Suppose F(x, y, z) = (x, y, 5z). Let W be the solid bounded by the paraboloid z = x² + y² and the plane z = 25. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the flux of through S. JS = SS F.dÃ= = S (b) Find the flux of ♬ out the bottom of S (the truncated paraboloid) and the top of S (the disk). Flux out the bottom= Flux out the top =
Suppose F(x, y, z) = (x, y, 5z). Let W be the solid bounded by the paraboloid z = x² + y² and the plane z = 25. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the flux of through S. JS = SS F.dÃ= = S (b) Find the flux of ♬ out the bottom of S (the truncated paraboloid) and the top of S (the disk). Flux out the bottom= Flux out the top =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Suppose F(x, y, z) = (x, y, 5z). Let W be the solid bounded by the paraboloid z = x² + y² and the plane z = 25. Let S be the
closed boundary of W oriented outward.
(a) Use the divergence theorem to find the flux of through S.
JSF.
F.dĀ:
=
S
(b) Find the flux of ♬ out the bottom of S (the truncated paraboloid) and the top of S (the disk).
Flux out the bottom=
Flux out the top =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e87940a-4964-4b75-8957-b270f7cb8a14%2Ff44994a5-21af-4957-a8fc-3807b9239599%2Fp29e8i_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose F(x, y, z) = (x, y, 5z). Let W be the solid bounded by the paraboloid z = x² + y² and the plane z = 25. Let S be the
closed boundary of W oriented outward.
(a) Use the divergence theorem to find the flux of through S.
JSF.
F.dĀ:
=
S
(b) Find the flux of ♬ out the bottom of S (the truncated paraboloid) and the top of S (the disk).
Flux out the bottom=
Flux out the top =
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