Kindly solve all parts of the problem related to Differential equations. These p
ID: 2844527 • Letter: K
Question
Kindly solve all parts of the problem related to Differential equations.
These problems are adapted from Problem #46 in Section 1.5. A reservoir has a 1 km2 surface area and an average depth of 2 m, and it is initially full of fresh water. At t t = 0, a polluted water starts to flow into the river at a rate of 200,000 m3 per month. The concentration of the pollutant at time t is given by c(t) = 10(1 + cos(t)) L/S2 Well-mixed water flows out, of the reservoir at the same rate. Set up an init ial value problem modelling the situation. Solve the 1VP Use? a computer to graph your solution. What happens to the level of pollution in the long run? Try to explain what you observe.Explanation / Answer
1)putting t=0
in equation gives
c(0)=10(1+cos(0))(2/(1000*1000))
c(0)=40*10^-6
2)differenting
will give
c'(t)=l/s^2*-sin(t)
3)In long run i.e.when t=infinity
sin(t)=[-1,1]
becoz sin always lie b/w[-1,1]
therefore c'(t)=2*10^-6
which is level of pollution
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