# A circle's center is at #(7 ,5 )# and it passes through #(5 ,8 )#. What is the length of an arc covering #(5pi ) /3 # radians on the circle?

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To find the length of an arc covering ( \frac{5\pi}{3} ) radians on the circle, first, calculate the radius of the circle using the given points. Then, use the formula for the length of an arc of a circle, which is ( s = r \theta ), where ( s ) is the arc length, ( r ) is the radius, and ( \theta ) is the angle in radians.

Given that the center of the circle is at ( (7, 5) ) and it passes through ( (5, 8) ), you can use the distance formula to find the radius. Once you have the radius, multiply it by ( \frac{5\pi}{3} ) 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 circle has its center at (2,2) and is tangent to both the x-axis and y-axis. A line tangent to this circle intersects the x-axis at (a,0) and the y-axis at (0,b). If the shaded area is equal to the area of the circle, then a + b = ? (EXACT ANSWER).
- A circle's center is at #(7 ,2 )# and it passes through #(5 ,6 )#. What is the length of an arc covering #(7pi ) /4 # radians on the circle?
- Points #(6 ,2 )# and #(1 ,5 )# are #(2 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?

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