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) = (8 ln(3t))i + (4t3)j

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 potential function f for the field F.F(x,y,z) = 9i + -ezj – yezk

Suppose you are the parent of a small child who is crying and pulling on their ear. Consider the null and alternative hypotheses for this situation:Ho: The child is healthyHa: The child has an ear infectionYou have a decision to make: Take the child to the doctor (you believe the alternative hypothesis) or wait it out (you believe the null hypothesis). If you make a Type II error, what happened?

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

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

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

Give a geometric description of the set of points whose coordinates satisfy the given conditions. x2 + y2 + z2 ≤ 64