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A circular arc has measure 5 m and Is Intercepted by a central angle of 07 radians. Find the radlus r of the circle. Do not round any Intermediate computations, and round your answer to the nearest tenth. r=square m

Pergunta

A circular arc has measure 5 m and Is Intercepted by a central angle of 07 radians. Find the radlus r of the circle.
Do not round any Intermediate computations, and round your answer to the nearest tenth.
r=square m

A circular arc has measure 5 m and Is Intercepted by a central angle of 07 radians. Find the radlus r of the circle. Do not round any Intermediate computations, and round your answer to the nearest tenth. r=square m

Solução

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DanielleElite · Tutor por 8 anos

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The radius \(r\) of the circle is approximately \(7.1m\).

Explicação

## Step 1<br />The problem involves the relationship between the length of an arc, the radius of the circle, and the angle subtended by the arc at the center of the circle. This relationship is given by the formula:<br />### \(s = r\theta\)<br />where \(s\) is the length of the arc, \(r\) is the radius of the circle, and \(\theta\) is the angle in radians.<br /><br />## Step 2<br />In this problem, we are given the length of the arc \(s = 5m\) and the angle \(\theta = 0.7\) radians. We are asked to find the radius \(r\).<br /><br />## Step 3<br />We can rearrange the formula to solve for \(r\):<br />### \(r = \frac{s}{\theta}\)<br /><br />## Step 4<br />Substitute the given values into the formula:<br />### \(r = \frac{5m}{0.7}\)<br /><br />## Step 5<br />Calculate the value of \(r\).
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