The number of hours, H, of daylight in Madrid as a function of date is approxima

Question

The number of hours, H, of daylight in Madrid as a function of date is approximated by the formula H=12 + 2.4 sin(0.0172(t-80))dt 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 February: average hours = B. in June: average hours = C. over a year: average hours =

Explanation / Answer

(A)No. of hours =int(12+2.4sin(0.0172(t-80)))dt from 31 to 59; =12(59-31)-2.4cos(0.0172(59-80))/0.0172+2.4cos(0.0172(31-80))/0.0172;the value depends on whether the angles are in radian or degree; find out the value and divide by 28; similarly in (B) and (C) change the limits and divide the value by total no. of days of the month or year

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