + √elnx dy-(xy) sin² ( * O) + (---) (-) sin² tan² ,dx ey+Inx dy y(In2x-lny) -ex. dx = 0

A: We can solve this using substitution method of ordinary differential equation

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A: To determine the optimizing function.

Q: Let S₁ be the surface generated by z = √/1-(y-1)2 revolved about the y-axis. Let S₂: y = r²+2.…

A: Consider the surface S1 that is generated by x=1-y-12 revolved about the y-axis. Use Desmos graphing…

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A: To find the dimensions of the box that minimizes the cost.

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Q: Q: Let T: R² → R² be given by T(x, y) = (x, −y). Then show that T is a linear operator.

A: Solution

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Q: We have the following. f(x, y, z) = 8(x² + y²) z-2-x²-y² E x² + y²=1 (a) Express the triple integral…

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Q: Consider the matrices 1 -2 7 and B = -1 A = 2 -4 8 4 -2 2 -1 2 1 a. Which of the following vectors…

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Q: A penny collection contains twelve 1967 pennies, seven 1968 pennies, and eleven 1971 pennies. If you…

A: Given  A penny collection contains twelve 1967 pennies, seven 1968 pennies, and eleven 1971 pennies.…

Q: QUESTION 3 The matrix below is the a row echelon form of the matrix associated to the linear…

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Q: w + 2x -y +z = 6 -w+x+2y-z = 3 2w-x + 2y + 2z = 14 w+x-y + 2z = 8

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Q: Now, solve the following problems involving radiation: 2. A man has been exposed to 1 mGy each of…

A: Please check the next step for details

Q: In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial…

A: Q5 asked and answered.

Q: Which of the following is an accurate description of the following parametric equations? x = a sect…

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Q: Given Proposition (~Av B)~(AB) Given Truth Values A B Main Column: Based on the column beneath the…

A: Solution:

Q: f5 4 18-21. The production function for making widgets is P(x, y) = 4,600x3/8y5/8 Where p is the…

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Q: a. Use diagonalization to solve for D¹0 if D: = 2]. 1 2 11

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Q: :-Solve the following equations (choose tow only):- 1: x²y=- 2xy + 2y = 2x³ ex

A: Solution of the cauchy Euler's differential equation

Q: 1. Provide an example of two sets A and B such that A ‡ B and both AU B and An B are countable. j.…

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Q: of determinants with respect to operations -4 3 0 0 6 1 2 70 -3 -2 1 1 -4 0 2/ Use the properties…

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Q: Use Stokes' Theorem to find the value of the line integral of the vector field Faround the curve…

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Q: Let A = PDP-1 and P and D as shown below. Compute A4. 1 - 2 0 --*| P= D= 4 - 2 5 01 A² = | А…

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Q: i. Prove that all positive integers n ≥ 4, n²> 3n+3. ii. Proof: Base case: n ≥ 4. 4² = 16 >3(4) + 3…

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