The number of hours, $H$, of daylight in Madrid as a function of date is approximated by the formula $$H=12 + 2.4 \sin\left(0.0172(t-80)\right),$$ where $t$ is the number of days since the start of the year. (We can think of $t=0$ as the stroke of midnight on Dec. 31/Jan 1; thus, January falls between $t=0$ and $t=31$, February falls between $t=31$ and $t=59$, etc.).

Find the average number of hours of daylight in Madrid (assuming in each case that it is not a leap year):

A. in November: average hours =

B. in July: average hours =

C. over a year: average hours =

Be sure that you give a reasonably accurate estimate for parts A and B, and that you can explain why the relative magnitudes of your answers to parts A, B, and C are reasonable.