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What is the length of the arc if: 11. r=10 n=20 A15(pi)/ 7 B13(pi)/ 5 C16(pi)/ 2 D11(pi)/ 4 E 10(pi)/ 9 F 9(pi)/ 4 12. r=3 n=6 Api/9 Bpi/12 Cpi/26 Dpi/10 E pi/8 F pi/4 13. r=4 n=7 A8(pi)/55 B 6(pi)/12 C7(pi)/45 D2(pi)/22 E 9(pi)/18 F 7(pi)/37 14. r=2 n=x Ax(pi)/15 Bx(pi)/30 Cx(pi)/60 Dx(pi)/90 E x(pi)/120 F x(pi)/150 15. r=y n=x A x*y*pi/90 Bx*y*pi/30 Cx*y*pi/45 Dx*y*pi/27 E x*y*pi/180 F x*y*pi/115

Respuesta :

Step-by-step explanation:

The formula for arc length [for the angle in degrees] is:

[tex]L = 2\pi r \left(\dfrac{n}{360}\right)[/tex]

here,

[tex]n[/tex] = degrees

[tex]r[/tex] = radius

using this we'll solve all the parts:

r = 10, n = 20:

[tex]L = 2\pi r \left(\dfrac{n}{360}\right)[/tex]

[tex]L = 2\pi (10) \left(\dfrac{20}{360}\right)[/tex]

from here, it is just simplification:

2 and 360 can be resolved: 360 divided by 2 = 180

[tex]L = \pi (10) \left(\dfrac{20}{180}\right)[/tex]

10 and 180 can be resolved: 180 divided by 10 = 18

[tex]L = \pi \left(\dfrac{20}{18}\right)[/tex]

finally, both 20 and 18 are multiples of 2 and can be resolved:

[tex]L = \pi \left(\dfrac{10}{9}\right)[/tex]

[tex]L = \dfrac{10\pi}{9}[/tex] Option (E)

r=3, n=6:

[tex]L = 2\pi r \left(\dfrac{n}{360}\right)[/tex]

[tex]L = 2\pi (3) \left(\dfrac{6}{360}\right)[/tex]

[tex]L = \dfrac{\pi}{10}[/tex] Option (D)

r=4 n=7

[tex]L = 2\pi r \left(\dfrac{n}{360}\right)[/tex]

[tex]L = 2\pi (4) \left(\dfrac{7}{360}\right)[/tex]

[tex]L = \dfrac{7\pi}{45}[/tex] Option (C)

r=2 n=x

[tex]L = 2\pi r \left(\dfrac{n}{360}\right)[/tex]

[tex]L = 2\pi (2) \left(\dfrac{x}{360}\right)[/tex]

[tex]L = \dfrac{x\pi}{90}[/tex] Option (D)

r=y n=x

[tex]L = 2\pi r \left(\dfrac{n}{360}\right)[/tex]

[tex]L = 2\pi (y) \left(\dfrac{x}{360}\right)[/tex]

[tex]L = \dfrac{xy\pi}{180}[/tex] Option (E)

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