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A particle in the $xy$-plane moves according to the following equations:

$$x(t) = 6t\cdot \cos{t} -6\sin{t}\,\text{and}\, y(t)= -6t\cdot \sin{t} -6\cos{t}$$

Find the total distance the particle has traveled from time $t = 0$ to $4$.

A

$0$

B

$24$

C

$32$

D

$48$

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