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Multivariable & Vectorhard
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Find the zzz-coordinate of the center of mass zˉ\bar{z}zˉ of a solid hemisphere H={(x,y,z)∣x2+y2+z2≤R2,z≥0}H = \{(x,y,z) \mid x^2 + y^2 + z^2 \le R^2, z \ge 0\}H={(x,y,z)∣x2+y2+z2≤R2,z≥0} if its density ρ(x,y,z)\rho(x,y,z)ρ(x,y,z) is proportional to the distance from the origin.