The minutes of daylight each day of the year in a certain northern town are approximately modeled by the function
f(x) = -1/25(x-173)^2 + 1424
Where x represents the day of the year (January 1 is x=1) and f(x) represents the minutes of sunlight.
To find the maximum number of daylight minutes, we need to find the vertex of the parabolic function f(x) = -1/25(x-173)^2 + 1424.
The x-coordinate of the vertex can be found by using the formula x = -b/2a, where a = -1/25 and b = 173.
x = -173 / (2*(-1/25))
x = -173 / (-2/25)
x = -173 * (-25/2)
x = 173 * 25 / 2
x = 4325 / 2
x = 2162.5
Therefore, the maximum number of daylight minutes occurs on day 2162.
To find the maximum number of daylight minutes, plug x = 2162 into the function f(x):
f(2162) = -1/25(2162-173)^2 + 1424
f(2162) = -1/25(1989)^2 + 1424
f(2162) = -1/25 * 3956041 + 1424
f(2162) = -158241.64 + 1424
f(2162) = 141977.36
Therefore, the maximum number of daylight minutes in this town is approximately 141977 minutes.
The vertex of this function means that on the longest day of the
year June 22nd (day 173)- this town saw
(Blank) minutes of sunlight.
:1,400
: 1,424
:: 1,350
: 450
:: 175
The correct answer is:
1,424 minutes