The irrigation system for a farm sprays water in circular patterns. Each sprinkler is connected to a pipe in the center of a circle and rotates around that pipe. The largest sprinkler sprays water 20 feet. What is the circumference of the circle irrigated by this sprinkler?

40 π ft or 125.6ft

Step-by-step explanation:

If the sprinkler can spray water 20 ft, that means the radius is 20 ft and to get the circumference we do 2 r π

or 2r*3.14

The answer is either 40 π ft

or 125.6ft

Here the irrigation sprinkler is pivoted at an angle
θ
=
40
∘
=
40
π
180
rad.
It waters a circular sector of area
A
=
2060
f
t
2
.
If the length of the sprinkler be
L
ft. It will be radius of the circular sector watered.
Hence
1
2
×
θ
in radian
×
L
2
=
A
⇒
L
=
√
2
A
θ
=
√
2
⋅
2060
⋅
180
40
π
≈
76.8
ft

The first step is to draw the graph. Once we do this, we can easily see that the vertex is at (12,64), which means that the hourly profit of coffee sold is highest at 12 cups of coffee. The x-intercepts are at x = 4 and x = 20, which means that between 0 and 4 (inclusive) cups of coffee sold, and after 20 cups sold, there is no profit.