A circle's center is at #(2 ,1 )# and it passes through #(3 ,2 )#. What is the length of an arc covering #(7pi ) /12 # radians on the circle?
arc length
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To find the length of an arc covering ( \frac{7\pi}{12} ) radians on the circle, we first need to find the radius of the circle using the given center and a point on the circle.
The distance formula can be used to find the radius of the circle, which is the distance between the center ((2, 1)) and the point ((3, 2)).
Then, once the radius is known, the formula for the length of an arc of a circle is used:
[ \text{Arc Length} = r \times \theta ]
Where: ( r ) = radius of the circle ( \theta ) = angle in radians
Substitute the values into the formula to find the length of the arc.
Let's go step by step:

Find the radius: [ r = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2} ]

Calculate the angle in radians ( \theta ): [ \frac{7\pi}{12} ]

Use the formula for the length of an arc: [ \text{Arc Length} = r \times \theta ]
Plug in the values for ( r ) and ( \theta ) into the formula to get the length of the arc.
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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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