The number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by: m(x)=-x^(2)+14 x How many centimeters of rain will produce the maximum number of mosquitoes? centimeters

Given quadratic function: We are given the quadratic function m(x) = -x^2 + 14x, which models the number of mosquitoes (in millions) as a function of rainfall x (in centimeters). To find the number of centimeters of rain that will produce the maximum number of mosquitoes, we need to find the vertex of the parabola represented by this quadratic function. The x-coordinate of the vertex will give us the amount of rainfall that maximizes the number of mosquitoes.Calculating the value of h: The vertex of a parabola given by the function f(x) = ax^2 + bx + c is at the point (h, k), where h = -b/(2a). In our case, a = -1 and b = 14. Let's calculate the value of h. h = -b/(2a) = -14/(2 * -1) = -14/(-2) = 7Rainfall that maximizes mosquitoes: The value of h = 7 centimeters represents the amount of rainfall that will produce the maximum number of mosquitoes according to the model m(x) = -x^2 + 14x.

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The number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by:

m(x)=-x^(2)+14 x
How many centimeters of rain will produce the maximum number of mosquitoes?
centimeters

The number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by: $\newline$ $m(x)=-x^{2}+14x$ $\newline$ How many centimeters of rain will produce the maximum number of mosquitoes? $\newline$ $\text{centimeters}$

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Q. The number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by:

\newline

m(x)=-x^{2}+14x

\newline

How many centimeters of rain will produce the maximum number of mosquitoes?

\newline

\text{centimeters}

Given quadratic function: We are given the quadratic function $m(x) = -x^2 + 14x$ , which models the number of mosquitoes (in millions) as a function of rainfall $x$ (in centimeters). To find the number of centimeters of rain that will produce the maximum number of mosquitoes, we need to find the vertex of the parabola represented by this quadratic function. The $x$ -coordinate of the vertex will give us the amount of rainfall that maximizes the number of mosquitoes.
Calculating the value of h: The vertex of a parabola given by the function $f(x) = ax^2 + bx + c$ is at the point $(h, k)$ , where $h = -\frac{b}{2a}$ . In our case, $a = -1$ and $b = 14$ . Let's calculate the value of h. $\newline$ $h = -\frac{b}{2a} = -\frac{14}{2 \cdot -1} = -\frac{14}{-2} = 7$
Rainfall that maximizes mosquitoes: The value of $h = 7$ centimeters represents the amount of rainfall that will produce the maximum number of mosquitoes according to the model $m(x) = -x^2 + 14x$ .