Which of the following is a potential function f for F(x, y, z) = (2x cos(yz). -x²z sin(yz) + 2yz?, -x²y sin(yz) + 2y³z)? Select the correct answer below: O x cos(yz) + y²z O x² cos(yz) + y²z O x² cos(yz) + y²2² O-2x cos(yz) + y²z²

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A: GIVEN GRAPH equation of line passing through x1, y1 &amp; x2, y2 is f(x)=y1+y2-y1x2-x1(x-x1)

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A: Explanation of the answer is as follows

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Q: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices +1, tj clockwise.

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A: Please see the attachment

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A: From the above details we have,

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Q: Given the system of linear equations 1.2x2.3y + 0.24z = - -1.2x +0.2y + 3.0z = 7.40 3.4x + 0.5y +…

A: Given the system of linear equations: 1.2x-2.3y+0.24z=-3.02-1.2x+0.2y+3.0z=7.403.4x+0.5y+1.4z=-0.10…

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Q: 2. (a) (b) (c) Determine if the vectors are linearly independent. Justify your answer. and HNO 8…

A: We use definition of linearly independent vectors.

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Q: let X = {1,2,3} Then the collection M-EP₁ X₁ { ¹ }, {2,3}} is a algebra L o 2

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A: The parametric equation of the surface is given as follows: rr, θ=r cos θ, r sin θ, 4-r2, where…

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A: Note  Pivots are entries that are used to make zero just above and below rows .

Q: 3. Find the solution of the following system of liner inequalities by graphing: (K + 2y > 5x + 3y…

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A: Using crank Nicolson method to calculate the numerical solution for ∂U∂t=∂2U∂x2  , 0&lt;x&lt;6,…