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.

Answer 2

In the daylight on January 1, the total number of hours is 9.38, in the daylight on May 4, the total number of hours is 13.27, and in the daylight on October 28, the total number of hours is 10.23.

Given :

• Function  --  $\rm D(x) = \dfrac{7}{3} sin\dfrac{2\pi}{365}x+\dfrac{35}{3}$

• x represents the number of days after March 21.

First, determine the number of days from January 1 to March 21 which is equal to 80.

Now, at (x = -80) the given function becomes:

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

$\rm D(-80) = -\dfrac{7}{3} sin\dfrac{160\pi}{365}+\dfrac{35}{3}$

$\rm D(-80) = -\dfrac{7}{3} (0.98130)+\dfrac{35}{3}$

$\rm D(-80) \approx 9.38$

In the daylight on January 1, the total number of hours is 9.38.

Now, determine the number of days from January 1 to May 4 which is equal to 44.

At (x = 44) the given function becomes:

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

$\rm D(44) = \dfrac{7}{3} sin\dfrac{88\pi}{365}+\dfrac{35}{3}$

$\rm D(44) = -\dfrac{7}{3} (0.6870)+\dfrac{35}{3}$

$\rm D(44) \approx 13.27$

In the daylight on May 4, the total number of hours is 13.27.

Now, determine the number of days from October 28 to May 4 which is equal to 221.

At (x = 221) the given function becomes:

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

$\rm D(221) = \dfrac{7}{3} sin\dfrac{442\pi}{365}+\dfrac{35}{3}$

$\rm D(221) = -\dfrac{7}{3} (-0.6152)+\dfrac{35}{3}$

$\rm D(221) \approx 10.23$

In the daylight on October 28, the total number of hours is 10.23.

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https://brainly.com/question/2253924