Question

The length x of an rectangle is decreasing at the rate $2cm/sec$ and width y is increasing at the rate of $2cm/sec$. When $x=12cm$ and $y=12cm$, the rate of change of the area of the rectangle is $kc{m}^2/sec$, then $k-9$ is _________

Answer 1

$\frac{dx}{dt}=-2\frac{dy}{dt}=2$
$x=12y=5$
$area=xy$
$x\frac{dy}{dt}+y\frac{dx}{dt}=k$
$12\times 2+5\left(-2\right)=k$
$24-10=14=k$
$k-9=14-9=5$