Answer: [tex]\frac{3}{7} \text{ cm/min}[/tex]
Step-by-step explanation:
The volume of the box is [tex]V=lwh=7h[/tex].
Differentiating both sides with respect to [tex]t[/tex] yields [tex]\frac{dV}{dt}=7 \frac{dh}{dt}[/tex].
It is given that [tex]\frac{dV}{dt}=-3[/tex], which yields [tex]\frac{dh}{dt}=-\frac{3}{7}[/tex].
Therefore, the height of the box is decreasing at a rate of [tex]\frac{3}{7} \text{ cm/min}[/tex].
