Question
In: Math
1. A 100-gallon tank initially holds 50 gal of brine containing 5 pounds of salt. Brine...
1. A 100-gallon tank initially holds 50 gal of brine containing
5 pounds of salt. Brine
containing 1 pound of salt per gallon enters the tank at the rate
of 4 gal/s, and the
well-mixed brine in the tank flows out at the rate of 3
gal/s.
(a) How much salt will the tank contain at the time when the tank
is full of brine?
(b) If the tank had an infinite capacity, what is the maximum
amount of salt that
it could contain?
4. y' − 2xy = 8x. find a general solution.
Solutions
milcah answered 2 years agoRelated Solutions
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?
(62). (Transient Behavior of a Mixing tank): A tank initially holds 80 gal of a brine...
(62). (Transient Behavior of a Mixing tank): A tank initially
holds 80 gal of a brine solution containing 0.125 lb of salt per
gallon. At t=0, another brine solution containing 1 lb of salt per
gallon is poured into the tank at a rate of 4 gal/min, while the
well-stirred mixture leaves the tank at a rate of 8 gal/min. (a)
Formulate a model for describing the transient behavior of the tank
(b) Find the amount of salt in the...
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 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 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 containing 100 kg of a 60% brine (60% salt) at 33°C is filled with...
A tank containing 100 kg of a 60% brine (60% salt) at 33°C is
filled with a 10% salt solution (28°C) at the rate of 10 kg/min.
The barometric pressure is 101.5 KPa. Solution is removed from the
tank at the rate of 15 kg/min. Find the kilograms of salt in the
tank after 10 min
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 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?
Tanks A and Bare filled with 100 gal and 200 gal of brine respectively. Initially, 40...
Tanks A and Bare filled with 100 gal and 200 gal of brine
respectively. Initially, 40 lb of salt dissolved in the solution in
tank A and 20 lb of salt dissolved in the solution in tankB. The
system is closed in that the well-mixed liquid pumped from A into B
and from B into A at a rate of 25gal/min each (so, the liquid
volumes do not change over the time in both tanks).
(a) Find the general equation...
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