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In a circle with a radius of 6 ft, an arc is intercepted by a central angle of 3π2 radians.



What is the length of the arc?


2π ft

​ 3π ​ ft

​ 6π ​ ft

​ 9π ​ ft

Respuesta :

calculista

Answer:

[tex]9\pi\ ft[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=6\ ft[/tex]

substitute

[tex]C=2\pi(6)[/tex]

[tex]C=12\pi\ ft[/tex]

step 2

we know that

The circumference of a circle subtends a central angle of 2π radians

so

using proportion

Find out the length of the arc for a central angle of 3π/2 radians

Let

x------> the length of the arc

[tex]\frac{12\pi}{2\pi}=\frac{x}{3\pi/2} \\ \\x=9\pi\ ft[/tex]

alejandrob938

Answer:

​ 9π ​ ft

Step-by-step explanation:

took the test to prove the answer right. picture below

Ver imagen alejandrob938

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