Question
In: Advanced Math
A tank contains100 gal of water and 50 oz of water and 50 oz of salt....
A tank contains100 gal of water and 50 oz of water and 50 oz of salt. water containing salt concentration of (1/4)(1 + (1/2)sint) oz/gal flows into the tank at a rate of 2gal/min, and the mixture in the tank flows out at the same rate.
a) find the amount of salt in the tank at any time
b) plot the solution for a time period long enough so that you see the ultimate behavior of the graph
c) the long-time behavior of solution is an oscillation about a certain constant level. what is the level? what is the amplitude of the oscillation?
Solutions
Colby Messinger answered 1 week agoRelated Solutions
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 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
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...
Consider a large tank holding 50 gal of pure water into which a brine solution of...
Consider a large tank holding 50 gal of pure water
into which a brine solution of salt begins to flow at a constant
rate of 6 gal/min. the brine leaves the tank at a rate of 5
gal/min. If the concentration of salt in the brine entering the
tank is 0.1 lbs per gallon, determine the function X that will
determine the amount of brine in the tank at any time t.
1. A 100-gallon tank initially holds 50 gal of brine containing 5 pounds of salt. Brine...
1. A 100-gallon tank initially holds 50 gal of brine containing
5 pounds of salt. Brine
containing 1 pound of salt per gallon enters the tank at the rate
of 4 gal/s, and the
well-mixed brine in the tank flows out at the rate of 3
gal/s.
(a) How much salt will the tank contain at the time when the tank
is full of brine?
(b) If the tank had an infinite capacity, what is the maximum
amount of salt...
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?
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?
A tank initially contains 150 gal of brine in which 20lb of salt are dissolved. A...
A tank initially contains 150 gal of brine in which 20lb of salt
are dissolved. A brine containing 3 lb/gal of salt runs into the
tank at the rate of 4 gal/min.The mixture is kept uniform by
stirring and flows out of the tank at the rate of 3 gal/min. Let y
represent the amount of salt at time t. Complete parts a through
e.
a. At what rate (pounds per minute) does salt enter the tank
at time t?...
Two tanks each contain 100 gal of water and tank 2 initially has 50 lbs of...
Two tanks each contain 100 gal of water and tank 2 initially has
50 lbs of salt uniformly dissolved in it. An external flow brings
adds 5 gal/min to tank 1 with 5 lbs of salt in it. Tank 1 feeds
tank 2 at 10 gal/min, and tank 2 feeds back to tank 1 at 5 gal/min.
Finally, an exit stream leaves tank 2 at 5 gal/min.
1) Use Laplace transforms to solve the system of ODEs modeling
this system...
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