Question

A tank initially contains 100 liters of water in which 50 grams
of salt are dissolved. A salt solution containing 10 grams of salt
per liter is pumped into the tank at the rate of 4 liters per
minute, and the well-mixed solution is pumped out of the tank at
the rate of 6 liters per minute. Let t denote time (in minutes),
and let Q denote the amount of salt in the tank at time t (in
grams). Write down the dierential equation dQ dt = something and
initial condition describing this mixing problem.

DO NOT SOLVE THE INITIAL VALUE PROBLEM. JUST WRITE DOWN THE D.E.
AND INITIAL CONDITION.

Answer #1

A tank originally contains 130 liters of water with 10 grams of
salt in solution. Beginning at t=0, water containing 0.1 grams of
salt per liter flows into the tank at a rate of 2 liters per minute
and the uniform mixture drains from the tank at a rate of 2 liters
per minute. Letting t be time in minutes and Q be the amount of
salt in the tank at time t measured in grams, formulate an initial
value...

A tank originally contains 120 liters of water with 5 grams of
salt in solution. Beginning at t=0, water containing 0.4 grams of
salt per liter flows into the tank at a rate of 2 liters per minute
and the uniform mixture drains from the tank at a rate of 2 liters
per minute. Letting t be time in minutes and Q be the amount of
salt in the tank at time t measured in grams, formulate an initial
value...

A tank contains 120 liters of fluid in which 50 grams of salt is
dissolved. Brine containing 1 gram of salt per liter is then pumped
into the tank at a rate of 4 L/min; the well-mixed solution is
pumped out at the same rate. Find the number
A(t) of grams of salt in the
tank at time t.
A(t) =
__________________

A tank contains 350 liters of fluid in which 50 grams of salt is
dissolved. Brine containing 1 gram of salt per liter is then pumped
into the tank at a rate of 5 L/min; the well-mixed solution is
pumped out at the same rate. Find the number
A(t)
of grams of salt in the tank at time t.

A large tank contains 100 liters of a salt solution with a
concentration of 50 grams/Liter. A salt solution which has a
concentration of 4grams/Liter is added at 2 Liters per minute. At
the same time, the solution drains from the tank at 2 liters per
minute.
Set up a differential equation describing the rate of change of
the amount of salt S with respect to time t:
dS/dt = _________________
Solve for the differential equation
S=____________________

A tank contains 210 liters of fluid in which 20 grams of salt is
dissolved. Brine containing 1 gram of salt per liter is then pumped
into the tank at a rate of 3 L/min; the well-mixed solution is
pumped out at the same rate. Find the number A(t) of grams of salt
in the tank at time t.

A tank contains 180 liters of fluid in which 20 grams of salt is
dissolved. Brine containing 1 gram of salt per liter is then pumped
into the tank at a rate of 6 L/min; the well-mixed solution is
pumped out at the same rate. Find the number
A(t)
of grams of salt in the tank at time t

A tank contains 420 liters of fluid in which 10 grams of salt is
dissolved. Pure water is then pumped into the tank at a rate of 6
L/min; the well-mixed solution is pumped out at the same rate. Find
the number A(t) of grams of
salt in the tank at time t.
A(t) =_______g

Initially 5 grams of salt are dissolved in 20 liters of water.
Brine with concentration of salt 2 grams of salt per liter is added
at a rate of 4 liters a minute. The tank is mixed well and is
drained at 3 liters a minute. Set up a diff equation for y(t), the
number of grams of salt in the tank at time t.Do not solve fory(t).
Your answer should look like:y0(t) = you ll in this side

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...

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