# A circle's center is at #(3 ,1 )# and it passes through #(0 ,2 )#. What is the length of an arc covering #( pi ) /6 # radians on the circle?

- Find the radius of the circle, this is done by Pythagoras

- arc length

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

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

Where:

- ( r ) is the radius of the circle
- ( \theta ) is the central angle in radians

Given that the center of the circle is at (3, 1) and it passes through (0, 2), we can calculate the radius using the distance formula. Then, we can use ( \frac{\pi}{6} ) radians as the angle to find the length of the arc.

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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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- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/6 #, vertex B has an angle of #(pi)/12 #, and the triangle's area is #32 #. What is the area of the triangle's incircle?
- Points #(7 ,1 )# and #(5 ,9 )# are #(3 pi)/4 # radians apart on a circle. What is the shortest arc length between the points?

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