\input notes
\nopagenumbers

\leavevmode
\vbox{\halign{\bf#\hss\cr Math 226: Calculus IV\cr
Quiz 6\quad Mar.~4/16, 1993\cr
}}
\hfill
\vbox{\halign{#\cr \hbox to 2.5truein{Name:\hrulefill}\cr
\hbox to 2.5truein{Section:\hrulefill}\cr
}}


\bigskip
1. Ground water seeps into a cylindrical retention pond at a rate of $100~{\rm ft}^3$
per minute. There is storm drain above the pond and when the water reaches this
level it drains out at a rate proportional to the height~$h$ of the pond {\sl
above} the storm drain. A county engineer measures the flow in the storm drain
to be $50~{\rm ft}^3$ per minute when~$h$ is 3~in. Find the limiting value
for~$h$.



\vfill
2. A 1000~gal tank contains 500~gal of water having a 2\% concentration of
impurities. Pure water is added to the tank at a rate of 5~gal/min. At the
same time the water in the tank is being filtered. The filtering process
takes 10~gal/min from the tank, removes 50\% of the impurities, and returns
the filtered water to the tank at the same rate. The tank is kept
well mixed. What is the concentration of impurities when the tank is filled
to capacity?



\bye

