$($e$.)85\mathrm{.}74$

$7.$ Suppose the formula for wind chill $C($in degrees Fahrenheit$)$ is given by $C=37\mathrm{.}050\mathrm{.}6844T-37\mathrm{.}59v^{0\mathrm{.}16}0\mathrm{.}4425v^{0\mathrm{.}16}$ where $v$ is the wind speed in miles per hour and $T$ is the temperature in degrees Fahrenheit. The wind speed is $23-3$ miles per hour and the temperature is $8-1$ Fahrenheit. Use $dC$ to estimate the relative error in calculating the wind chill. Round your answer to two decimal places.

a$.\frac{dC}{C}=-12\mathrm{.}62$

b$.\frac{dC}{C}=-12\mathrm{.}62$

c$.\frac{dC}{C}=-0\mathrm{.}19$

d$.\frac{dC}{C}=-17\mathrm{.}81$

e$.\frac{dC}{C}=-12\mathrm{.}81$