# A circle has a chord that goes from #( pi)/6 # to #(7 pi) / 6 # radians on the circle. If the area of the circle is #135 pi #, what is the length of the chord?

Length of the chord

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The length of the chord is ( \frac{1}{2} \times \text{radius} \times (\theta_2 - \theta_1) ), where ( \theta_1 ) and ( \theta_2 ) are the angles in radians corresponding to the ends of the chord on the circle.

Given that the area of the circle is ( 135\pi ), we can find the radius using the formula for the area of a circle ( A = \pi r^2 ).

[ 135\pi = \pi r^2 ] [ r^2 = 135 ] [ r = \sqrt{135} = 3\sqrt{15} ]

The length of the chord is then:

[ \text{Length of chord} = \frac{1}{2} \times 3\sqrt{15} \times \left(\frac{7\pi}{6} - \frac{\pi}{6}\right) ] [ = \frac{1}{2} \times 3\sqrt{15} \times \frac{6\pi}{6} ] [ = \frac{9\sqrt{15}\pi}{2} ]

Therefore, the length of the chord is ( \frac{9\sqrt{15}\pi}{2} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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