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 .

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

During what age range is brain growth the fastest? At what age does the brain finish pruning the prefrontal cortex? 

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.

Evaluate the line integral along the curve C.ds, C is the curve r(t) = (6 sin 2t)i + (6 cos 2t)j + 5tk, 2 ≤ t ≤ 4

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

Evaluate the line integral along the curve C.ds, C is the curve r(t) = (6 sin 2t)i + (6 cos 2t)j + 5tk, 2 ≤ t ≤ 4

Match the following terms with the descriptions. 

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.

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