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Problem 15 Consider the surfaces z = x² + y² and y = x. (a) Describe two surfaces. (b) Describe the curve generated by the intersection of the two surfaces.

Problem 15 Consider the surfaces z = x² + y² and y = x. (a) Describe two surfaces. (b) Describe the curve generated by the intersection of the two surfaces.

Advanced Engineering Mathematics
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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Only a, and b
Problem 15 Consider the surfaces z = x² + y² and y = x. (a) Describe two surfaces. (b) Describe the curve generated by the intersection of the two surfaces. (c) Using x = t, find the parametric representation of the intersection curve found in (b). (d) Find the unit tangent vector T at t = 0. (e) Find the tangential component of acceleration at at t = 0. (f) Find the normal component of acceleration an at t = 0. (g) Find the curvature at t = 0. (1,1,0). Ans: (c) (t, t, 2t²); (d) (2); (e) 0; (f) 4; (g) 2
Transcribed Image Text:Problem 15 Consider the surfaces z = x² + y² and y = x. (a) Describe two surfaces. (b) Describe the curve generated by the intersection of the two surfaces. (c) Using x = t, find the parametric representation of the intersection curve found in (b). (d) Find the unit tangent vector T at t = 0. (e) Find the tangential component of acceleration at at t = 0. (f) Find the normal component of acceleration an at t = 0. (g) Find the curvature at t = 0. (1,1,0). Ans: (c) (t, t, 2t²); (d) (2); (e) 0; (f) 4; (g) 2
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