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Which of the following sets of parametric equations is for the surface obtained by rotating th curve x = 1 10+z² about the z-= Note: Parametric surfaces can depend on any two variables, c have to be just on u and v.

Which of the following sets of parametric equations is for the surface obtained by rotating th curve x = 1 10+z² about the z-= Note: Parametric surfaces can depend on any two variables, c have to be just on u and v.

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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Which of the following sets of parametric equations is for the surface obtained by rotating the curve x = 1 10+z² about the z-axis? Note: Parametric surfaces can depend on any two variables, doesn't have to be just on u and v . sin u 10+v² v ER and 0 < u < 2π. X - x = v, Y 9 - Y cos z = 10+v² v ER and 0 ≤ 0 < 2π. 9 22 = sin v X = 10+u² VER and 0 <u≤ 2π. Y Y COS u 10+v² = 29 = sin X = cos 10+z² 10+z² z ER and 0 ≤ 0 < 2π COS V 10+u² 22 9 2 = u for sin 10+v² for 2 = v for 2 = 2 for None of the given choices
Transcribed Image Text:Which of the following sets of parametric equations is for the surface obtained by rotating the curve x = 1 10+z² about the z-axis? Note: Parametric surfaces can depend on any two variables, doesn't have to be just on u and v . sin u 10+v² v ER and 0 < u < 2π. X - x = v, Y 9 - Y cos z = 10+v² v ER and 0 ≤ 0 < 2π. 9 22 = sin v X = 10+u² VER and 0 <u≤ 2π. Y Y COS u 10+v² = 29 = sin X = cos 10+z² 10+z² z ER and 0 ≤ 0 < 2π COS V 10+u² 22 9 2 = u for sin 10+v² for 2 = v for 2 = 2 for None of the given choices
Given a lamina in the shape of the region in the first quadrant bounded by the circle x² + y² = a² and the coordinate axes. The area density varies as the sum of the distances from the two straight edges. Which represents the moment of mass with respect to the ï axis of the entire lamina? k fő fo k få f /a²-x² a²-x² a²-x² a²-x² (xy + y²) dx dy k fő fo None of the given choices a k få ſva² (x² + xy) dx dy (xy + y²) dy dx (x² + yx) dy dx
Transcribed Image Text:Given a lamina in the shape of the region in the first quadrant bounded by the circle x² + y² = a² and the coordinate axes. The area density varies as the sum of the distances from the two straight edges. Which represents the moment of mass with respect to the ï axis of the entire lamina? k fő fo k få f /a²-x² a²-x² a²-x² a²-x² (xy + y²) dx dy k fő fo None of the given choices a k få ſva² (x² + xy) dx dy (xy + y²) dy dx (x² + yx) dy dx
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