Using Green’s Theorem, compute for the given path C. Assume C is closed and positive orientated. F = (-5x + 3y)i + (8x – 4y)j; C is the region bounded above by y = -4×2 + 32 and below by in the first quadrant

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.

True or False:If  the and , the appropriate decision is to REJECT the null hypothesis.

Find the triple scalar product (u x v) ∙ w of the given vectors.u = -5i – 3j + 4k; v = 5i – 3j + 8k; w = 9i – 5j – 4k

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

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) = (7 ln(9t))i + (8t3)j

Write the equation for the plane.The plane through the points P(-1, 7, -36) , Q(2, 6, -17) and R(1, -7, 30). 

Solve the problem.Write an iterated triple integral in the order for the volume of the tetrahedron cut from the first octant by the plane .

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