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

Answer:

$\frac{2 \pi r}{\frac{360^{\circ}}{n^{\circ}}}$ best completes this argument

Step-by-step 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 $\frac{360^{\circ}}{n^{\circ}}$

So, Number of sectors =  $\frac{360^{\circ}}{n^{\circ}}$

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

$\Rightarrow \frac{\pi \cdot d}{\frac{360^{\circ}}{n^{\circ}}}$

Diameter d = 2r (r = radius)

$\Rightarrow \frac{2 \pi r}{\frac{360^{\circ}}{n^{\circ}}}$

Option b is true

Hence$\frac{2 \pi r}{\frac{360^{\circ}}{n^{\circ}}}$ best completes this argument