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F(x, y) = (6yey — 9)i + 6xej (a) Show that F is a conservative vector field. fy - 9x = 9m (b) Find a potential function for F. $(x, y) = +K, where K is the constant of integration. (c) Find the work performed by the force field on a particle that moves along the sawtooth curve represented by the parametric equations 6 x = t + sin ¹(sin t), y = -sin-¹(sin t); (0 ≤ t ≤ 8π)

F(x, y) = (6yey — 9)i + 6xej (a) Show that F is a conservative vector field. fy - 9x = 9m (b) Find a potential function for F. $(x, y) = +K, where K is the constant of integration. (c) Find the work performed by the force field on a particle that moves along the sawtooth curve represented by the parametric equations 6 x = t + sin ¹(sin t), y = -sin-¹(sin t); (0 ≤ t ≤ 8π)

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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6 x = t + sin ¹(sin t), y = sin ¹(sin t); (0 ≤ t ≤ 8π) - ㅠ Y 3 x MAMA 0 10 15 20 -3 NOTE: Enter the exact answer. W =
Transcribed Image Text:6 x = t + sin ¹(sin t), y = sin ¹(sin t); (0 ≤ t ≤ 8π) - ㅠ Y 3 x MAMA 0 10 15 20 -3 NOTE: Enter the exact answer. W =
F(x, y) = (6yey — 9)i + 6xej (a) Show that F is a conservative vector field. fy - 9x = 9m (b) Find a potential function for F. $(x, y) = +K, where K is the constant of integration. (c) Find the work performed by the force field on a particle that moves along the sawtooth curve represented by the parametric equations 6 x = t + sin ¹(sin t), y = -sin-¹(sin t); (0 ≤ t ≤ 8π)
Transcribed Image Text:F(x, y) = (6yey — 9)i + 6xej (a) Show that F is a conservative vector field. fy - 9x = 9m (b) Find a potential function for F. $(x, y) = +K, where K is the constant of integration. (c) Find the work performed by the force field on a particle that moves along the sawtooth curve represented by the parametric equations 6 x = t + sin ¹(sin t), y = -sin-¹(sin t); (0 ≤ t ≤ 8π)
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