Question

The hours of daylight, y, in Utica in days x from January 1, 2013 can be modeled by the equation y = 2.89sin(0.0145x-1.40) + 10.99. How many hours of daylight, to the nearest tenth, does this model predict for February 21, 2013?

Answer 1

9.3 hours

Explanation:

Given

`y = 2.89\sin(0.0145x-1.40) + 10.99.`

Required

Hours of sunlight on Feb 21, 2013

First, calculate the number of days from Jan 1, 2013 to Feb 21, 2013

`days = 52`

So:

`x = 52`

So, we have:

`y = 2.89\sin(0.0145x-1.40) + 10.99.`

`y = 2.89\sin(0.0145*52-1.40) + 10.99.`

`y = 2.89\sin(0.754-1.40) + 10.99.`

`y = 2.89\sin(-0.646) + 10.99.`

`y = 2.89*-0.6020 + 10.99.`

`y = -1.740 + 10.99.`

`y = 9.25`

`y = 9.3` --- approximated