Question

The function t = 21.55 cosine (startfraction pi over 6 endfraction (m minus 7) ) 43.75 models the average high temperature in degrees fahrenheit each month throughout the year in anchorage, alaska, where m = 1 for january and m = 12 for december. approximately how many months is the average high temperature above freezing (32°f)? 7 8 10 11

Answer 1

To determine the number of months with average high temperature above freezing in Anchorage, Alaska, we can solve the inequality: 21.55 cosine [(pi/6) * (m - 7)] + 43.75 > 32.

Step-by-step explanation:

The given function t = 21.55 cosine [(pi/6) * (m - 7)] + 43.75 models the average high temperature in degrees Fahrenheit each month throughout the year in Anchorage, Alaska, where m = 1 for January and m = 12 for December.

To determine approximately how many months is the average high temperature above freezing (32°F), we need to find the values of m for which t > 32. We can set up the inequality:

21.55 cosine [(pi/6) * (m - 7)] + 43.75 > 32

Solving this inequality will give us the approximate number of months.

Answer 2

The given function models the average high temperature each month in Anchorage, Alaska, the number of months is the average high temperature above freezing (32°f) is C. 10 months.

Step-by-step explanation:

The given function t = 21.55 cos(π/6(m - 7)) - 43.75 models the average high temperature in degrees Fahrenheit each month throughout the year in Anchorage, Alaska.

In this equation, m represents the month, with m=1 for January and m=12 for December.

To determine the number of months where the average high temperature is above freezing (32°F), we need to find the values of m for which t is greater than 32°F.

Substituting 32 for t in the equation and solving for m, we have 32 = 21.55 cos(π/6(m - 7)) - 43.75.

By solving this equation, we find that the average high temperature is above freezing for 10 months (September to June).

Therefore the correct answer is C. 10 months.