i. Suppose Q is a solid region bounded by the plane x + 2y + 3z = 6 and the coordinate planes with density o(x, y, z) = x²yz. Find the centre of mass. ii. Find the centre of mass of a solid of constant density bounded below by x² + y² = 4 in the plane z = 0 and above by the paraboloid z = 4-x² - y².
i. Suppose Q is a solid region bounded by the plane x + 2y + 3z = 6 and the coordinate planes with density o(x, y, z) = x²yz. Find the centre of mass. ii. Find the centre of mass of a solid of constant density bounded below by x² + y² = 4 in the plane z = 0 and above by the paraboloid z = 4-x² - y².
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Transcribed Image Text:i. Suppose Q is a solid region bounded by the plane x + 2y + 3z = 6 and the
coordinate planes with density o(x, y, z) = x²yz. Find the centre of mass.
ii. Find the centre of mass of a solid of constant density bounded below by x² + y² = 4
in the plane z = 0 and above by the paraboloid z = 4-x² - y².
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