Question

describe the shaded sector in the figure by inequalities in ( r ) and ( \theta ).
assume that the radii of the circles are 5 and 10.
(use symbolic notation and fractions where needed.)
( r_{\text {left }} leq r leq r_{\text {right }} )
( r_{\text {left }}= )
( r_{\text {right }}= )
( \theta_{\text {left }} leq \theta leq \theta_{\text {right }} )
(use symbolic notation and fractions where needed. use ( pi ) notation.)
( \theta_{\text {left }}= )

Explanation:

Step1: Determine the range of \( r \)

The shaded sector is between two circles with radii \( 5 \) and \( 10 \). So, \( r_{\text{left}} = 5 \) and \( r_{\text{right}} = 10 \).

Step2: Determine the range of \( \theta \)

The angle of \( 45^{\circ} \) is given. Convert \( 45^{\circ} \) to radians: \( 45^{\circ}=\frac{\pi}{4} \) radians. The other angle (assuming the sector is from \( \frac{\pi}{4} \) to \( \frac{\pi}{2} \)). So, \( \theta_{\text{left}}=\frac{\pi}{4} \)

Answer:

\( r_{\text{left}} = 5\)
\( r_{\text{right}} = 10\)
\( \theta_{\text{left}}=\frac{\pi}{4}\)