Question
In: Advanced Math
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 ]
Solutions
Colby Messinger answered 7 months agoRelated Solutions
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 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 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) =
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...
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?
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.
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 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?
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