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anonymous

  • one year ago

HELP PLEASE!!!! Find the area of a sector with an arc length of 60 in. and a radius of 15 in. A. 117.75 in.² B. 282.60 in.² C. 450 in.² D. 6,750 in.²

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  1. jiteshmeghwal9
    • one year ago
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    Area of a sector=\(\Large{\frac{\theta}{360} \times \pi r^2}\)

  2. anonymous
    • one year ago
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    thank you!

  3. anonymous
    • one year ago
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    would the answer be A?

  4. anonymous
    • one year ago
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    because it says its wrong

  5. anonymous
    • one year ago
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    is 60 the theta

  6. jim_thompson5910
    • one year ago
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    60 is not the theta 60 is the distance around the curve. It's the length of the arc this shaded distance |dw:1436594438367:dw|

  7. jim_thompson5910
    • one year ago
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    if the radius is 15, then what is the total circumference?

  8. anonymous
    • one year ago
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    30?

  9. jim_thompson5910
    • one year ago
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    use the formula C = 2*pi*r

  10. jim_thompson5910
    • one year ago
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    you're close

  11. anonymous
    • one year ago
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    i got 94.24

  12. anonymous
    • one year ago
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    when i plugged it in

  13. jim_thompson5910
    • one year ago
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    yeah \[\Large 30\pi \approx 94.2477796\]

  14. jim_thompson5910
    • one year ago
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    I'm going to leave it as 30pi to keep things as exact as possible

  15. anonymous
    • one year ago
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    okay so what i do with that

  16. jim_thompson5910
    • one year ago
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    30pi is the entire circumference the arc length is 60 we divide the two to get the fraction of the circle in which this arc is applied to \[\Large \frac{60}{30\pi} = \frac{2}{\pi}\]

  17. jim_thompson5910
    • one year ago
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    now what we do is multiply that by the area pi*r^2 = pi*15^2 = 225pi \[\large 225\pi*\frac{2}{\pi} = 225\cancel{\pi}*\frac{2}{\cancel{\pi}} = 225*2 = 450\]

  18. anonymous
    • one year ago
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    thank you so much!

  19. jim_thompson5910
    • one year ago
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    |dw:1436594886725:dw|

  20. jim_thompson5910
    • one year ago
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    no problem

  21. anonymous
    • one year ago
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    can you help me with another problem? @jim_thompson5910

  22. jim_thompson5910
    • one year ago
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    sure

  23. jim_thompson5910
    • one year ago
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    what's your question?

  24. anonymous
    • one year ago
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    Find the length of the radius of . A. 2004-05-03-07-00_files/i0360003.jpg B. 2004-05-03-07-00_files/i0360004.jpg C. 2004-05-03-07-00_files/i0360005.jpg D. 2004-05-03-07-00_files/i0360006.jpg

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  25. anonymous
    • one year ago
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    wait sorry

  26. anonymous
    • one year ago
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    A. r=1 B. r= 3 C. r=12 D. r=15 i have to find the length of the radius

  27. jim_thompson5910
    • one year ago
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    does it give you the entire circumference?

  28. jim_thompson5910
    • one year ago
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    oh wait nvm, we don't need that info

  29. anonymous
    • one year ago
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    no it does not

  30. jim_thompson5910
    • one year ago
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    notice how the central angle is 4pi/9 what happens when you divide that central angle by 2pi? what do you get?

  31. jiteshmeghwal9
    • one year ago
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    \[\frac{\theta}{360} \times 2 \pi r= s\]\[\frac{\frac{4}{9}\pi} {360} \times 2 \pi r=\frac{20}{3} \pi\]solve for 'r'.

  32. anonymous
    • one year ago
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    i have to put theta over 180 pi and then pi*radius

  33. jim_thompson5910
    • one year ago
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    I guess a shortcut is to use the formula \[\Large s = \theta*r\] this formula only works if theta is in radian mode. In this case, theta = 4pi/9 and s = 20pi/3 \[\Large s = \theta*r\] \[\Large \frac{20\pi}{3} = \frac{4\pi}{9}*r\] do you see how to solve for r from here?

  34. anonymous
    • one year ago
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    i know that the pi's cancel out right?

  35. jim_thompson5910
    • one year ago
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    yep

  36. anonymous
    • one year ago
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    simplify the fractions then?

  37. jim_thompson5910
    • one year ago
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    not quite

  38. jim_thompson5910
    • one year ago
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    we now have 20/3 = (4/9)*r how would you isolate r ?

  39. anonymous
    • one year ago
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    divide?

  40. jim_thompson5910
    • one year ago
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    divide both sides by what

  41. anonymous
    • one year ago
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    i'm not sure

  42. jim_thompson5910
    • one year ago
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    |dw:1436596805511:dw|

  43. jim_thompson5910
    • one year ago
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    or you can multiply both sides by the reciprocal of 4/9 the reciprocal of 4/9 is 9/4 |dw:1436596829027:dw|

  44. anonymous
    • one year ago
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    i got 15

  45. jim_thompson5910
    • one year ago
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    |dw:1436596853297:dw|

  46. jim_thompson5910
    • one year ago
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    yes, r = 15

  47. anonymous
    • one year ago
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    thank you!

  48. jim_thompson5910
    • one year ago
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    no problem

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