A circle has a chord that goes from #( pi)/3 # to #(5 pi) / 12 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?
The length of a chord is given by
- find the radius with the given information
- find the arc length
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The length of the chord is ( \frac{5}{12} \times \text{radius} - \frac{\pi}{3} \times \text{radius} ). Given that the area of the circle is ( 48\pi ), we can find the radius using the formula for the area of a circle, ( \pi r^2 = 48\pi ). Solving for ( r ), we get ( r = \sqrt{48} = 4\sqrt{3} ). Substituting the value of ( r ) into the formula for the length of the chord, we get ( \frac{5}{12} \times 4\sqrt{3} - \frac{\pi}{3} \times 4\sqrt{3} = \frac{5\sqrt{3}}{3} - \frac{4\pi\sqrt{3}}{3} ). This can be simplified to ( \frac{5\sqrt{3} - 4\pi\sqrt{3}}{3} ) or ( \frac{(5 - 4\pi)\sqrt{3}}{3} ). Therefore, the length of the chord is ( \frac{(5 - 4\pi)\sqrt{3}}{3} ).
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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.
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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