Question

The hours of daylight,y, in Utica in days, x, from January 1, 2013 can be modeled by the equation y=3.06sin(0.017x-1.40) + 12.23. How many hours of daylight, to the nearest tenth,does this model predict for February 14, 2013?
(1) 9.4
(2) 10.4
(3)12.1
(4)12.2

Answer 1

The month of January has 31 days, so from January 1st to February 14th, there are 31 + 14 or 45 days, namely x = 45.

y = 3.06 * sin[ 0.017(45) - 1.40 ] + 12.23.

make sure your calculator is in Degree mode.

Answer 2

Answer:

Option (4) 12.2

Step-by-step explanation:

Hours of daylight, y, in Utica in days, x, from January 1, 2013 can be modeled by the equation

y = 3.06 sin ( 0.017x - 1.40 ) + 12.23

We have to calculate the hours of daylight from the given equation for February 14, 2013.

From January 1, 2013 to February 14, 2013 number of days = 31 + 14 = 45 days.

Now we place x = 45 days in the equation

y = 3.06 sin (0.017 × 45 - 1.40) + 12.23

= 3.06 sin ( 0.765 - 1.40 ) + 12.23

= 3.06 sin ( - 0.635 ) + 12.23

= 3.06 ( - 0.0111) + 12.23

= -0.0339 + 12.23 = 12.196 = 12.20

Option (4) 12.2 is the correct answer.