Answer:
The number of mosquitoes is maximum for 6.5 inches rainfall.
Step-by-step explanation:
The given function is
.... (1)
where, M(x) is number of mosquitoes in millions and x the June rainfall in inches.
We need to find the rainfall that produces the maximum number of mosquitoes.
Differential the above function with respect to x.
.... (2)
Equate first derivative equal to 0.



Differential function (2) with respect to x.

Double derivative is negative. So, the value of function is maximum at x=6.5.
Therefore, the number of mosquitoes is maximum for 6.5 inches rainfall.
Y= 4x
I think that’s the answer
Answer:
I believe the answer is 162 per season is the unit rate , I am really sorry if I am wrong.
![\bf \textit{using the 2nd fundamental theorem of calculus}\\\\ \cfrac{dy}{dx}\displaystyle \left[ \int\limits_{0}^{x}\ cos^{-1}(t)dt \right]\implies cos^{-1}(x) \\\\\\ f'(0.3)\iff cos^{-1}(0.3)\approx 1.26610367277949911126](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Busing%20the%202nd%20fundamental%20theorem%20of%20calculus%7D%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%5Cdisplaystyle%20%5Cleft%5B%20%5Cint%5Climits_%7B0%7D%5E%7Bx%7D%5C%20cos%5E%7B-1%7D%28t%29dt%20%5Cright%5D%5Cimplies%20cos%5E%7B-1%7D%28x%29%0A%5C%5C%5C%5C%5C%5C%0Af%27%280.3%29%5Ciff%20cos%5E%7B-1%7D%280.3%29%5Capprox%201.26610367277949911126)
now.. 0.3 is just a value...we'e assuming Radians for the inverse cosine, so, if you check, make sure your calculator is in Radian mode