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Initially, a pendulum swings through an arc of $3\text{ feet}$. On each successive swing, the length of the arc is $0.8$ of the previous length.

After $10\text{ swings}$, what total length will the pendulum have swung (to the nearest tenth of a foot)?

A

$13.0\text{ feet}$

B

$13.4 \text{ feet}$

C

$13.7 \text{ feet}$

D

$12.5\text{ feet}$

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