47. a) Find the mass of a wire represented by the part of the parabola x = y², -1 ≤ y ≤ 1, if the density is 8(x, y)= x. Set-up an expression for the y-coordinate of the center of mass. b) Evaluate Je √x²+ y² ds where C is the curve with parametric equations x = 4 cos(t), y = 4 sin(t), z = 3t, and 0 ≤ t ≤ 27.
47. a) Find the mass of a wire represented by the part of the parabola x = y², -1 ≤ y ≤ 1, if the density is 8(x, y)= x. Set-up an expression for the y-coordinate of the center of mass. b) Evaluate Je √x²+ y² ds where C is the curve with parametric equations x = 4 cos(t), y = 4 sin(t), z = 3t, and 0 ≤ t ≤ 27.
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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47. a) Find the mass of a wire represented by the part of the parabola x = y², −1 ≤ y ≤ 1, if the density is 8(x, y) = x. Set-up an expression for
the y-coordinate of the center of mass.
b) Evaluate Ic x² + y² ds where C is the curve with parametric equations x = 4 cos(t), y = 4 sin(t), z = 3t, and 0 ≤ t ≤ 2π.
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