# A circle's center is at #(5 ,5 )# and it passes through #(2 ,7 )#. What is the length of an arc covering #(7pi ) /8 # radians on the circle?

so length of arc is:

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To find the length of an arc covering ( \frac{7\pi}{8} ) radians on the circle, you need to use the formula for the length of an arc of a circle. First, find the radius of the circle using the distance formula between the center of the circle and a point on its circumference:

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

Substitute the coordinates of the center ((5, 5)) and the point ((2, 7)):

[ \text{Radius} = \sqrt{(2 - 5)^2 + (7 - 5)^2} = \sqrt{9 + 4} = \sqrt{13} ]

Now, the formula for the length of an arc of a circle is given by:

[ \text{Arc Length} = \text{Radius} \times \text{Angle in Radians} ]

Substitute the given angle ( \frac{7\pi}{8} ) and the radius ( \sqrt{13} ):

[ \text{Arc Length} = \sqrt{13} \times \frac{7\pi}{8} ]

Simplify:

[ \text{Arc Length} = \frac{7\sqrt{13}\pi}{8} ]

So, the length of the arc covering ( \frac{7\pi}{8} ) radians on the circle is ( \frac{7\sqrt{13}\pi}{8} ) units.

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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 circle has a chord that goes from #( pi)/3 # to #(2 pi) / 3 # radians on the circle. If the area of the circle is #16 pi #, what is the length of the chord?
- A triangle has corners at #(5 , 2 )#, #(4 ,7 )#, and #(5 ,6 )#. What is the radius of the triangle's inscribed circle?
- 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 #4 #. What is the area of the triangle's incircle?
- What is the area of a circle which diameter is 8.5m?
- How do you graph a circle a circle with a center at #(0, -6)# and a radius of 1?

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