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The number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes) as a function of rainfall (in
centimeters) is modeled by:
m(x) = -(x – 5)2 + 25
What is the maximum possible number of mosquitoes?
million mosquitoes
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Answer 1

25 million

Explanation:

Answer 2

The maximum possible number of mosquitoes is 25 millions

Explanation:

Let

m(x) -----> the number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes)

x ----> the rainfall in centimeters

we have

`m(x)=-(x-5)^(2) +25`

This is a quadratic equation (vertical parabola) open downward

The vertex is the maximum

we know that

The maximum possible number of mosquitoes is equal to the y-coordinate of the vertex

Find out the coordinate of the vertex

The general equation of a vertical parabola in vertex form is equal to

`y=a(x-h)^(2) +k`

where

a is a coefficient

(h,k) is the vertex

so

In this problem

a=-1 (open downward)

(h,k)=(5,25)

The y-coordinate is 25

therefore

The maximum possible number of mosquitoes is 25 millions