The sector shows the area of a lawn that will be watered by a sprinkler. what is the area, rounded to the nearest tenth? use 3.14 for

The area of the sector which represents the lawn irrigated by the sprinkler is:

Recall:

Given:

length of arc = 10 feet

First, find the radius using the length of arc formula.

radius = 19.2 ft

Find the area of the sector:

Area of sector =

The area of the sector which represents the lawn irrigated by the sprinkler is:

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Step-by-step explanation:

step 1

Find the radius of the circle

we know that

A circumference of the circle subtends a central angle of 360 degrees

so

using proportion

step 2

Find the area of sector

we know that

The area of the circle subtends a central angle of 360 degrees

so using proportion

Let

x ----> the area of the sector

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

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