A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(3, 1)$ $(3 ,1 )$ . What is the length of an arc covering $\frac{15 π}{8}$ $(15pi ) /8$ radians on the circle?

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A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(3, 1)$ $(3 ,1 )$ . What is the length of an arc covering $\frac{15 π}{8}$ $(15pi ) /8$ radians on the circle?

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Answer 1 · 2016-08-11T21:51:57

$= 18.75$ $=18.75$

Explanation:

Circle's center is at $(2, 4)$ $(2,4)$ and it passes through $(3, 1)$ $(3,1)$
Therefore Length of the $r a d i u s = r$ $radius=r$ =Distance between these points $(2, 4) and (3, 1)$ $(2,4) and (3,1)$
or
$r a d i u s = r = \sqrt{{(3 - 2)}^{2} + {(4 - 1)}^{2}}$ $radius =r=sqrt((3-2)^2+(4-1)^2)$
$= \sqrt{1^{2} + 3^{2}}$ $=sqrt(1^2+3^2)$
$= \sqrt{1 + 9}$ $=sqrt(1+9)$
$= \sqrt{10}$ $=sqrt10$
$= 3.16$ $=3.16$
Therefore Circumfernce of the Circle $= 2 π r = 2 π \times 3.16 ≅ 20$ $=2pir=2pitimes3.16~=20$
Arc covers $\frac{15 π}{8}$ $(15pi)/8$ radians on the Circle
In other words Arc covers $\frac{15 π}{8} \div 2 π = \frac{15}{16} \times$ $(15pi)/8-:2pi=15/16times$ (circumference of the Circle)
Therefore Length of the Arc $= \frac{15}{16} \times 2 π r = \frac{15}{16} \times 20 = 18.75$ $=15/16 times2pir=15/16 times20=18.75$

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A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(3, 1)$ $(3 ,1 )$ . What is the length of an arc covering $\frac{15 π}{8}$ $(15pi ) /8$ radians on the circle?

1 Answer

Explanation:

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A circle's center is at (2,4)(2 ,4 ) and it passes through (3,1)(3 ,1 ). What is the length of an arc covering 15π8(15pi ) /8 radians on the circle?

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A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(3, 1)$ $(3 ,1 )$ . What is the length of an arc covering $\frac{15 π}{8}$ $(15pi ) /8$ radians on the circle?