Question

]solomon needs to justify the formula for the arc length of a sector. which expression best completes this argument? the circumference of a circle is given by the formula c=pi * d , where d is the diameter. because the diameter is twice the radius, c= 2 * pi * r. if equally sized central angles, each with a measure of n°, are drawn, the number of sectors that are formed will be equal to 360°/n° the arc length of each sector is the circumference divided by the number of sectors, or _____. therefore, the arc length of a sector of a circle with a central angle of n° is given by 2*pi*r*n/360 or pi*r*n/180 . a. 2*pi*r/270/n b. 2*pi*r/360/n c. 2*pi*r/180/n d. 2*pi*r/90/n

Answer 1

2 pie r/ 360 over n

Explanation:

just did this

Answer 2

`(2 \pi r)/((360^(\circ))/(n^(\circ)))` best completes this argument

Explanation:

Circumference of circle =
`\pi \cdot d`

Where d is the diameter of circle

We are given that if equally sized central angles, each with a measure of n°, are drawn, the number of sectors that are formed will be equal to
`(360^(\circ))/(n^(\circ))`

So, Number of sectors =
`(360^(\circ))/(n^(\circ))`

The arc length of each sector is the circumference divided by the number of sectors

`\Rightarrow (\pi \cdot d)/((360^(\circ))/(n^(\circ)))`

Diameter d = 2r (r = radius)

`\Rightarrow (2 \pi r)/((360^(\circ))/(n^(\circ)))`

Option b is true

Hence
`(2 \pi r)/((360^(\circ))/(n^(\circ)))` best completes this argument