Answer:
Step-by-step explanation:
The volume of an object stays the same no matter how you shape it, so the volume of the new sphere is the sum of the volume of the two metal spheres assuming that nothing is lost during the process of creating the new sphere.
Let denote the amount of salt in the tank at time
. We're told that
.
For , the salt flows in at a rate of (1/5 lb/gal)*(5 gal/min) = 1 lb/min. When the regulating mechanism fails, 20 lbs of salt is dumped and no more salt flows for
. We can capture this in terms of the unit step function
and Dirac delta function
as
(in lb/min)
The salt from the mixed solution flows out at a rate of
Then the amount of salt in the tank at time changes according to
Let denote the Laplace transform of
,
. Take the transform of both sides to get
Solve for , then take the inverse of both sides.
