The number of hours of daylight in a city in the northern hemisphere shows periodic behavior over time.

- The average number of daylight hours is 12

- The maximum number of daylight hours is 14.4

- The period is 365 days

- The day with the least sunlight is december 20

which equation models the number of hours of daylight on the day that comes t days after the shortest day of the previous year

A) H (t) = - 14.4 sin (0.017t)

B) H (t) = 14.4 sin (0.017t)

C) H (t) = - 2.4 sin (0.017t) + 12

D) H (t) = 2.4 sin (0.017t) + 12

Question

Mathematics

Blimpie

8 September, 13:13

The number of hours of daylight in a city in the northern hemisphere shows periodic behavior over time.

- The average number of daylight hours is 12

- The maximum number of daylight hours is 14.4

- The period is 365 days

- The day with the least sunlight is december 20

which equation models the number of hours of daylight on the day that comes t days after the shortest day of the previous year

A) H (t) = - 14.4 sin (0.017t)

B) H (t) = 14.4 sin (0.017t)

C) H (t) = - 2.4 sin (0.017t) + 12

D) H (t) = 2.4 sin (0.017t) + 12

+1

Answers (1)

Know the Answer?

Irvin Lutz · Answer 1

D.

After the 20th of December, the length of the day will start to increase. Therefore, the coefficient of sine must be positive. Moreover, the average value of 12 will be added to the value of sine as this is the average value.