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anonymous

  • one year ago

https://media.education2020.com/evresources/2092539_2f57b746-c73f-4a4b-8c7e-ce9ee207b927.png Find the length of the radius for circle C.

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  1. mathstudent55
    • one year ago
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    When the radius of a circle is r, what is the circumference of the circle?

  2. anonymous
    • one year ago
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    C= 2 pi r

  3. mathstudent55
    • one year ago
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    Great. The circumference of a circle is an arc that corresponds to a central angle of 360 degrees or 2 pi radians.

  4. mathstudent55
    • one year ago
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    Now look in your figure.

  5. mathstudent55
    • one year ago
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    You have a central angle of 4pi/9 radians corresponding to an arc length of 20pi/3 units.

  6. mathstudent55
    • one year ago
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    |dw:1433104768403:dw|

  7. nincompoop
    • one year ago
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    maybe explain what \(\pi \) corresponds to as in a unit circle

  8. mathstudent55
    • one year ago
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    If we divide the circumference by the central angle, we get the radius.

  9. anonymous
    • one year ago
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    So how do we get the circumference from what we have now

  10. anonymous
    • one year ago
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    Since we don't have the radius I'm confused 😕

  11. mathstudent55
    • one year ago
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    In a circle, the central angle is \(2 \pi \) rad. Dividing the circumference by the central angle gives us the radius. \(\dfrac{2 \pi r}{2 \pi} =r \)

  12. mathstudent55
    • one year ago
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    Let me explain more clearly.

  13. mathstudent55
    • one year ago
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    In this problem we are dealing with an arc length, and a radius, and a central angle.

  14. anonymous
    • one year ago
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    But how can we use r when we don't have the radius

  15. nincompoop
    • one year ago
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    we can skip the circumference since we are only dealing with an arc the length of an arc is calculated by the formula, \(\large s = r \times \theta \) you are given the measurements of s and angle

  16. mathstudent55
    • one year ago
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    When the central angle is given is radians, the length of the arc is the central angle multiplied by the radius.

  17. anonymous
    • one year ago
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    Ok so

  18. anonymous
    • one year ago
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    What would the circumference be

  19. mathstudent55
    • one year ago
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    Since you are given the length of the arc and the central angle, and we are dealing with radian measures, divide the length of the arc by the central angle and you get the radius.

  20. nincompoop
    • one year ago
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    then we know how to approach how to calculate r \(\large \ r = \frac{s}{\theta} \rightarrow \huge \frac{20 \pi}{3} \div \frac{4 \pi}{9} \) follow the rules when dividing two fractions

  21. mathstudent55
    • one year ago
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    \(s = r \theta\) \(r = \dfrac{s}{\theta} \) You have s, the arc length, and theta, the central angle. Plug them is and find r.

  22. anonymous
    • one year ago
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    I got it thanks so much

  23. anonymous
    • one year ago
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    I have one more question.

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  24. nincompoop
    • one year ago
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    have you been paying attention or not? now you are being asked to solve for s the arc length, \(s = \large r \times \theta \)

  25. mathstudent55
    • one year ago
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    In the second problem you use the arc length formula directly. \(s = r \theta\) You are given r, the radius, and theta, the central angle. just multiply them together.

  26. anonymous
    • one year ago
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    Last question.

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  27. mathstudent55
    • one year ago
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    You mean the red section of the circle?

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