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A2 - Applied Math 250 Assignment#2 Winter 2009 due January...

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Unformatted text preview: Applied Math 250 Assignment #2 Winter 2009 due January 27th A/ Problem Set 1 #6 (all), #7, #8a, #11 Note: Don’t spend too much time struggling with #6viii; read the question, and keep in mind that the value of the method of undetermined coefficients is that it should be a quicker method than using an integrating factor! B / I/ Suppose that after one experiment, a tank used for hydrodynamical experiments contains 200 litres of a dye solution with a concentration of 1 gram/ litre. For the next experiment, the tank is to be rinsed with clear water and filled to 300 litres. If the clear water is pumped in at 3 litres/minute, and the solution (well-mixed) is drained at 2 litres/minute, what concentration of dye is left when the tank is filled? How does this change if the clear water is pumped in at only 2.5 litres/ minute? 11/ a) Suppose that a given radioactive element A decomposes into a second ra- dioactive element B, and that B in turn decomposes into a third element C. If the amount of A present initially is are, if the amounts of A and B present at a later time t are :r and y, respectively, and if [91 and k2 are the rate constants of these two reactions, find y as a function of it. Note: Consider In and kg to be positive, so, for example, one of the equations dz you’ll need is E = —k1x (the other equation is slightly less simple). Also, you may assume that 1;] 75 k2. Radon is an intensely radioactive gas (with a half—life of 3.8 days) that is pro— duced as the immediate product of the decay of radium (which has a half-life of 1600 years). The atmosphere contains traces of radon near the ground as a result of seepage from soil and rocks, all of which contain minute quantities of radium. In recent years there has been concern in some parts of Canada about possibly dangerous accumulations of radon in the enclosed basements of houses whose concrete feundations and underlying ground contain appre— ciably greater quantities of radium than normal because of nearby uranium mining. If the rate constants (fractional losses per unit time, in years) for the decay of radium and radon are k1 = 000043 and k2 = 66, use the result of part (a) to determine how long after the completion of a basement the amount of radon will be at a maximum. ...
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