Question
In: Advanced Math
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
that contains 1414 grams of salt per liter enters the tank at the
rate 44 L/min. The solution is mixed and drains from the tank at
the rate 66 L/min.
Let yy be the number of g of salt in the tank after tt
minutes.
The differential equation for this situation would be:
dydt=dydt=
Given the initial condition y(0)y(0) = 100 The particular solution
would be
y(t)y(t)=
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Colby Messinger answered 2 years agoRelated Solutions
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.
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...
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 200 gallon tank initial contains 100 gallons of water and 20 pounds of dissolved salt....
A 200 gallon tank initial contains 100 gallons of water and 20
pounds of dissolved salt. Brine solution begins to enter the tank
at the rate of 2 gal/min with a salt concentration of 2 lb/gal. The
well mixed solution leaves the tank at the rate of 1 gal/min. Find
the amount of salt inside the tank 50 minutes after the process
starts?
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 ]
Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds...
Suppose that a large mixing tank initially holds 500 gallons of
water in which 50 pounds of salt have been dissolved. Another brine
solution is pumped into the tank at a rate of 3 gal/min, and when
the solution is well stirred, it is then pumped out at a
slower rate of 2 gal/min. If the concentration of the
solution entering is 2 lb/gal, determine a differential equation
(in lb/min) for the amount of salt A(t) (in lb)
in the...
A tank contains 10 gallons of water. Salt water containing a concentration of 4t ounces per...
A tank contains 10 gallons of water. Salt water containing a
concentration of 4t ounces per gallon flows into the tank at a rate
of 4 gallons per minute and the mixture in the tank flows out at
the same rate.
(a)Construct the mathematical model for this flow process
(b)Use integrating factors to solve for Q(t).
(c)If the tank contains Q0 amount of salt at time t = 0, use this
as an initial condition to solve for the constant...
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...
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