Let D be the solid tetrahedron in the first octant bounded by the coor- dinate planes together with the plane x + y + z = 1. (The vertices of D are at (0,0, 0), (1,0,0), (0, 1,0), (0,0, 1), so to draw...

Extracted text: Let D be the solid tetrahedron in the first octant bounded by the coor- dinate planes together with the plane x + y + z = 1. (The vertices of D are at (0,0, 0), (1,0,0), (0, 1,0), (0,0, 1), so to draw D, you can simply connect each of these vertices to every other. You should see a figure with four triangular sides.) Assuming that D has uniform density, find its center of mass (T, J, z). Hint #1: since D is symmetric in x,y, z, we must have I = y = z, so you only need to compute one of these. Hint #2: this tetrahedron has base 1/2 and height 1, so its volume is (1/3) x base x height = 1/6.