the number of hours of daylight on a given day in city a is given by the following function, where x is the…

the number of hours of daylight on a given day in city a is given by the following function, where x is the number of days after january 1. y = 2 sin((2π/365)(x - 81)) + 12 use this function to answer parts a through e. a. what is the amplitude of this function? 2 (simplify your answer.) b. what is the period of this function? 365 (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) c. how many hours of daylight are there on the longest day of the year? hours (round to the nearest hour as needed.)

the number of hours of daylight on a given day in city a is given by the following function, where x is the number of days after january 1. y = 2 sin((2π/365)(x - 81)) + 12 use this function to answer parts a through e. a. what is the amplitude of this function? 2 (simplify your answer.) b. what is the period of this function? 365 (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) c. how many hours of daylight are there on the longest day of the year? hours (round to the nearest hour as needed.)

Answer

Explanation:

Step1: Recall sine - function properties

The general form of a sine function is $y = A\sin(B(x - C))+D$. The maximum value of $\sin(B(x - C))$ is 1.

Step2: Identify the values in the given function

For the function $y = 2\sin\left(\frac{2\pi}{365}(x - 81)\right)+12$, we have $A = 2$ and $D=12$.

Step3: Calculate the maximum value of the function

When $\sin\left(\frac{2\pi}{365}(x - 81)\right)=1$, we find $y$ by substituting into the function: $y=2\times1 + 12$. $y=2 + 12=14$.

Answer:

14