Question
In: Advanced Math
Consider a tank containing at time t = 0, 100 gallons of brine. Assume that water...
Consider a tank containing at time t = 0, 100 gallons
of brine. Assume that water containing 1/4 lb of salt per gallon is
entering the tank at a rate of 3 gallons per minute, and that the
well stirred solution is leaving the tank at the same rate. Find a
differential equation for the amount of salt A(t) in the tank at
time t > 0
**PLEASE SHOW ALL STEPS CLEARLY SINCE I REALLY WANT TO UNDERSTAND THE WHOLE PROCESS** **If possible please type the solution?***
Thank you!
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Consider a tank containing at time t = 0, 100 gallons of brine. Assume that water...
Consider a tank containing at time t = 0, 100 gallons
of brine. Assume that water containing 1/4 lb of salt per gallon is
entering the tank at a rate of 3 gallons per minute, and that the
well stirred solution is leaving the tank at the same rate. Find a
differential equation for the amount of salt A(t) in the tank at
time t > 0
**PLEASE SHOW ALL STEPS CLEARLY SINCE I REALLY WANT TO
UNDERSTAND THE WHOLE...
A 100 gallon tank initially contains 10 gallons of fresh water. At t=0 a brine solution...
A 100 gallon tank initially contains 10 gallons of fresh water.
At t=0 a brine solution containing 1 pound of salt per gallon is
poured into the tank at the rate of 4 gal/min., while the
well-stirred mixture leaves the tank at the rate of 2 gal/min. Find
the amount of salt in the tank at the moment of overflow.
Enter answer as numerical decimal correct to two decimal places.
pounds.
At time t=0 a tank holds 550 gallons of water with 100 pounds of dissolved salt....
At time t=0 a tank holds 550 gallons of water with 100 pounds of
dissolved salt. An input pipe brings in solution at 8 gallons per
minute at a concentration of 2 pounds per gallon. An output pipe
carries away solution at 2 gallons per minute. Find how much salt
is in the tank after 45 minutes.
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 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) A 50 gallon tank initially contains 10 gallons of fresh water. At t = 0...
A) A 50 gallon tank initially contains 10 gallons of fresh
water. At t = 0 t = 0 a brine solution containing 1 pound of salt
per gallon is poured into the tank at the rate of 4 gal/min., while
the well-stirred mixture leaves the tank at the rate of 1 gal/min.
Find the amount of salt in the tank at the moment of overflow.
B) A tank contains 100100 g of salt and 400400 L of water. Water...
5. (Mixing Problem) A very large tank is initially filled with 100 gallons of water containing...
5. (Mixing Problem) A very large tank is initially filled with
100 gallons of water containing 5 pounds of salt. Beginning at time
t = 0, a brine solution with a concentration of 1 pound of salt per
gallon flows into the top of the tank at 3 gallons per second, the
mixture is stirred, and the mixture flows out of the bottom of the
tank at 2 gallons per second. (a) Letting w = pounds of salt in the...
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...
A tank contains 365 gallons of water and 50 oz of salt. Water containing a salt...
A tank contains 365 gallons of water and 50 oz of
salt. Water containing a salt concentration of
1/6(1 + 1/4 sin t)
oz/gal flows into the tank at a rate of 8 gal/min, and the mixture
in the tank flows out at the same rate.
The long-term behavior of the solution is an oscillation about a
certain constant level.
a) What is this level?
b) What is the amplitude of the oscillation?
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