Question

3 Consider two tanks, A and B, each holding 200 litres of water. A pipe pumps water from tank A to tank B at a rate of 5 1/min. At the same time another pipe pumps liquid from tank B to tank A at the same rate. At time t = 0, X0 kg of a chemical X is dissolved into tank A, and tank B has yo kg of the same chemical X dissolved into it. i) Write down the system of differential equations satisfied by c(t) and y(t), the quantity of the chemical X in tanks A and B respectively, ii) Find the eigenvalues and eigenvectors of the resulting matrix form. iii) Show that the amount of the chemical X in either tank approaches (30+ yo) ast approaches infinity.

Answer 1

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- " The eigen roluce (f) eigen rector of resulting matrix form in TP(X) = 1A-XII] PO PU Telenas. 200 so DOO PCA)- [E.+9]-[koo]. PCA) = 1[A+ Yo] » ^[ato Yo] 0 P(x) [x = -10 when [1/2] ther. Ri= ( 2 ] - when [= then R2 { } ] - ☺ From evo & © the solo ic. =>\ x=C, R, e Yot to Rect) cs Stanned with CamScanner

The amount of chemical & in either approached h(notyo). took By consider the (6,cs) at some Contents then we geti The city exotica - cale nde kot cele maig where the inital reluce of c, & c. > C= korteCz = more Replacing the reluce we get bores Je more Die beste moment to when the inital to find roluce tayo then . + Hotyo 3040 (13) ***kastes, sobre ( 4 ) 1 V - *** (*) Syed) with CamScanner