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 .

Find the triple scalar product (u x v) ∙ w of the given vectors.u = -5i – 3j + 4k; v = 5i – 3j + 6k; w = 10i – 6j – 5k

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

Identify each given point of the function as a local maximum, local minimum, or saddle point. (-5, -4) [minmaxsaddle1]   (-5, 4) [minmaxsaddle2]   (5, -4) [minmaxsaddle3]   (5, 4) [minmaxsaddle4]  

Find the length of the curve with the given vector equation.r(t) = 3ti + j + k; -9≤ t ≤ -6

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.