Question
In: Advanced Math
A tank initially contains 50 gallons of pure water. Starting at time t = 0 a...
A
tank initially contains 50 gallons of pure water. Starting at time
t = 0 a brine containing 2 pounds of dissolved salt per gallon
flows into the tank at the rate of 3 gallons per minute. The
mixture is kept uniform by stirring and the well stirred mixture
simultaneously flows out of the tank at the same rate.
a) How much salt is in the tank at any time t > 0 ?
b) How much salt is present at the end of 25 minutes?
c) How much salt is present after a long time?
Solutions
Colby Messinger answered 5 months agoRelated Solutions
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...
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 contains 25lb of salt dissolved in 100 gallons of...
At time t = 0 a tank contains 25lb of salt dissolved in 100
gallons of water. assume that water containing 2lb salt/gallon
enters the tank at a rate of 5 gal/min and the well-stirred
solution is leaving the tank at the same rate.
solve for Q(t) [Amount of salt in tank at time t ]
initially a large tank with a capacity of 300 gallons contains 150 gallons of clean water....
initially a large tank with a capacity of 300 gallons contains
150 gallons of clean water. A solution of salt with a concentration
of 2 lb / gal flows into the tank at a rate of 50 gal / min. The
solution is perfectly well mixed while the solution is extracted at
a rate of 25 gal / min. Find:
a) the amount of salt in the tank at the time it is filled (in
pounds)
b) the speed at...
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...
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...
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 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?
A tank contains 360 gallons of water and 50 oz of salt. Water containing a salt...
A tank contains 360 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? (Round your
answers to...
A 2 liter tank of water contains 3 grams of salt at time t = 0...
A 2 liter tank of water contains 3 grams of salt at time t = 0
(in minutes). Brine with concentration 3t grams of salt per liter
at time t is added at a rate of one liter per minute. The tank is
mixed well and is drained at 1 liter per minute. At what positive
time is there a minimum amount of salt and what is that amount?
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