Question
In: Math
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.
Solutions
milcah answered 2 years agoRelated Solutions
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 ]
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?
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 t=0,a tank contains Q0 g of the salt dissolved in 100L of water, assume that...
at t=0,a tank contains Q0 g of the salt dissolved in 100L of
water, assume that water containing 1/4g of salt per L in entering
the tank at a rate of r L/min. at the same time, the well-mixed
mixture is draining from the tank at the same rate.
a) set up the differential equation and initial condition for
the salt amount Q as a function of time.
b)find the amount of salt in the tank as a function of...
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) =
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?
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...
Suppose that a large mixing tank initially holds 400 gallons of water in which 65 pounds...
Suppose that a large mixing tank initially holds 400 gallons of
water in which 65 pounds of salt have been dissolved. Another brine
solution is pumped into the tank at a rate of 6 gal/min, and when
the solution is well stirred, it is pumped out at a slower rate of
5 gal/min. If the concentration of the solution entering is 3
lb/gal, find the amount of salt in the tank after 10 minutes.
PLEASE SHOW ALL WORK AND USE...
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.
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