Question

Water is draining from a large tank. After tmin, there are150000-7500t +t2 litres of water in the tank.

a) Determine the average rate at which the water empties from the tank in the interval between 5 and 10 minutes.

b) Determine the average rate at which the water empties from the tank in the interval between 9 and 10 min.

c) Estimate the rate at which the water runs out after exactly 10 min.

d) How much water is in the tank at exactly 10 min?

Answer #1

A tank is initially filled with 1000 litres of a salt solution
containing 1000 grams of salt. A solution containing 10 g/l runs
into the tank at the rate of 5 l/min and the well stirred mixture
runs out of the tank at the same rate.
(i) Determine the differential equation with initial condition
that models this situation.
(ii) Determine how long it will take for the salt in the tank
reaching 2500g.

consider a large tank initially holding 300 L of solution in
which 20 Kg of sugar was dissolved, a solution of sugar begins to
flow at a constant rate of 9 L/min into the tank. the solution
inside the tank is kept well stirred and is flowing out of the tank
at the rate of 6 L/min. if the concentration of sugar in the
solution entering the tank is 0.5 Kg/L. determine the mass of the
sugar in the tank...

A tank contains 1000 L of pure water. Brine that contains 0.05
kg of salt per liter of water enters the tank at a rate of 5 L/min.
Brine that contains 0.04 kg of salt per liter of water enters the
tank at a rate of 10 L/min. The solution is kept thoroughly mixed
and drains from the tank at a rate of 15 L/min.
(a) How much salt is in the tank after t minutes?
(b) How much salt...

a full tank with a capacity of 500 gal originally
contains water with 200lb of salt. water containing 1lb of salt per
gallon is entering at a rate of 4 gal/min and the mixture is
allowed to flow out at a rate of 6 gal/min thus the tank is
draining. how much salt is in the tank when it is half full?

A tank contains 1000 L of pure water. Brine that contains 0.05
kg of salt per liter of water enters the tank at a rate of 5 L/min.
Brine that contains 0.04 kg of salt per liter of water enters the
tank at a rate of 10 L/min. The solution is kept thoroughly mixed
and drains from the tank at a rate of 15 L/min.
(a) How much salt is in the tank after t minutes?
y=

A large storage tank, open to the atmosphere at the top and
filled with water, develops a small hole in its side at a point
14.0 m below the water level. If the rate of flow from the leak is
2.20 ✕ 10−3 m3/min, determine the following. (a) Determine the
speed at which the water leaves the hole. m/s (b) Determine the
diameter of the hole. mm

A tank contains 1000 L of brine (saltwater) with 15 kg of
dissolved salt. Pure water enters the tank at a rate of 10 L/min.
The solution is kept thoroughly mixed and drains from the tank at
the same rate. How much salt is in the tank after t minutes?

A large tank is filled with 80 gallons of fluid in
which 2 pounds of salt are dissolved. Brine containing 1/2 pound of
salt per gallon is pumped into the tank at a rate of 3 gal/min. The
well-mixed solution is then pumped out at the same rate of 3
gal/min. Find the concentration of salt in the tank after 30
minutes.

A large storage tank, open at the top and filled with water,
develops a small hole in its side at a point 16.8 m below the water
level. The rate of flow from the leak is found to be 3.00 10-3
m3/min. (a) Determine the speed at which the water leaves the hole.
22.22 Incorrect: Your answer is incorrect. The water speed at the
top of the tank can be assumed to be zero since the flow rate from
the...

A tank contains 1280 L of pure water. Solution that contains
0.02 kg of sugar per liter enters the tank at the rate 3L/min, and
is thoroughly mixed into it. The new solution drains out of the
tank at the same rate.
(a) How much sugar is in the tank at the beginning?
(b) Find the amount of sugar after t minutes.
y(t)=
As t becomes large, what value is y(t)
approaching ? In other words, calculate the following limit....

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