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A circle's center is at #(4 ,1 )# and it passes through #(2 ,4 )#. What is the length of an arc covering #(pi ) /3 # radians on the circle?

Answer 1

#s = pi/3 sqrt(13) #

using distance equation find the radius: #sqrt((x_2-x_1)^2 - (y_2-y_1)^2)# #sqrt(4+9) = sqrt(13)# now arclength #s = rtheta# #s = pi/3 sqrt(13) #

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Answer 2

Carson Arnold

To find the length of an arc covering π/3 radians on the circle, you can use the formula for the length of an arc:

Arc Length = r * θ

Where: r is the radius of the circle, θ is the angle in radians subtended by the arc.

First, find the radius of the circle using the distance formula between the center and any point on the circle:

r = √[(x2 - x1)^2 + (y2 - y1)^2]

Substitute the given coordinates: r = √[(2 - 4)^2 + (4 - 1)^2] r = √[(-2)^2 + (3)^2] r = √[4 + 9] r = √13

Now, plug in the values of r and θ into the formula for arc length:

Arc Length = (√13) * (π/3)

Arc Length ≈ (π/3) * √13

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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.