Let v = zk be the velocity field (in meters per second) of a fluid in R3. Calculate the flow rate (in cubic meters per second) through the upper hemisphere (z > 0) of the sphere x 2 + y2 + z2 = 1.

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A: Given that And x=3 and x=6. The density is 0.37.

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Q: Let v = zk be the velocity field (in meters per second) of a fluid in R3. Calculate the flow rate…

A: volume ( V)= 2/3pi r3 radius of sphere in vector form can be written as = x i^ + y j^ + z k^ so…

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Q: Use the Divergence Theorem to find the rate at which a fluid with flux F = through the cube formed…

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Q: Evaluate the line integral | 27x²yzds with respect to s along the curve C : x = t, y = t³, z = ; t(0…

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A: Given data:- Surface density is equal to 0.37 kg/unit2 y=xlnx-3xy=1 Bounded by, x=3 and x=6

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Q: A fluid with density 1,330 flows with velocity v = yi +j+ zk. Find the rate of flow upward through…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: Calculate the flux integral. ∫S(2i+zk )dA where S is z=x^2+y^2 with 0≤x≤1, 0≤y≤2 oriented upward.

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Q: Find the mass of a thin wire lyingalong the curve r(t) = √2t i + √2t j + (4 - t2)k, 0 ≤ t ≤ 1,if the…

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Q: „ Compute the flux of F = xi + yj + zk through the curved surface of the cylinder x? + y² = 1…

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Q: * Q. (41), p.305 : Find the volume of the solid generated of revolving V3 1 y V1 + x2 SxS V3 3 < x s…

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Q: Find the moment of mass from the x-axis for y = x In(x) – 3x and y density is equal to 0.37…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.