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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

Respuesta :

Answer:

D. [tex]H(t)=2.4\sin (0.017t)+12[/tex]

Step-by-step explanation:

We are given that,

The number of hours in daylight in a city is represented by a periodic function.

Now, according to the options, the periodic function being represented is the sine function.

The average number of daylight hours is 12 with maximum and minimum number of daylight hours is 14.4 and 9.6.

So, we get option A and B are not correct as they do not include the average 12 hours of daylight.

Further, the period is given to be 365 days.

Then the period of the sine function will be [tex]\frac{2\pi}{365}=0.017[/tex]

Thus, the function is of the form [tex]H(t)=a\sin (0.017t)+12[/tex].

Now, we will find the value of 'a'.

Since, sine function has maximum value when t= 90° and is given by 14.4

So for t= 90°, the value of [tex]a\sin (0.017t)= 1[/tex]

Thus, [tex]14.4=a+12[/tex]

i.e. [tex]a==14.4-12[/tex]

i.e. a= 2.4

Hence, the required function is [tex]H(t)=2.4\sin (0.017t)+12[/tex].

Answer:

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

Step-by-step explanation:

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