# A circle's center is at #(8 ,3 )# and it passes through #(2 ,5 )#. What is the length of an arc covering #( pi ) /6 # radians on the circle?

Length of the arc is

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To find the length of an arc covering ( \frac{\pi}{6} ) radians on a circle, you can use the formula:

[ \text{Arc Length} = r \times \theta ]

where ( r ) is the radius of the circle and ( \theta ) is the angle in radians.

Given that the circle has a center at ( (8, 3) ) and passes through ( (2, 5) ), we can find the radius ( r ) using the distance formula:

[ r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]

[ r = \sqrt{(2 - 8)^2 + (5 - 3)^2} ]

[ r = \sqrt{36 + 4} ]

[ r = \sqrt{40} ]

[ r = 2\sqrt{10} ]

Now, plug in the values of ( r = 2\sqrt{10} ) and ( \theta = \frac{\pi}{6} ) into the arc length formula:

[ \text{Arc Length} = 2\sqrt{10} \times \frac{\pi}{6} ]

[ \text{Arc Length} = \frac{\pi\sqrt{10}}{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.

- A triangle has corners at #(2 ,4 )#, #(6 ,5 )#, and #(4 ,3 )#. What is the area of the triangle's circumscribed circle?
- A circle has a center that falls on the line #y = 5/3x +1 # and passes through #(8 ,2 )# and #(3 ,2 )#. What is the equation of the circle?
- What is the equation of the circle with a center at #(4 ,1 )# and a radius of #5 #?
- A triangle has corners at #(5 ,1 )#, #(3 ,9 )#, and #(4 ,7 )#. What is the area of the triangle's circumscribed circle?
- A circle has a center that falls on the line #y = 7/9x +7 # and passes through # ( 4 ,1 )# and #(3 ,7 )#. What is the equation of the circle?

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