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A particle moves in the xy-plane according to the equations $\cfrac{dx}{dt}=3{ t }^{ 2 }+2$ and $\cfrac{dy}{dt}=-4t+12.$

Find the position of the particle when the particle reaches its maximum height, given that when $t = 0$, the particle is at the point $\left( 0, \, 1 \right)$.

A

$(33, 19)$

B

$(33, 18)$

C

$(34, 18)$

D

$(29, 0)$

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