7. Let E be the ball of radius 1 centered at the point (0, 0, -1). (a) Show that E is given in Cartesian coordinates by the equation x² + y² + z² + 2z ≤ 0. (b) Write E is spherical coordinates. (c) Suppose the density on E is proportional to the distance to the origin, with the largest density being equal to 4. Use spherical coordinates to compute the mass and center of mass of E.

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