Answer
$\frac{dR}{dt}=\frac{1}{50}$
Work Step by Step
We are given:
$R_{1}=75$ and $R_{2}=50$
$\frac{dR_{1}}{dt}=-1$ and $\frac{dR_{2}}{dt}=0.5$
$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$
diffrentiating above with respect to t:
$\frac{1}{R^2}\frac{dR}{dt}=\frac{1}{R_{1}^2}\frac{dR_{1}}{dt}+\frac{1}{R_{2}^2}\frac{dR_{2}}{dt}$
$(\frac{1}{R_{1}}+\frac{1}{R_{2}})^2\frac{dR}{dt}=\frac{1}{R_{1}^2}\frac{dR_{1}}{dt}+\frac{1}{R_{2}^2}\frac{dR_{2}}{dt}$
on putting in the values:
$(\frac{1}{75}+\frac{1}{50})^2\frac{dR}{dt}=\frac{1}{75^2}(-1)+\frac{1}{50^2}(0.5)$
$(\frac{5}{150})^2\frac{dR}{dt}=\frac{1}{150^2}(0.5)$
$\frac{dR}{dt}=\frac{1}{50}$
thus,$\frac{dR}{dt}=\frac{1}{50}$
