Use a parameterization to find the fluxplanes x = 0, x= 1, and z = 0.The flux isSSF.F•n do of F=z²i + xj - 4zk in the outward direction (normal away from the x-axis) across the surface cut from the parabolic cylinder z = 9 - y² by theS

A parabolic cylinder z =9-y2 by the planes x=0, x=1, and z=0

Answered: Use a parameterization to find the flux…

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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7. Let F(x, y,z)=-2yi +2xj. Use Stokes' Theorem to find F-dr where C is a circle (a) Parallel to the yz-plane, of radius a, centered at a point on the x-axis, with either orientation. (b) Parallel to the xy-plane, of radius a, centered at a point on the z-axis, oriented counterclockwise as viewed from a point on the z-axis above the circle.
b) F(x,y) represents a velocity field of a fluid over a surface S defined by z = 6-3x-2y. If the magnitude of the velocity in the direction of the unit normal vector, n, on S is 32/√14, compute the flux of F(x,y) over the surface S in the first octant oriented upward, using the projection of S on the xy-plane.
+25y²,0, 10- through the surface 3 Find the outward flux of F = =1.
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Consider the curve C with parametrisation where t E R. r(t) = = cos(5t) cosh(t) i+ sin(5t) cosh(t) -j+tanh(t)k, (a) Show that C lies on the surface of the sphere described by the equation x² + y² + z² = 1. (b) Find the vector equation of the line L that is tangent to C at the point r(0).
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Use a parameterization to find the flux ・SSF•ndo Fondo of F=z²i+xj-4zk in the outward direction (normal away from the x-axis) across the surface cut from the parabolic cylinder z=9-y² by the S planes x=0, x= 1, and z=0.