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The rate of electricity used in a single family home is given by $r( t ) ={ t }^{ 2 }+6t+3,$ where $r$ is measured in kilowatts/minute.

On the interval $[0, 6]$, how many kilowatts have been used after $3$ minutes if the initial usage was measured to be $10$ kilowatts?

A

$55$

B

$45$

C

$27$

D

$33$

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