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krisandlance
15.04.2020 •
Mathematics
G V. (10 points) Suppose that a large tank initially holds 400 gallons of brine, which contains 20 pounds of salt. Pure water is pumped into the tank at a rate of 5 gallons per minute. When the solution in the tank is well stirred, it is pumped out at a rate of 4 gallons per minute. a. Write the initial value problem that represents the change in the amount of salt at time t. b. Solve the initial value problem.
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Ответ:
Step-by-step explanation:
If you assume concentration of salt per unit water remains constnat, find the constant.
Initially, for 400 gal of water, you have 20 pounds of salt
20lb/400gal=0.05lb salt per gal of water.
Now do part a)
I will use the following variables:
the equation is
total salt=initial salt+salt in-salt out
we know that
is 20lb
subsitute all in
part b)
to solve this initial value problem, I would need to be given either a goal amount of salt (
) or a time elapsed
. Since none are given, the IVP cannot be solved.
Ответ: