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A circle's center is at #(2 ,5 )# and it passes through #(1 ,4 )#. What is the length of an arc covering #( pi ) /3 # radians on the circle?

Answer 1

Autumn Armstrong

length of arc#=(sqrt2*pi)/3=1.48096" "#units

To solve for the length of arc s: Use the formula

#s=r*theta# using the given data: #theta=pi/3# and computed value of #r#

to compute for r: use distance formula with points center #(x_c, y_c)=(2, 5)# and the given point #(x_1, y_1)=(1, 4)#

#r=sqrt((x_c-x_1)^2+(y_c-y_1)^2)#

#r=sqrt((2-1)^2+(5-4)^2)#

#r=sqrt2#

Solve arc length #s#

#s=r*theta=sqrt2 *pi/3#

#s=(sqrt2*pi)/3=1.48096" "#units

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Answer 2

Jayden Jackson

The length of an arc covering π/3 radians on the circle is equal to the radius multiplied by the central angle in radians. Given the center of the circle at (2, 5) and it passes through (1, 4), the radius of the circle can be calculated using the distance formula. Then, the length of the arc can be found by multiplying the radius by π/3.

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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.