Question
In: Advanced Math
A tank contains 1000L of pure water. Brine that contains 0.05kg of salt per liter enters...
A tank contains 1000L of pure water. Brine that contains 0.05kg of salt per liter enters the tank at a rate of 5L/min. Also, brine that contains 0.09kg of salt per liter enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15L/min. Answer the following questions.
1. How much salt is in the tank after t minutes? Answer (in
kilograms):
S(t)=
2. How much salt is in the tank after 2 hours? Answer (in kilograms):
Solutions
Expert Solution
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Colby Messinger answered 2 years agoRelated Solutions
A tank initially contains 80gal of pure water. Brine containing 2lb of salt per gallon enters...
A tank initially contains 80gal of pure water. Brine containing
2lb of salt per gallon enters the tank at 2gal/min, and the
(perfectly mixed) solution leaves the tank at 3 gal/min. Thus the
tank is empty after exactly 80 min.
(A) Find the amount of salt in the tank after t minutes.
(b) What is the maximum amount of salt ever in the tank?
A tank contains 9,000 L of brine with 11 kg of dissolved salt. Pure water enters...
A tank contains 9,000 L of brine with 11 kg of dissolved salt.
Pure water enters the tank at a rate of 90 L/min. The solution is
kept thoroughly mixed and drains from the tank at the same rate.
(a) How much salt is in the tank after t minutes?
(b) How much salt is in the tank after 10 minutes? (Round your
answer to one decimal place.)
A tank contains 100kg of salt and 2000L of water. Pure water enters a tank at...
A tank contains 100kg of salt and 2000L of water. Pure water
enters a tank at the rate 6L/min. The solution is mixed and drains
from the tank at the rate 3L/min. ) Find the concentration(kg/L) of
salt in the solution in the tank as time approaches infinity.
(Assume your tank is large enough to hold all the solution.)
A tank contains 60 kg of salt and 1000 L of water. Pure water enters a...
A tank contains 60 kg of salt and 1000 L of water. Pure water
enters a tank at the rate 12 L/min. The solution is mixed and
drains from the tank at the rate 6 L/min.
(a) What is the amount of salt in the tank initially?
amount = (kg)
(b) Find the amount of salt in the tank after 3 hours.
amount = (kg)
(c) Find the concentration of salt in the solution in the tank as
time approaches infinity. (Assume...
A tank contains 90 kg of salt and 2000 L of water: Pure water enters a...
A tank contains 90 kg of salt and 2000 L of water: Pure water
enters a tank at the rate 8 L/min. The solution is mixed and drains
from the tank at the rate 4 L/min. What is the amount of salt in
the tank initially? Find the amount f salt in the tank after 4.5
hours. Find the concentration of salt in the solution in the tank
as the time approaches infinity. (Assume your tank is large enough
to...
A tank contains 100 gal of water. Brine enters the tank at the rate of 3...
A
tank contains 100 gal of water. Brine enters the tank at the rate
of 3 gal/min. The mixture, thoroughly stirred, leaves the tank at
the rate of 2 gal/min. If the salt concentration in the brine at
the end of 20 minutes is to be 2 lb/gal, what should be the salt
concentration in the brine entering the tank?
A tank contains 100 gal of water. Brine enters the tank at the rate of 3...
A
tank contains 100 gal of water. Brine enters the tank at the rate
of 3 gal/min. The mixture, thoroughly stirred, leaves the tank at
the rate of 2 gal/min. If the salt concentration in the brine at
the end of 20 minutes is to be 2 lb/gal, what should be the salt
concentration in the brine entering the tank?
a 600gal tank initially containing 75lb of salt. Brine containing 1lb of salt per gallon enters...
a 600gal tank initially containing 75lb of salt. Brine
containing 1lb of salt per gallon enters the tank at a rate of
5gal/s, and the well mixed brine in the tank flows out at a rate of
3gal/s. How much salt will the tank contain when it is full of
brine?
A tank contains 20 kg of salt dissolve in 7000 L of water. Brine that contain...
A tank contains 20 kg of salt dissolve in 7000 L of water. Brine
that contain 0.041 kg of salt per liter of water enters the tank at
a rate of 25 L/min. The solution is kept thoroughly mixed and
drains from the tank at the same rate. How much Kg salt remains in
the tank if as time approaches to infinite?
A tank contains 40 lb of salt dissolved in 400 gallons of water. A brine solution...
A tank contains 40 lb of salt dissolved in 400 gallons of water.
A brine solution is pumped into the tank at a rate of 4 gal/min; it
mixes with the solution there, and then the mixture is pumped out
at a rate of 4 gal/min. Determine
A(t),
the amount of salt in the tank at time t, if the
concentration of salt in the inflow is variable and given by
cin(t)
= 2 + sin(t/4) lb/gal.
A(t) =
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