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anonymous

  • one year ago

find arc length of a circle with a radius of 5 and a central angle of 7 rad.

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  1. jim_thompson5910
    • one year ago
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    |dw:1444528017439:dw|

  2. jim_thompson5910
    • one year ago
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    |dw:1444528026996:dw| \[\Large \text{Arc length} = \frac{\text{radian angle}}{2\pi \ \text{radians}}*(\text{circumference})\] \[\Large S = \frac{\theta}{2\pi}*(2\pi*r)\] \[\Large S = \frac{\theta}{\cancel{2\pi}}*(\cancel{2\pi}*r)\] \[\Large S = \theta*r\]

  3. jim_thompson5910
    • one year ago
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    The formula \(\Large S = \theta*r\) works only if \(\Large \theta\) (greek letter theta) is in radians

  4. anonymous
    • one year ago
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    so 35? @jim_thompson5910

  5. jim_thompson5910
    • one year ago
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    correct

  6. anonymous
    • one year ago
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    thanks

  7. jim_thompson5910
    • one year ago
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    hmm something is off though, I think theta needs to be restricted

  8. jim_thompson5910
    • one year ago
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    the formula only works if theta is between 0 and 2pi

  9. jim_thompson5910
    • one year ago
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    7 radians = 7*(180/pi) = 401.070456591577 degrees approximately this angle is over 360 degrees so what needs to happen is you need to find the reference angle to 7 radians |dw:1444528584599:dw|

  10. jim_thompson5910
    • one year ago
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    |dw:1444528610304:dw|

  11. jim_thompson5910
    • one year ago
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    does it really say "7 radians" ? or is it some fraction with pi in it?

  12. anonymous
    • one year ago
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    it says 7 rads

  13. jim_thompson5910
    • one year ago
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    hmm so strange. Usually the central angle is something between 0 and 2pi

  14. anonymous
    • one year ago
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    off topic, but |dw:1444529191578:dw| what does the "w" STAND FOR?

  15. jim_thompson5910
    • one year ago
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    v = linear velocity w (some books use \(\Large \omega\) which is the greek letter omega) = angular velocity r = radius

  16. anonymous
    • one year ago
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    thanks

  17. jim_thompson5910
    • one year ago
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    the angular velocity or speed is how fast the object is revolving around a fixed center point one example of an angular velocity is pi radians per second. Each second, the object rotates pi radians or 180 degrees

  18. jim_thompson5910
    • one year ago
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    no problem

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