If you are outdoors, the wind may make it feel a lot colder than the thermometer reads. You feel the windchill temperature, which if the air temperature is 20^circ F is given in 'F by W(v)=48.17-27.2v^0.16 where vis the wind velocity in mph for 5leqslant vleqslant 60^1 (a) If the air temperature is 20^circ F and the wind is blowing at 30 mph.what is the windchill temperature, to the nearest degree? The windchill temperature is square -F (b) Find W'(30) and explain what this means interms of windchill. Round your answer to three decimal places. W'(30)=boxed (square )square

Question

If you are outdoors, the wind may make it feel a lot colder than the thermometer reads. You feel the windchill temperature, which if the air temperature is 20^circ F is given in 'F by W(v)=48.17-27.2v^0.16 where vis the wind velocity in mph for 5leqslant vleqslant 60^1 (a) If the air temperature is 20^circ F and the wind is blowing at 30 mph.what is the windchill temperature, to the nearest degree? The windchill temperature is square -F (b) Find W'(30) and explain what this means interms of windchill. Round your answer to three decimal places. W'(30)=boxed (square )square

Answer 1

(a) To find the windchill temperature when the air temperature is

and the wind is blowing at 30 mph, we need to substitute

into the given formula for

.

First, calculate

:

Now, substitute this value back into the equation:

Rounding to the nearest degree, the windchill temperature is approximately

.(b) To find

, we need to take the derivative of

with respect to

and then evaluate it at

.

Taking the derivative with respect to

:

Now, substitute

into the derivative:

Rounding to three decimal places,

.This means that for every 1 mph increase in wind velocity, the windchill temperature decreases by approximately 0.137 degrees Fahrenheit when the wind is blowing at 30 mph.

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