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

Solve the problem. Unless stated otherwise, assume that the projectile flight is ideal, that the launch angle is measured from the horizontal, and that the projectile is launched from the origin over a horizontal surfaceA projectile is fired at a speed of 1160 m/sec at an angle of 36°. How long will it take to get 29 km downrange? Round your answer to the nearest whole number.