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Gandalf the wizard was walking down the street when a violent wind blew off his hatl His hat is the surface S pictured below, and has parametrization 7 (u, v) = ((1 – u'/3) cos(v) – 4u², (1 – u'/3) sin(v), 5u) where 0

Gandalf the wizard was walking down the street when a violent wind blew off his hatl His hat is the surface S pictured below, and has parametrization 7 (u, v) = ((1 – u'/3) cos(v) – 4u², (1 – u'/3) sin(v), 5u) where 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 20T
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Gandalf the wizard was walking down the street when a violent wind blew off his hat! His hat is the surface S pictured below, and has parametrization 7 (u, v) = ((1 – u'/3) cos(v) – 4u², (1 – u'/³) sin(v), 5u) where 0 <u<1 and 0 <v < 27. The hat is oriented so that the normal vectors point outward. If the vector field F with F = (2 sin(z?) + x, x cos () + y,ysin(e *")), is such that curl(F) describes the wind velocity, find the flux of the wind through Gandalf's hat. That is, find curl(F) - ds. dS. z V Hint: Look at the grid curves of the hat to help determine the boundary. You can also try plotting in math3d!
Transcribed Image Text:Gandalf the wizard was walking down the street when a violent wind blew off his hat! His hat is the surface S pictured below, and has parametrization 7 (u, v) = ((1 – u'/3) cos(v) – 4u², (1 – u'/³) sin(v), 5u) where 0 <u<1 and 0 <v < 27. The hat is oriented so that the normal vectors point outward. If the vector field F with F = (2 sin(z?) + x, x cos () + y,ysin(e *")), is such that curl(F) describes the wind velocity, find the flux of the wind through Gandalf's hat. That is, find curl(F) - ds. dS. z V Hint: Look at the grid curves of the hat to help determine the boundary. You can also try plotting in math3d!
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