Consider the curve C shown in the accompanying figure, which is the intersection between surfaces S1 and S2, with S1: z = a2 - x2 and S2: x + y + z = a2 + a, for a> 1.The figure is in the first attached imageA parameterization of curve C is:The answers are in the second attached image z = a? – a?Ca +y+z = a² + a A) F(t) = tî+ (t² – t + a) ĵ+ (a² –t²) k, para 0

S1=a2-x2 S2: x+4+z=a2+a Let us start solving above equations

Answered: z = a? – a? C a +y+z = a² + a

Math

Advanced Math

z = a? – a? C a +y+z = a² + a

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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Question

Consider the curve C shown in the accompanying figure, which is the intersection between surfaces S1 and S2, with S1: z = a² - x² and S2: x + y + z = a² + a, for a> 1.

The figure is in the first attached image

A parameterization of curve C is:

The answers are in the second attached image

A) F(t) = tî+ (t² – t + a) ĵ+ (a² –t²) k, para 0<t <a
B) F(t) =tî+ (at – t + a) ĵ+ (a² – at) k, para 0<t<a
C) F(t) = t î+ (a² + a – t) ĵ+ (a² – t²) k, para 0<t< a
D) F(t) = tî+ (t² – t + a) ĵ+ (a² – t²) k, para 0<t < 2a

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