A circle's center is at #(7 ,5 )# and it passes through #(5 ,8 )#. What is the length of an arc covering #(7pi ) /4 # radians on the circle?
≈ 19.83
To calculate the length of arc , require to know radius of circle.
The 2 points here are the centre and the point it passes through. This distance is the radius of the circle.
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First, find the radius of the circle using the distance formula. Then, use the formula for the length of an arc of a circle, which is given by ( \text{arc length} = r \cdot \theta ), where ( r ) is the radius of the circle and ( \theta ) is the central angle in radians.
Given the coordinates of the center and a point on the circle, you can find the radius using the distance formula. Then, you can calculate the arc length using the formula mentioned above.
Let's proceed with the calculations:

Calculate the radius using the distance formula:
( r = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2} )( r = \sqrt{(5  7)^2 + (8  5)^2} )
( r = \sqrt{(2)^2 + (3)^2} )
( r = \sqrt{4 + 9} )
( r = \sqrt{13} ) 
The arc length is given by:
( \text{arc length} = r \cdot \theta )( \text{arc length} = \sqrt{13} \times \frac{7\pi}{4} )
( \text{arc length} = \frac{7\pi\sqrt{13}}{4} )
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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