Question

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.

Answer #1

A tank contains 70 lb of salt dissolved in 200 gallons of water.
A brine solution is pumped into the tank at a rate of 2 gal/min; it
mixes with the solution there, and then the mixture is pumped out
at a rate of 2 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 large tank contains 800 gal of water in which 42 lb of salt
are dissolved. Brine
containing 2 lb of of dissolved salt per gal is pumped into the
tank at a rate of
4 gal per minute, and the mixture, kept uniform by stirring, is
pumped out at
the same rate.
(a) Find the amount x(t) of salt in the tank, at time t.
(b) How long will it take for the amount of salt in the tank...

A tank contains 30 gallons of brine solution containing 10 lb of
salt. Another brine solution of concentration of 3 lb/gallon is
poured into the tank at the rate of 2 gallons/min. The well stirred
solution in the tank is drained out at the rate of 2 gallons/min.
Let the amount of salt in the tank at time ? be ?(?).
Write the differential equation for A(t) and solve it.

suppose a large tank has 300 gallon of brine solution. Brine
sol. was being pumped into the tank at a rate of 3 gal/min. it
mixed with the solution there and then the mixture was pumped out
at the rate of 2 gal/min. the concentraion of salt in the inflo or
solution entering was 2 lb/gal. initially, 50 pounds of salt were
dissolved in the 300 gallons.
find the amount of salt in tank at time t.
if the tank...

A tank initially contains 150 gal of brine in which 60 lb of
salt are dissolved. A brine containing 4 lb/gal of salt runs into
the tank at the rate of 6 gal/min. The mixture is kept uniform by
stirring and flows out of the tank at the rate of 5 gal/min. Let y
represent the amount of salt at time t. Complete parts a through
f.
a. At what rate (pounds per minute) does salt enter the tank
at...

suppose a large tank has 300 gallon of brine solution. Brine
sol. was being pumped into the tank at a rate of 3 gal/min. it
mixed with the solution there and then the mixture was pumped out
at the rate of 2 gal/min. the concentraion of salt in the inflo or
solution entering was 2 lb/gal. initially, 50 pounds of salt were
dissolved in the 300 gallons. Please answer clearly. Thank u.
a find the amount of salt in tank...

A 110 gallon tank initially contains 5 lbs salt dissolved in 60
gallons of water. Brine containing 1 lb salt per gallon begins to
flow into the tank at the rate of 3 gal/min and the well-mixed
solution is drawn off at the rate of 1 gal/min. How much salt is in
the tank when it is about to overflow? (Round your answer to the
nearest integer.)

A tank contains 100 gal of brine made by dissolving 80 lb of
salt in water. Pure water
runs into the tank at the rate of 4 gal/min, and the mixture,
kept uniform by stirring runs
out at the same rate. Find the amount of salt in the tank at
t=8 min.

A tank is filled with 10 gallons of brine in which is dissolved
5 lb of salt. Brine containing 3 lb of salt per gallon enters the
tank at a rate of 2 gal per minute, and the well-stirred mixture is
pumped out at the same rate. (a) Find the amount of salt in the
tank at any time t. (b) How much salt is in the tank after 10
minutes? (c) How much salt is in the tank after...

A tank contains 100 gallons of pure water. A salt solution with
concentration 2.5 lb/gal enters the tank at a rate of 4 gal/min.
Solution drains from the tank at a rate of 4 gal/min. Find the
eventual concentration of the salt solution using a qualitative
analysis rather than by actually solving the DE.

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