Question
In: Advanced Math
A tank originally contains 120 gal of fresh water. Then water containing 1/2 lb of salt...
A tank originally contains 120 gal of fresh water. Then water containing 1/2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 11 min the process is stopped, and fresh water is poured into the tank at a rate of 2 gal/min, with the mixture again leaving at the same rate. Find the amount of salt Q(11) in the tank at the end of an additional 11 min.
Round your answer and intermediate answer to two decimal places.
Amount of salt in the tank at the end of an additional 11 min is Q(11)= _____ lbs.
Solutions
Colby Messinger answered 1 year agoRelated Solutions
A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of...
A tank originally contains 100 gal of fresh water. Then water
containing 1 2 lb of salt per gallon is poured into the tank at a
rate of 2 gal/min, and the mixture is allowed to leave at the same
rate. After 10 min the process is stopped, and fresh water is
poured into the tank at a rate of 4 gal/min, with the mixture again
leaving at the same rate. Find the amount of salt in the tank at...
A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of...
A tank originally contains 100 gal of fresh water. Then water
containing
1
2
lb of salt per gallon is poured into the tank at a rate of 2
gal/min, and the mixture is allowed to leave at the same rate.
After 10 min the process is stopped, and fresh water is poured into
the tank at a rate of
6 gal/min,
with the mixture again leaving at the same rate. Find the amount
of salt in the tank at...
A tank contains 200 gal of water and 50oz of salt. Water containing a salt concentration...
A tank contains 200 gal
of water and 50oz of salt. Water containing a salt concentration of
1/8(1+1/2 sint) oz/gal flows into the tank at a rate of 4 gal/min,
the mixture flows out at the same rate.
A) find the amount of salt in the tank at any moment. Q(t)
=
B) the amplitude of oscillation is
C) level of the amplitude is
2. A tank initially contains 120 L of pure water. A salt mixture containing a concentration of...
2. A tank initially
contains 120 L of pure water. A salt mixture containing a
concentration of 1.5 g/L enters the tank at a rate of 2 L/min, and
the well-stirred mixture leaves the tank at the same rate. Find an
expression for the amount of salt in the tank at any time
t. Also, find the limiting amount of salt in the tank as
t →∞.
A tank contains 365 gallons of water and 50 oz of salt. Water containing a salt...
A tank contains 365 gallons of water and 50 oz of
salt. Water containing a salt concentration of
1/6(1 + 1/4 sin t)
oz/gal flows into the tank at a rate of 8 gal/min, and the mixture
in the tank flows out at the same rate.
The long-term behavior of the solution is an oscillation about a
certain constant level.
a) What is this level?
b) What is the amplitude of the oscillation?
A tank contains 360 gallons of water and 50 oz of salt. Water containing a salt...
A tank contains 360 gallons of water and 50 oz of salt. Water
containing a salt concentration of 1 6 (1 + 1 4 sin t) oz/gal flows
into the tank at a rate of 8 gal/min, and the mixture in the tank
flows out at the same rate. The long-term behavior of the solution
is an oscillation about a certain constant level. a) What is this
level? b) What is the amplitude of the oscillation? (Round your
answers to...
A tank contains 40 lb of salt dissolved in 400 gallons of water. A brine solution...
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.
A(t) =
A tank contains 10 gallons of water. Salt water containing a concentration of 4t ounces per...
A tank contains 10 gallons of water. Salt water containing a
concentration of 4t ounces per gallon flows into the tank at a rate
of 4 gallons per minute and the mixture in the tank flows out at
the same rate.
(a)Construct the mathematical model for this flow process
(b)Use integrating factors to solve for Q(t).
(c)If the tank contains Q0 amount of salt at time t = 0, use this
as an initial condition to solve for the constant...
A tank contains 70 kg of salt and 2000 L of water. Water containing 0.4kg/L of...
A tank contains 70 kg of salt and 2000 L of water. Water
containing 0.4kg/L of salt enters the tank at the rate 16L/min. The
solution is mixed and drains from the tank at the rate 4L/min. A(t)
is the amount of salt in the tank at time t measured in
kilograms.
(a) A(0) = (kg)
(b) A differential equation for the amount of salt in the tank
is =0=0. (Use t,A, A', A'', for your variables, not
A(t), and move everything...
A tank contains 100 gal of water. Brine enters the tank at the rate of 3...
A
tank contains 100 gal of water. Brine enters the tank at the rate
of 3 gal/min. The mixture, thoroughly stirred, leaves the tank at
the rate of 2 gal/min. If the salt concentration in the brine at
the end of 20 minutes is to be 2 lb/gal, what should be the salt
concentration in the brine entering the tank?
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