Answer:
Increasing,[tex]310000ft^3/s[/tex]
Step-by-step explanation:
We are given that
a=150 feet
b=80 feet
c=50 feet
[tex]\frac{da}{dt}=100ft/s[/tex]
[tex]\frac{db}{dt}=-20ft/s[/tex]
[tex]\frac{dc}{dt}=5ft/s[/tex]
We have to find the volume of the box of the box increasing,decreasing or not changing at all at that instant.
We know that
Volume of box=[tex]lbh[/tex]
Using the formula
Volume of box,V=abc
Differentiate w.r.t t
[tex]\frac{dV}{dt}=\frac{da}{dt}bc+\frac{db}{dt}(ac)+\frac{dc}{dt}(ab)[/tex]
Substitute the values
[tex]\frac{dV}{dt}=100(80\times 50)-20(150\times 50)+5(150\times 80)[/tex]
[tex]\frac{dV}{dt}=310000ft^3/s[/tex]
Hence, the volume of the box is increasing .
