The number of mosquitoes, M(x), in millions, in a certain area depends on the June rainfall, x, in inches. The function that models the phenomenon is LaTeX: M\left(x\right)=16x-x^2M ( x ) = 16 x − x 2. Find the amount of rainfall that will maximize the number of mosquitoes. What is the maximum number of mosquitoes? (Hint: find the vertex

8 inches of rainfall will maximize the number of mosquitoes.

Maximum number of mosquitoes = 64 millions

Step-by-step explanation:

We are given the following in the question:

where M(x) is the number of mosquitoes in millions and x is the rainfall in inches.

First, we differentiate M(x) with respect to x, to get,

Equating the first derivative to zero, we get,

Again differentiation M(x), with respect to x, we get,

Thus, by double differentiation test the maxima occurs at x = 8 for M(x).

Thus, maximum number of mosquitoes are there when the rainfall is 8 inches.

Maximum number of mosquito:

Thus, maximum number of mosquito is 64 millions.

Vertex: (8,64)

The attached image shows the graph.

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.