A circle's center is at #(8 ,1 )# and it passes through #(2 ,5 )#. What is the length of an arc covering #(5 pi ) /6 # radians on the circle?

Answer 1

Mason Adams

(8,1) and (2,5)

#d^2=(8-2)^2+(1-5)^2#

#d^2=36+16#

#d=sqrt 52#

The distance between the points is #sqrt53# so the radius of the circle is #sqrt52#

Length of an arc is #theta/360xxpiD#

Where #theta# is the angle of the arc and #D# is the diameter of the circle.

#[5pi]/6=150^@#

Length=#150/360xxpixx2sqrt52#

Length is 18.87862233

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Answer 2

Sadie Allen

To find the length of an arc covering $\frac{5\pi}{6}$ radians on the circle, first, we need to find the radius of the circle using the given coordinates of the center and a point on the circle.

Using the distance formula, the distance between the center $(8, 1)$ and the point $(2, 5)$ is:

$r = \sqrt{(8 - 2)^2 + (1 - 5)^2}$

Once you find the radius, you can use the formula for the length of an arc of a circle, given by:

$\text{Arc Length} = r \times \text{angle in radians}$

Substitute the radius value and the given angle $\frac{5\pi}{6}$ into the formula to find the length of the arc.

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Answer from HIX Tutor

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.