A circle's center is at $(3, 2)$ $(3 ,2 )$ and it passes through $(5, 8)$ $(5 ,8 )$ . What is the length of an arc covering $\frac{7 π}{4}$ $(7pi ) /4$ radians on the circle?

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A circle's center is at $(3, 2)$ $(3 ,2 )$ and it passes through $(5, 8)$ $(5 ,8 )$ . What is the length of an arc covering $\frac{7 π}{4}$ $(7pi ) /4$ radians on the circle?

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Answer 1 · 2016-08-14T17:45:14

Length of the Arc $= 34.77$ $=34.77$

Explanation:

Circle's center is at $(3, 2)$ $(3,2)$ and it passes through $(5, 8)$ $(5,8)$
Therefore Length of the $r a d i u s = r$ $radius=r$ =Distance between these points $(3, 2) and (5, 8)$ $(3,2) and (5,8)$
or
$r a d i u s = r = \sqrt{{(5 - 3)}^{2} + {(8 - 2)}^{2}}$ $radius =r=sqrt((5-3)^2+(8-2)^2)$
$= \sqrt{2^{2} + 6^{2}}$ $=sqrt(2^2+6^2)$
$= \sqrt{4 + 36}$ $=sqrt(4+36)$
$= \sqrt{40}$ $=sqrt40$
$= 6.32$ $=6.32$
Therefore Circumference of the Circle $= 2 π r = 2 π \times 6.32 = 39.74$ $=2pir=2pitimes6.32=39.74$
Arc covers $\frac{7 π}{4}$ $(7pi)/4$ radians on the Circle
In other words Arc covers $\frac{7 π}{4} \div 2 π = \frac{7}{8} \times$ $(7pi)/4-:2pi=7/8times$ (circumference of the Circle)
Therefore Length of the Arc $= \frac{7}{8} \times 2 π r = \frac{7}{8} \times 39.74 = 34.77$ $=7/8 times2pir=7/8 times39.74=34.77$

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A circle's center is at $(3, 2)$ $(3 ,2 )$ and it passes through $(5, 8)$ $(5 ,8 )$ . What is the length of an arc covering $\frac{7 π}{4}$ $(7pi ) /4$ radians on the circle?

1 Answer

Explanation:

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A circle's center is at $(3, 2)$ $(3 ,2 )$ and it passes through $(5, 8)$ $(5 ,8 )$ . What is the length of an arc covering $\frac{7 π}{4}$ $(7pi ) /4$ radians on the circle?