VI. Find the mass of a surface S, with parametrization R(u, v) = (e" sin v, e" cos v, 2e"), for Ju < 1, Jv| < n, given that the density at every point (r, y, z) in S is equal to 6z.

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Q: VIII. C ) Find the mass of the surface S, with density function 6(x, y, z) = 3r, parametrized by…

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Q: 7. Let F be the fluid force on a side of a semicircular plate of radius r meters, submerged…

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Q: 3. A curved lamina is in the shape of the surface defined by R(u, v) = (u cos v, u + v, u sin v),…

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Q: 1. Consider the spiral ramp r(u, v) = ( u cos v, u sin v, v ) with 0 < u < 3 and 0<v < 2n. Use a…

A: Consider the given information.

Q: Find the mass of a surface S, with parametrization R(u, v) = (e" sin v, e" cos v,2e"), for |u| <…

A: Here is the solution of the given problem:

Q: b) Given F(x, y, z) = (x³ + cosh z) i+(2y³ – 3x²y) j – (x² + 4y²z) k. Use Gauss's theorem to…

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Q: Let S be the surface defined by the vector function R(u, v) = (e", eº, u² + v²), u = [0,2], v € [−1,…

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Q: 2. Calculate the centroid of the thin plate R which bounded by r = 1, y = 0 and, 2² + y² = 4.

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