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anonymous

  • one year ago

If the length of an arc is 12 inches and the radius of the circle is 10 inches, what is the measure of the arc? 216 degrees 270 degrees 288 degrees

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  1. anonymous
    • one year ago
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    @campbell_st whered that answer go?

  2. wampominater
    • one year ago
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    do you still need help?

  3. anonymous
    • one year ago
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    yes please...

  4. wampominater
    • one year ago
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    ok

  5. wampominater
    • one year ago
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    so, the first thing you need is the formula for arc length, which is \[arclength = 2piR(\frac{ \theta }{ 360 })\]

  6. wampominater
    • one year ago
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    now, look at the values you are given

  7. wampominater
    • one year ago
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    you have the arc length and the radius, so plug those in.

  8. wampominater
    • one year ago
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    and what do you get when you do that?

  9. anonymous
    • one year ago
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    where am i plugging the arc length into?

  10. wampominater
    • one year ago
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    look at the formula, see where it says arc length? you plug the value you have for arc length right there.

  11. anonymous
    • one year ago
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    yeah and i can plug in the radius too. but what am i solving for?|dw:1438157454848:dw|

  12. wampominater
    • one year ago
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    yep! now you want to solve for theta.

  13. anonymous
    • one year ago
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    theta?

  14. wampominater
    • one year ago
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    so to make it easier, replace theta with x. it is the symbol in the numerator of the fraction: \[\theta\]

  15. anonymous
    • one year ago
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    oh okay.

  16. wampominater
    • one year ago
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    so the first step is to isolate x, the best way to do that is to first deal with everything outside the parenthesis

  17. wampominater
    • one year ago
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    you know all the values for those, just solve 2πr

  18. wampominater
    • one year ago
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    and then, what you want to do is divide both sides by the value that you get for 2πr, which will isolate the fraction and let you solve that next

  19. anonymous
    • one year ago
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    62.8?

  20. wampominater
    • one year ago
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    yep!

  21. wampominater
    • one year ago
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    now divide both sides by 62.8

  22. wampominater
    • one year ago
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    what do you get?

  23. anonymous
    • one year ago
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    okay |dw:1438157770787:dw| now divide by it?

  24. wampominater
    • one year ago
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    mhm, so it would be 12 over 62.8

  25. wampominater
    • one year ago
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    that leaves you with \[\frac{ 12 }{ 62.8 } = \frac{ x }{ 360 }\]

  26. wampominater
    • one year ago
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    now, go ahead and divide 12 by 62.8, what does that get you?

  27. anonymous
    • one year ago
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    couldnt you do that as a proportion?

  28. wampominater
    • one year ago
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    yes, you could if you like

  29. anonymous
    • one year ago
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    seems easier

  30. anonymous
    • one year ago
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    |dw:1438157995138:dw|

  31. wampominater
    • one year ago
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    yep! so that would be the answer i believe.

  32. anonymous
    • one year ago
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    isnt right

  33. wampominater
    • one year ago
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    hmm, let me see if i did something wrong

  34. anonymous
    • one year ago
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    yeah man

  35. wampominater
    • one year ago
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    hmm, im not sure what I did Wrong, sorry :(

  36. anonymous
    • one year ago
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    |dw:1438158390561:dw|

  37. anonymous
    • one year ago
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    @aric200

  38. UsukiDoll
    • one year ago
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    actually there is a dupe question and that also led to a dead end http://openstudy.com/study#/updates/52eafc6ae4b0d95ca6b32d90

  39. wampominater
    • one year ago
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    hmm, could be the question then? idk if you looked at the work usuki, is it right?

  40. anonymous
    • one year ago
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    its supposed to be 12 pi and copy paste takes out the pi part

  41. UsukiDoll
    • one year ago
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    I think the question is a bit screwed up... yes ! 12 pi that's what we need

  42. wampominater
    • one year ago
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    there we go! lol

  43. wampominater
    • one year ago
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    ok so then, it is 12π and not 12?

  44. UsukiDoll
    • one year ago
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    because that's also a dupe question http://openstudy.com/study#/updates/4e2c15f60b8b3d38d3ba2d2d

  45. anonymous
    • one year ago
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    yep

  46. wampominater
    • one year ago
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    alright, do you need help still then or are you good?

  47. anonymous
    • one year ago
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    so its 216?

  48. UsukiDoll
    • one year ago
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    I don't know if I should touch on this.. if there's a duplicate question. why not look at the past and learn in the future?

  49. wampominater
    • one year ago
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    good point, i didnt look :p

  50. wampominater
    • one year ago
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    yes it is 216

  51. UsukiDoll
    • one year ago
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    I could go over it for verification purposes so given radius at 10 ( r = 10) Arc length is 12pi (s=12pi) we need theta \[s = \theta r \rightarrow \frac{s}{r} = \theta \] \[\frac{12 \pi}{10} = \theta \] that bad boy is in radians and we need degrees so multiply that 12pi/10 with 180/pi so the pi's cancel \[\frac{12 \pi}{10} \cdot \frac{180}{\pi} = \theta \] \[\frac{12 }{10} \cdot \frac{180}{1} = \theta \] \[\frac{2160}{10} = \theta \] \[216 = \theta \]

  52. anonymous
    • one year ago
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    what would be the symbol/variable for arc length?

  53. UsukiDoll
    • one year ago
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    arc length is s radius is r angle is the theta

  54. wampominater
    • one year ago
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    Alright, well thanks for the Help @UsukiDoll , ill be more careful in the future. goodnight!

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