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The wind-chill index (that is, apparent temperature) is a function W of actual temperature T ...

Question:

The wind-chill index (that is, apparent temperature) is a function {eq}W {/eq} of actual temperature {eq}T {/eq} ({eq}^{\circ} {/eq}C) and wind speed {eq}v {/eq} (km/hr):

{eq}W(T,v) = 13.12 + 0.6215T - 11.37v^{0.16} + 0.3965Tv^{0.16} {/eq}.

Assume that {eq}T = -23^{\circ} {/eq}C and {eq}v = 22 {/eq} km/hr.

(a) Compute {eq}\frac{\partial W}{\partial T} {/eq} and {eq}\frac{\partial W}{\partial v} {/eq} at the point {eq}(-23,22) {/eq}.

(b) If the actual temperature were to decrease by one degree, then by how much would you expect the apparent temperature to drop? (Use your answer in (a).)

(c) If the actual wind speed were to decrease by 1 km/hr, then by how much would you expect the apparent temperature to rise? (Use your answer in (a).)

Differentiation:

Differentiation is used to determine the rate of change in one variable with respect to other variables. Differentiation is a measure of how a function changes its value as the input changes.

Answer and Explanation: 1

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Given

The wind-chill index is given by {eq}W\left( {T,v} \right) = 13.12 + 0.6215T - 11.37{v^{0.16}} + 0.3965T{v^{0.16}} {/eq}.

{eq}T = - 23^\circ...

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