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Evaluate the line integral along the curve C.ds, C is the curve r(t) = (9 sin t)i + (9 cos t)j + 5tk, 2 ≤ t ≤ 4

Use the probability distribution from number 13 for this problem. Suppose you roll this weighted die twice. The outcomes of a 4 on the first roll and a 6 on the second roll are considered:

Write the equation for the plane.The plane through the points P(-1, 7, -44) , Q(2, -3, 20) and R(1, -1, 4). 

Find the triple scalar product (u x v) ∙ w of the given vectors.u = -5i – 3j + 4k; v = 6i – 2j + 3k; w = 9i – 3j – 6k

Solve the problem.A 150-lb sign is hanging from the end of a hinged boom, supported by a cable inclined at 36° with the horizontal. Find the tension in the cable and the compression in the boom rounded to the nearest pound.

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