Question

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

Answer 1

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

Explanation:

Guessed on the quiz and got it right

Answer 2

Option D

Explanation:

Given that the number of hours of daylight in a city in the northern hemisphere shows periodic behavior over time

Let t be the independent variable and no of hours H(t) be the dependent variable on t.

Maximum H(t) = 14.4 and average =12

Period = 365 days

If we fix a sine curve for this since period is 365, we must have coefficient of t as

`(2\pi)/(365) =0.017`

So the function H(t) will have sine term as sin 0.017t ... i

Since average = 12, we have

H(t) = 12+a sin 0.017t

for some suitable a.

To find a, use maximum

Maximum is when angle is 90 degrees i.e. when sine value =1

max H(5) = 14.4 = 12+a (1)

a =2.4

Hence correct equation would be'H(t) = 2.4sin(0.017t)+12

OPtion D is right answer.