Problem 39E

39. If two resistors with resistances $R_{1}$ and $R_{2}$ are connected in parallel, as in the figure, then the total resistance $R$, measured in ohms $(\Omega)$, is given by

$$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$$

If $R_{1}$ and $R_{2}$ are increasing at rates of $0.3 \Omega / \mathrm{s}$ and $0.2 \Omega / \mathrm{s}$, respectively, how fast is $R$ changing when $R_{1}=80 \Omega$ and $R_{2}=100 \Omega ?$

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