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 Oct 27, 2023
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A particle's position in the plane t seconds after it starts moving is

x = 6 cos kt

y = 6 sin kt

for some constant k.  If the particle moves a distance of 120 pi for every second, then what is k?

 

 

The distance traveled by the particle in t seconds is given by the perimeter of the ellipse it traces out. The semi-major and semi-minor axes of the ellipse are 6 and 6, respectively, so the distance traveled is 2π⋅6⋅6=72π.

Since the distance traveled is 120 pi for every second, we have k⋅72π=120π. Solving for k, we find k=35​​.

 Dec 12, 2023

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