Evaluate 11 F. dS, with F(x, y, z) = (x, y, z), and S the part...
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Evaluate 11₁₁ F. dS, with F(x, y, z) = (x, y, z), and S the part of the plane x+y+z=1 with x ≥ 0, y ≥0, and z≥ 0. Let v = (0, 0, z) be the velocity field (in meters per second) in R³. Compute the volume flow rate (in cubic meters per second) through the upper upper hemisphere (z ≥ 0) of the unit sphere x² + y² + z² = 1. Evaluate 11₁₁ F. dS, with F(x, y, z) = (x, y, z), and S the part of the plane x+y+z=1 with x ≥ 0, y ≥0, and z≥ 0. Let v = (0, 0, z) be the velocity field (in meters per second) in R³. Compute the volume flow rate (in cubic meters per second) through the upper upper hemisphere (z ≥ 0) of the unit sphere x² + y² + z² = 1.
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