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The area of a sector of a circle is given by the equation [tex]A = \frac{\pi r^2 S}{360}[/tex], where [tex]r[/tex] is the radius of the circle and [tex]S[/tex] is the angle measure of the sector.

If Mia solved this equation for [tex]S[/tex], which of the following equations did she write?

A. [tex]360 A + \pi r^2[/tex]
B. [tex]360 A - \pi r^2[/tex]
C. [tex]\frac{360 + A}{\pi r^2}[/tex]
D. [tex]\frac{360 A}{\pi r^2}[/tex]

Sagot :

GinnyAnsweridn
To solve the given equation for the angle measure [tex]\( S \)[/tex] of the sector, we start with the equation for the area [tex]\( A \)[/tex] of a sector of a circle:

[tex]\[ A = \frac{\pi r^2 S}{360} \][/tex]

We need to isolate [tex]\( S \)[/tex] on one side of the equation. Here is the step-by-step process:

1. Multiply both sides by 360:
[tex]\[ 360A = \pi r^2 S \][/tex]

2. Divide both sides by [tex]\( \pi r^2 \)[/tex]:
[tex]\[ S = \frac{360 A}{\pi r^2} \][/tex]

Thus, the resulting equation, which expresses [tex]\( S \)[/tex] in terms of [tex]\( A \)[/tex] and [tex]\( r \)[/tex], is:

[tex]\[ S = \frac{360 A}{\pi r^2} \][/tex]

Therefore, the correct equation Mia wrote is:

[tex]\[ \boxed{\frac{360 A}{\pi r^2}} \][/tex]
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