Question

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

Answer 1

The value of m when the average daily high temperature T is 76°F, based on a solved equation, is 6 months since the beginning of the year.

Given function of the average daily high temperature in Seattle:

T = –15 cos(πm/6)+ 61

Where T = the temperature in °F,

m = the number of months since the beginning of the year

When the average daily high temperature T is 76°F, we can set up the equation to find m:

76 = -15 cos(πm/6) + 61

Subtract 61 from both sides:

15 = -15 cos(πm/6)

Divide both sides by -15:

-1 = cos(πm/6)

To find the value of m, we need to find the angle whose cosine is -1. This angle is π, or 180 degrees. So:

πm/6 = π

Multiply both sides by 6/π:

m = 6

Thus, the value of m when the average daily high temperature T is 76°F is 6 months since the beginning of the year.

Answer 2

`m = 6`

Explanation:

`T = -15cos((\pi m)/(6)) +61`

`76 = -15cos((\pi m)/(6)) +61`

`76-61 = -15cos((\pi m)/(6))`

`15 = -15cos((\pi m)/(6))`

`(15)/(-15) = cos((\pi m)/(6))`

`-1 = cos((\pi m)/(6))`

`cos^(-1)( -1) = (\pi m)/(6)`

`\pi = (\pi m)/(6)`

`6\pi = \pi m`

`m = 6`