Question

An agricultural sprinkler distributes water in a circular pattern of radius 110 ft. It supplies water to a depth of e−r feet per hour at a distance of r feet from the sprinkler. (Do not substitute numerical values; use variables only.) (a) If 0 < R ≤ 110, what is the total amount of water supplied per hour to the region inside the circle of radi

Answer 1

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)

$W(R) = 2\pi [1-(R+1)e^{-R}]$

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)