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Using Green’s Theorem, compute for the given path C. Assume C is closed and positive orientated. F = (9x + 2y)i + (8x – 6y)j; C is the region bounded above by y = -3×2 + 96 and below by in the first quadrant

Find the potential function f for the field F.F(x,y,z) = 5i + -ezj – yezk

Find the requested partial derivative of the given function. f(x, y) = x ln (y – x) Find

Find the length of the curve with the given vector equation.r(t) = 3ti + j + k; 2≤ t ≤ 7

Test the vector field F to determine if it is conservative.F = i + j – k

Solve the problem.A 450-lb sign is hanging from the end of a hinged boom, supported by a cable inclined at 48° with the horizontal. Find the tension in the cable and the compression in the boom rounded to the nearest pound.

Find the unit tangent vector of the given curve.r(t) = 3t2i – 12t2j + 4t2k

Bonus: What is the halo effect? In what circumstances is it used? What does it tell healthcare professionals? 

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.Find the acceleration vector.r(t) = (4 ln(2t))i + (3t3)j

Using Green’s Theorem, compute for the given path C. Assume C is closed and positive orientated. F = (4x + 9y)i + (2x – 9y)j; C is the region bounded above by y = -2×2 + 54 and below by in the first quadrant