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The average daily high temperature in Seattle is modeled by the function T = –15 cos(πm/6)+ 61, where T is the temperature in °F, and m is the number of months since the beginning of the year. What is the value of m when the average daily high temperature T is 76°F

The Average Daily High Temperature In Seattle Is Modeled By The Function T 15 Cosπm6 61 Where T Is The Temperature In F And M Is The Number Of Months Since The class=

Sagot :

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Answer:

[tex]m = 6[/tex]

Step-by-step explanation:

[tex]T = -15cos(\frac{\pi m}{6}) +61[/tex]

[tex]76 = -15cos(\frac{\pi m}{6}) +61[/tex]

[tex]76-61 = -15cos(\frac{\pi m}{6})[/tex]

[tex]15 = -15cos(\frac{\pi m}{6})[/tex]

[tex]\frac{15}{-15} = cos(\frac{\pi m}{6})[/tex]

[tex]-1 = cos(\frac{\pi m}{6})[/tex]

[tex]cos^{-1}( -1) = \frac{\pi m}{6}[/tex]

[tex]\pi = \frac{\pi m}{6}[/tex]

[tex]6\pi = \pi m[/tex]

[tex]m = 6[/tex]

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