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The model for long-term average temperature f (x), in degrees Celsius, at the Willburn airport is represented by the equation f of x is equal to 5 times cosine of the quantity x over 12 end quantity plus 14 and 5 tenths period If x represents the month of the year, in which months will the temperature be 17°C?

The Model For Longterm Average Temperature F X In Degrees Celsius At The Willburn Airport Is Represented By The Equation F Of X Is Equal To 5 Times Cosine Of Th class=

Answer :

we have the function

[tex]f(x)=5\cos (\frac{x}{12})+14.5[/tex]

For f(x)=17C

substitute and solve for x

[tex]\begin{gathered} 17=5\cos (\frac{x}{12})+14.5 \\ 5\cos (\frac{x}{12})=17-14.5 \\ 5\cos (\frac{x}{12})=2.5 \\ \cos (\frac{x}{12})=\frac{1}{2} \end{gathered}[/tex]

Remember that

[tex]\cos (60^o)=\frac{1}{2}[/tex]

60 degrees=pi/3

so

x/12=pi/3

x=4pi

therefore

The answer is the third option

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