Question

Let W be the sold prism shown below (not drawn to scale). This prism has sides on the three coordinate planes with 0 sxs 8, 0sys 11, and 0szs 24. (a) When setting up a triple integral to find the volume of the solid, what is the shape of the "shadow" f we integrate in the order dy dz de -Select- (b) What is the equation of the diagonal plane that forms the slanted surface? and x, y, and z are all measured (e) Suppose the density at a point (x.y.r) is proportional to the cube of the distance of the point from the origin. Assume density is measured in kg/cm p(x, y. ) For instructor's notes only, Do not write in the box below. Submit Answer Seve Progress

Answer 1

selid pism Given W u Also oSy <, osz 24 itegate in the erder dy dz dr, uoll be we (0,0,2) taking pris m ún the x-plane{dzd) the ue jection t the (8,0,0) Solid Pus m W So the shadou usill be btained x-plana inthe doraus the fhom tune oolid pis, shadow in x-plane twe Co, 24) Shadou of solid pism W n x-plane shan order dydzdx we

b from ne eW. dagenal plane thatforms pases only teugh (,0,0) and 2-axis at (o,0,24) and that the we the slanted -axis at asis Euation thisplane not fhe 1. - 24 24 3 + Z = point (x.yz) (0,0,0) ditance of c a Clarly aingin the d x-oy-0) (2-0)= ty+ and cube et thi distance d' 3 (xy 3 iven that dlendity pl.y) We ane Propertional to d So, p.y,z) d3

ehere k peportionay constant pory.)=kd take R-, then 3/2 xy2)