A circle's center is at #(4 ,0 )# and it passes through #(6 ,9 )#. What is the length of an arc covering #(5pi ) /3 # radians on the circle?

Answer 1

#s = sqrt(85)*(5pi)/3 ~~ 48.27#

First we must find the radius of the circle.

We know the distance from the center to any point it passes through is the radius.

So, using the distance formula: #d = sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
#d = sqrt((4-6)^2+(0-9)^2) = sqrt(85)#
So, the radius is #sqrt(85)#
And we know the formula for arc length is: #s = rtheta# Where s is the arc length, r is the radius, and theta is the angle in radians.
Plugging in, #s = sqrt(85)*(5pi)/3#
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Answer 2

#s = 5sqrt(85)pi/3#

Let r = the radius

#r = sqrt((6 - 4)^2 + (9 - 0)^2)#
#r = sqrt(85)#

Let s = the arc length

#s = rtheta# where #theta# is the given angle
#s = 5sqrt(85)pi/3#
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Answer 3

To find the length of an arc covering (5π/3) radians on the circle, we first need to find the radius of the circle using the given coordinates. The distance between the center of the circle (4, 0) and the point on the circle (6, 9) can be found using the distance formula. Then, we can use the formula for the length of an arc on a circle, which is given by the formula:

Arc Length = radius * angle (in radians).

After finding the radius and given angle, we can calculate 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.

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.

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