SOLUTION: The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x)=19x-x^2. What rainfall produces the maximum number of mosquitoes? Hint

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Question 131506: The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x)=19x-x^2. What rainfall produces the maximum number of mosquitoes? Hint: Find the maximum of the parabola.
Answer by AdolphousC(70) About Me  (Show Source):
You can put this solution on YOUR website!
You need either a calculator or some paper and pencil for this one. If you have a calc plug the equation into the y= and use 2nd trace maximum.
If you don't have a calculator then you first need to find the zeros. This is easy using factoring.
19x-x^2
Factor out an x x(19-x) set each to zero.
x = 0 and x = 19.
those are where the parabola crosses the x-axis. Since parabolas are symmetrical, the x value of the max falls 1/2 way between the zeros at 9.5
Plug in 9.5 for x in the original equation. Solve for the number of Mosquitos and there is your answer.