Question
In: Advanced Math
A tank with a capacity of 90L originally contains 50L of brine with the concentration of...
A tank with a capacity of 90L originally contains 50L of brine with the concentration of 1g of salt per liter of water. Additional brine solution containing sat of concentration 2g/L flows into the tank at a rate of 3L/min. The well-stirred mixture flows out the tank at a rate of 2L/min. Let P(t) be the amount of salt in the tank at time t. Formulate initial value problems accurately describes P(t), for 0<t<40. Solve the solution
Solutions
Colby Messinger answered 1 month agoRelated Solutions
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 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...
A tank initially contains 150 gal of brine in which 20lb of salt are dissolved. A...
A tank initially contains 150 gal of brine in which 20lb of salt
are dissolved. A brine containing 3 lb/gal of salt runs into the
tank at the rate of 4 gal/min.The mixture is kept uniform by
stirring and flows out of the tank at the rate of 3 gal/min. Let y
represent the amount of salt at time t. Complete parts a through
e.
a. At what rate (pounds per minute) does salt enter the tank
at time t?...
A tank is filled to capacity with 400 gallons water containing 30 lbs of salt. Brine...
A tank is filled to capacity with 400 gallons water containing
30 lbs of salt. Brine containing 2 lbs of salt per gallon is pumped
into the tank at a rate of 3 gallons per minute. The well mixed
solution is pumped out at rate of 3.5 gallons per minute. Determine
the differential equation of the model and solve for an equation
relating amount of salt in tank at time t. Determine the time until
the tank is empty.
A large tank holds 1000 L of water into which flows a brine solution with concentration...
A large tank holds 1000 L of water into which flows a brine
solution with concentration of 1 kg / L at a rate of 6 L / min. The
solution in the tank is kept well stirred and is flowing out of the
tank at a rate of 5 L / min. Determine when the concentration of
salt will reach 0.5 kg / L.
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 400 gallons of brine (salt in solution) in which 125 pounds of salt...
A tank contains 400 gallons of brine (salt in solution) in which
125 pounds of salt has been dissolved. Freshwater (with no salt
added) runs into the tank at a rate of 4 gallons per minute, and
the stirred mixture is drained from the tank at the same rate. (1)
Find the amount of salt in the tank after an hour. (2) How long
does it take to reduce the amount of salt in the tank to 10
pounds?
A 4,500 litre tank contains 2,500 litres of brine. There is 50 kg of salt initially...
A 4,500 litre tank contains 2,500 litres of brine. There is 50
kg of salt initially present. Pure water is being put into the tank
at 20 litres/min. Brine solution is draining away at a rate of 15
litres/min.
a)Create a mathematical model of the dissolved salt in the
solution. Give amount of salt in terms of time (t).
b)Calculate how much salt is in the system after 15 minutes. State
all of the assumptions that you are using.
c)Create...
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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