Question

Please help me thank you

Answer 1

`r = (5)/(3)`

Explanation:

The formula to find the arc length of a circle is:

`\boxed{\begin{array}{l}\underline{\sf Arc\; length}\\\\\textsf{Arc length $=r \theta$}\\\\\textsf{where:}\\\phantom{ww}\bullet\; \textsf{$r$ is the radius.}\\ \phantom{ww}\bullet\;\textsf{$\theta$ is the angle measured in radians.}\end{array}}`

Given values:

`\textsf{Arc length}=(5\pi)/(2)`

`\theta=(3\pi)/(2)`

To find the radius, substitute the given values into the formula:

`(5\pi)/(2)=r \cdot (3\pi)/(2)`

Now, solve for r by multiplying both sides of the equation by 2/3π:

`(5\pi)/(2)\cdot (2)/(3\pi)=r \cdot (3\pi)/(2) \cdot (2)/(3\pi)`

`r=(5\diagup\!\!\!\!\!\pi)/(\diagup\!\!\!\!\!2)\cdot (\diagup\!\!\!\!\!2)/(3\diagup\!\!\!\!\!\pi)`

`r = (5)/(3)`

Therefore, the radius of the provided circle is:

`\Large\boxed{\boxed{r = (5)/(3)}}`