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Math 112 Solutions for 3.6, p. 279

2.
$ -6\pi$ cm$ ^{2}$/sec.
4.
$ 1.8\pi$ in$ ^{3}$/sec.
5.
$ \frac{dh}{dt}=\frac{2.4}{\pi}$ ft/min.
7.
150,000 ft/hr
9.
$ -\frac{1}{\sqrt 2}$ ft/sec.
10.
-9 m/sec.
13.
$ \frac{100\pi}{3}$ m/hr.
14.
$ \frac{dP}{dt}=0.051k$.
17.
$ \frac{1}{2}$ /year.
19.
We are told $ \frac{dV}{dt}=-kS$. From $ V=\frac{4}{3}\pi r^{3}$, we get $ \frac{dV}{dt}=4\pi r^{2}\frac{dr}{dt}$. But $ S=4\pi r^{2}$, so $ 4\pi
r^{2}\frac{dr}{dt}=-k(4\pi r^{2})\Rightarrow \frac{dr}{dt}=-k$.





Jason Grout 2003-03-06