Answer:
the total amount of water supplier per hour to the region within a circle of radius R=110 ( that is from distance r, 0<r<110)
![W(R) = 2\pi [1-(R+1)e^{-R}]](https://tex.z-dn.net/?f=W%28R%29%20%3D%202%5Cpi%20%5B1-%28R%2B1%29e%5E%7B-R%7D%5D)
Step-by-step explanation:
if f(r) describes the water supplied at a distance r , the total amount supplied inside a region that goes from 0 until the circle of radius R, is the sum of all f(r) values from 0 until R, that is the integral value over these limits.
The formula deduction can be found in the attached picture
There is an "r" that multiplies e^-r as result of changing from rectangular coordinates to polar ones.(dx*dy --> r*dr*da)
Considering that the shaded area is the part of the semi circle outside the triangle:
Area of circle= Pi x radius2 (this means radius squared)
Area of triangle= 1/2 x base x height
1/2 (because it is a semi circle) x 3.14 (in replacement of pi as directed by question) x 9squared= 127.17
127.17 - (1/2 x 18 x 9) = 46.17cmsquared
The second one, 82% is Erin's highest score
Do sin(90)*13/15 which gives you 0.87 then do inverse of sin-1(0.87) which angle A = 60.45 degrees