Respuesta :
Answer:
dh/dt = 3.01 inches/minute
The height of the liquid is changing at the rate of 3.01 inches/minute
Step-by-step explanation:
Volume of liquid in the box is ;
V = length × width × height
V = lbh ......1
If the volume of the liquid is increasing at a rate of 562 cubic inches per minute.
dV/dt = 562 cubic inches per minute
Length l = 11 inches
Width b = 17 inches
From equation 1; differentiating the equation we have;
dV/dt = bh(dl/dt) + lh(db/dt) + lb(dh/dt) ....2
Since the length and width of water is not changing then;
dl/dt = db/dt =0
Equation 2 becomes;
dV/dt = lb(dh/dt)
dh/dt = (dV/dt)/lb
Substituting the values;
dh/dt = 562/(11×17) inch/minute
dh/dt = 3.01 inches/minute
The height of the liquid is changing at the rate of 3.01 inches/minute
