SOLUTION: f(x)= .0106x^2 + 1.24x + 565 if 1 < or equal x < 84
-.0202x^2 + 6.97x + 295 if 84 < or equal x < 263
.0148x^2 -11.1x + 2632 if 263 < or equal x < or equal 365
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Question 348989: f(x)= .0106x^2 + 1.24x + 565 if 1 < or equal x < 84
-.0202x^2 + 6.97x + 295 if 84 < or equal x < 263
.0148x^2 -11.1x + 2632 if 263 < or equal x < or equal 365
where x represents the number of days of the year, starting on jan 1 (x=1)
Determine the number of minutes of daylight on days 32, 90 and 270. Round to the nearest minute and label each. **** I have this part done ******
On what day is the number of minutes the greatest? Show your work!!!
****** This is the part I cannot figure out ******
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
We know that the summer solstice happens around June 21 every year, so that is where we should be looking for the answer to this problem. Note that the summertime function (the one that applies in the range day 84 to day 263) has a lead coefficient that is less than zero, hence the parabola for the middle part of the year opens downward. Hence the vertex of this parabola will be a maximum.
For a parabola represented by the function:
\ =\ ax^2\ +\ bx +\ c)
Has an 
-coordinate given by 
. Calculate the -coordinate of the middle quadratic and you have your answer.
John
My calculator said it, I believe it, that settles it
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