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 .

Evaluate the line integral along the curve C.ds, C is the curve r(t) = (4 sin t)i + (4 cos t)j + 12tk, 2 ≤ t ≤ 4

Provide an appropriate answer.Find when u = -5 and v = -7 if w(x, y, z) = , x = , y = u + v, and z =

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 .

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