Question

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=____________________

Answer #1

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...

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 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...

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 2 liter tank of water contains 3 grams of salt at time t = 0
(in minutes). Brine with concen-
tration 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 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 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 that holds 2000 liters initially contains 150 liters of
water into which 30 grams of salt has been dissolved. Water is
flowing into the tank at a rate of 20 liters/minute with a
concentration of sin^2(πt) at any time, t. The liquid is well
mixed, and flows out at a rate of 10 liters/minute. Set up, do not
solve, a 1st order IVP to find the amount of salt in the tank at
any time, t, after t...

A 1000-liter (L) tank contains 500L of water with a salt
concentration of 10g/L. Water with a salt concentration of 50g/L
flows into the tank at a rate of R(in)=80L/minutes (min). The fluid
mixes instantaneously and is pumped out at a specified rate
R(out)=40L/min. Let y(t) denote the quantity of salt in the tank at
time t. Set up and solve the differential equation for y(t).

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.

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