Section 12.7 (Homework)Ali Al ZaabiMA 242, section 001, Spring 2012Instructor: J. Louis CappsCurrent Score : 22 / 22 Due : Thursday, April 19 2012 11:03 PM EDT1. 3/3 points | Previous AnswersEvaluate the iterated integral.163840 1.64e+052. 3/3 points | Previous AnswersEvaluate the triple integral where E = {(x, y, z) | 0 x 1, 0 y x, x z 2x}.0.126 0.1263. 3/3 points | Previous AnswersEvaluate the triple integral where E is the solid tetrahedron with vertices (0, 0, 0), (0, 1, 0), (1, 1, 0), and (0, 1, 1).1/120 0.008334. 3/3 points | Previous AnswersUse a triple integral to find the volume of the given solid.The solid bounded by the elliptic cylinder 4x2+ z2= 4 and the planes y = 0 and y = z + 2 12.6 12.6WebAssignThe due date for this assignment is past. Your work can be viewed below, but no changes can be made.5. 2/2 points | Previous AnswersFind five other iterated integrals that are equal to the given iterated integral. (Select the five that apply.)6. 4/4 points | Previous AnswersFind the mass and center of mass of the given solid E with the given density function ρ.E is the tetrahedron bounded by the planes x = 0, y = 0, z = 0, x + y + z = 1; ρ(x,y,z) = yMass0.0417 0.0417Center of mass( 0.2 0.2 , 0.4 0.4 ,0.2 0.2 )7. 4/4 points | Previous AnswersSuppose X, Y, and Z are random variables with joint density function f(x, y, z) = Ce-(0.5x+0.2y+0.1z)if x 0, y 0, z 0, and f(x, y, z) = 0 otherwise.(a) Find the value of the constant C.0.01 0.01(b) Find P(X 1, Y 1).0.0713 0.0713(c) Find P(X 1, Y 1, Z 1). 0.00679
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