Unformatted text preview: Applied Math 250 Assignment #2 Spring 2009 due May 26th A/ Problem Set 1 #6 (all), #7, #Sa, #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 / 1/ 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 4 litres/minute, and the solution (wellmixed) 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 :30, if the amounts of A and B present at a later time t are m and g, respectively, and if k1 and k2 are the rate constants of these two reactions, ﬁnd y as a function of 25. Note: Consider [£1 and kg to be positive, so, for example, one of the equations
da: you’ll need is E = —k1:r (the other equation is slightly less simple). Also, you may assume that 131 74 k2. Radon is an intensely radioactive gas (with a halflife of 3.8 days) that is pro
duced as the immediate product of the decay of radium (which has a halflife
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 foundations 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 = 0.00043 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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 Spring '08
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