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A particle moves in the $xy$-plane according to the equations $x( t ) =\ln { ( 3-t ) } $ and $y( t ) ={ 2te }^{ -t }$, find the velocity of the particle at $t=2$.

A

$\left<1,-2{ e }^{ -2 }\right>$

B

$\left<1,6{ e }^{ -2 }\right>$

C

$\left<-1,-2{ e }^{ -2 }\right>$

D

$\left<-1,6{ e }^{ -2 }\right>$

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