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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 18T

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Question

(a) Find a vector parametric equation for the ellipse that lies on the plane 3x + 2y + z = -4 and inside the
cylinder x2 + y = 16.
r(u, v) = | <ucos(v),usin(v),-4+3ucos(v)-2usin(v)>
for 0 < u <4 and 0 < v < 2n .
(b) đA = 7, x7, = <0,0,0>
и
(0) dA = ||dA|| = .x r.|
u*(14)^(0.5)
u
(d) Set up and evaluate a double integral for the surface area of the ellipse.
Surface area =
16*pi*(14)^(0.5)

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