There are three interconnected tanks, each with volume 10 liters and containing saline solution. Fresh water is pumped into tank 3 at 1 liter/min. Solution from tank 3 is pumped to tank 2 at 1 liter/min. Solution from tank 2 is pumped to tank 1 at 1 liter/min, Solution is pumped from tank 1 at 1 liter per min. At time t=0, tank 3 has 1 gram of salt per liter, tank 2 has fresh water, and tank 1 has 2 grams of salt per per liter, Let x(t) be the amount of salt in tank 1 at time t, y(t) the amount of salt in tank 2 at time t, and z(t) the amount of salt in tank 3 at timet. The system of differential equations describing the tank system is x%3D y%3D x(0) = y(0) = z(0) = Characteristic polynomial: Eigenvalue: Matrix exponential: The solution is x(t) = y(t) = z(t) = Find the approximate time required to reduce the concentration in tank 3 to half the original concentration.
There are three interconnected tanks, each with volume 10 liters and containing saline solution. Fresh water is pumped into tank 3 at 1 liter/min. Solution from tank 3 is pumped to tank 2 at 1 liter/min. Solution from tank 2 is pumped to tank 1 at 1 liter/min, Solution is pumped from tank 1 at 1 liter per min. At time t=0, tank 3 has 1 gram of salt per liter, tank 2 has fresh water, and tank 1 has 2 grams of salt per per liter, Let x(t) be the amount of salt in tank 1 at time t, y(t) the amount of salt in tank 2 at time t, and z(t) the amount of salt in tank 3 at timet. The system of differential equations describing the tank system is x%3D y%3D x(0) = y(0) = z(0) = Characteristic polynomial: Eigenvalue: Matrix exponential: The solution is x(t) = y(t) = z(t) = Find the approximate time required to reduce the concentration in tank 3 to half the original concentration.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Transcribed Image Text:There are three interconnected tanks, each with volume 10 liters and containing saline solution. Fresh water is pumped into tank 3 at 1
liter/min. Solution from tank 3 is pumped to tank 2 at 1 liter/min. Solution from tank 2 is pumped to tank 1 at 1 liter/min. Solution is
pumped from tank 1 at 1 liter per min. At time t=0, tank 3 has 1 gram of salt per liter, tank 2 has fresh water, and tank 1 has 2 grams of
salt per per liter, Let x(t) be the amount of salt in tank 1 at time t, y(t) the amount of salt in tank 2 at time t, and z(t) the amount of salt in
tank 3 at timet.
The system of differential equations describing the tank system is
%3D
x(0) =
y(0) =
z(0) =
Characteristic polynomial:
Eigenvalue:
Matrix exponential:
The solution is
x(t) =
y(t) =
z(t) =
Find the approximate time required to reduce the concentration in tank 3 to half the original concentration.
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