Respuesta :
On October 24, 218 days after March 20, there will be 10 hours of sunlight.
The number of daily sunlight hours of a particular location is modelled by the trigonometric equation,
l(t) = 12 + 3.5sin (2[tex]\pi[/tex]/365t)
Here , L(t)= Number of sunlight hours in a day.
t = Number of days after 20th March .
Now we are required to determime the day during first 365 on which there are 10 sunlight hours ,that is, we need the value of "t" for which L(t) =10 hours. So in the given equation by putting L(t)= 10 and solving for t , follows as,
l(t) = 12 + 3.5sin (2[tex]\pi[/tex]/365t)
10 = 12 + 3.5sin (2[tex]\pi[/tex]/365t)
10-12 = 3.5sin (2[tex]\pi[/tex]/365t)
-2 = 3.5sin (2[tex]\pi[/tex]/365t)
-2/3.5 = sin (2[tex]\pi[/tex]/365t)
-0.574 = sin (2[tex]\pi[/tex]/365t)
For the inverse function of y = sin x
sin ⁻¹(y) =x + 2n[tex]\pi[/tex]
Now as we are required to calculate the day having 10 sunlight hours in first 365 days so putting n=0 we get,
t = -35.3521 or t =217.9422
Now t can not be negative as we want to find the day after march 20 having 10 sunlight hours. So neglecting t=-35.3521 . Now we get t=217.9422 .
Rounding off we get ,t=218 which is the required answer.
Hence, 218 days after march 20 i.e on October 24 it will have 10 sunlights.
Learn more about trigonometric equation here:
brainly.com/question/27821667
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