Question

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

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 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 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 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 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 500-liter tank initially contains 200 liters of a liquid in
which 150 g of salt have been dissolved. Brine that has 5 g of salt
per liter enters the tank at a rate of 15 L / min; the well mixed
solution leaves the tank at a rate of 10 L / min.
Find the amount A (t) grams of salt in the tank at time t.
Determine the amount of salt in the tank when it is full.

A salt solution containing 2 grams of salt per liter of water
is poured into the tank at a rate 3 liter/min where initially
contains 30 liters of pure water. The mixture then was drained at
the same rate as its poured into the tank. Solve,
Hint:
(??(?) = ???????? ????????????? (??) × ???? ???? (??)? −
????(???? ????????????? (???) ×
i. the initial-value problem that describes the amount of salt
in the tank for t > 0
??
????...

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