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A particle's position in the plane \(t\) seconds after it starts moving is \(\begin{align*} x &= 6\cos(kt),\\ y &= 6\sin(kt), \end{align*}\) for some constant \(k\). If the particle moves a distance of \(120\pi\) every second, then what is \(k\)?

 Nov 5, 2019
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The answer is 32 pi.

 Nov 6, 2019

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