question 18 1 pts suppose the function h(t)=8.5 sin(0.017t - 1.35)+12 models the hours of sunlight for a…

question 18 1 pts suppose the function h(t)=8.5 sin(0.017t - 1.35)+12 models the hours of sunlight for a town in alaska, where t = 1 is the first day of the year. based on the function, what is the approximate range of daylight hours for the town? o 3.5 to 20.5 o 4 to 20 o 4.5 to 19.5 o 5 to 19

question 18 1 pts suppose the function h(t)=8.5 sin(0.017t - 1.35)+12 models the hours of sunlight for a town in alaska, where t = 1 is the first day of the year. based on the function, what is the approximate range of daylight hours for the town? o 3.5 to 20.5 o 4 to 20 o 4.5 to 19.5 o 5 to 19

Answer

Answer:

A. 3.5 to 20.5

Explanation:

Step1: Recall sine - function range

The range of the sine function $y = \sin(x)$ is $[- 1,1]$.

Step2: Find minimum of $H(t)$

When $\sin(0.017t - 1.35)=-1$, $H(t)=8.5\times(-1)+12$. $H(t)=12 - 8.5=3.5$.

Step3: Find maximum of $H(t)$

When $\sin(0.017t - 1.35)=1$, $H(t)=8.5\times1 + 12$. $H(t)=12 + 8.5=20.5$. So the range of $H(t)$ is from 3.5 to 20.5.