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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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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