Question

Assume that the number of hours of daylight in New Orleans in 1994 is given by the function D(x) = 7 3 sin 2π 365 x + 35 3 , where x represents the number of days after March 21. (a) Find the number of hours of daylight on January 1, May 4 and October 28. (Round your answers to two decimal places.)

Answer 1

Answer:

Here, the given function that represents the number of hours of daylight in New Orleans in 1994 is,

$D(x) = \frac{7}{3} \sin \frac{2\pi }{365}x + \frac{35}{3}$

Where,

x = the number of days after March 21

The number of days from 1 January to march 21 = 80

If x = -80, then,

$D(-80) = \frac{7}{3} \sin \frac{2\pi }{365}(-80) + \frac{35}{3}$

            $=\frac{7}{3} \sin (-\frac{160 \pi}{365}) + \frac{35}{3}$

            $=-\frac{7}{3} \sin (\frac{160 \pi}{365}) + \frac{35}{3}$

            $=-\frac{7}{3}(0.98130)+\frac{35}{3}$

           $\approx 9.38$

Therefore, the number of hours of daylight on January 1 are 9.38.

The number of days from march 21 to may 4 = 44

If x =44, then,

$D(44) = \frac{7}{3} \sin \frac{2 \pi}{365}(44) + \frac{35}{3}$

         $=\frac{7}{3} \sin (\frac{88 \pi}{365}) + \frac{35}{3}$

         $=\frac{7}{3}(0.6870) + \frac{35}{3}$

         $\approx 13.27$

Therefore, the number of hours of daylight on May 4 are 13.27.

The number of days from October 28 to may 4 = 221

If x = 221, then,

$D(221) = \frac{7}{3} \sin \frac{2 \pi}{365}(221) + \frac{35}{3}$

           $=\frac{7}{3} \sin (\frac{442 \pi}{365}) + \frac{35}{3}$

           $=\frac{7}{3}(-0.6152)+\frac{35}{3}$

           $\approx 10.23$

Therefore, the number of hours of daylight on October 28 are 10.23.