assume that all variables are implicit functions of time t. find the indicated rate .

Question

^{x^2+2y^2+6y=9 , dx/dt =3 when x=3 and y=-3 ;find dy/dt}

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Answer 1

x² + 2y² + 6y = 9

2x(dx/dt) + 4y(dy/dt) + 6(dy/dt) = 0

Since x=3, y=3, and dx/dt = 3, 18 + 12(dy/dt) + 6(dy/dt) = 0

18(dy/dt) = -18

dy/dt = -1