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anonymous

  • one year ago

A certain windshield wiper clears a portion of a sector as shown. If the angle that the wiper pivots during each swing is 120°, find the area of the windshield that is cleaned during each swing.

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  1. anonymous
    • one year ago
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  2. Z4K4R1Y4
    • one year ago
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    have you done radians?

  3. anonymous
    • one year ago
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    @Z4K4R1Y4 nope I have no idea what that is

  4. Z4K4R1Y4
    • one year ago
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    |dw:1433038449394:dw| does this make sense?

  5. anonymous
    • one year ago
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    yes a little thank you @Z4K4R1Y4

  6. Z4K4R1Y4
    • one year ago
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    so what would be the area of the full circle i've drawn?

  7. Z4K4R1Y4
    • one year ago
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    \[area= \pi*r ^{2}\]

  8. anonymous
    • one year ago
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    1256.63? @Z4K4R1Y4

  9. Z4K4R1Y4
    • one year ago
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    yes

  10. Z4K4R1Y4
    • one year ago
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    now we want to find the sector with angle 120

  11. anonymous
    • one year ago
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    45238.9342? @Z4K4R1Y4

  12. Z4K4R1Y4
    • one year ago
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    not quite.

  13. Z4K4R1Y4
    • one year ago
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    full circle = 360 degrees

  14. Z4K4R1Y4
    • one year ago
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    if we divide 360 by 120 we get three

  15. Z4K4R1Y4
    • one year ago
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    so that means 120 is 1/3 of 360. right?

  16. anonymous
    • one year ago
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    Right. :) @Z4K4R1Y4

  17. Z4K4R1Y4
    • one year ago
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    so if the area of full circle (angle 360) is 1256.63 then the area of the sector of angle 120 would be 1/3 of 1256.63. right?

  18. anonymous
    • one year ago
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    It would be 418.876667? @Z4K4R1Y4

  19. Z4K4R1Y4
    • one year ago
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    Right!!

  20. Z4K4R1Y4
    • one year ago
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    now for the next part...

  21. Z4K4R1Y4
    • one year ago
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    |dw:1433039404347:dw|

  22. Z4K4R1Y4
    • one year ago
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    \[area of full circle = \pi * r ^{2}\] ... but this time r =5

  23. anonymous
    • one year ago
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    78.5398163? @Z4K4R1Y4

  24. Z4K4R1Y4
    • one year ago
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    yes!

  25. Z4K4R1Y4
    • one year ago
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    now for the area of the sector of angle 120.

  26. Z4K4R1Y4
    • one year ago
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    area of full circle (360 degrees) = 78.53... so area of sector of angle 120 would be 1/3 of 78.53...

  27. Z4K4R1Y4
    • one year ago
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    yh we're caculating the white part of raius 5

  28. Z4K4R1Y4
    • one year ago
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    *radius

  29. Vocaloid
    • one year ago
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    alright, just making sure, I saw your diagram had the arrow pointing to the black part as the part not cleared by the wiper

  30. Z4K4R1Y4
    • one year ago
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    the second diagram is only showing the white part

  31. Z4K4R1Y4
    • one year ago
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    @alexwaldorf do you under stand the calculation?

  32. Z4K4R1Y4
    • one year ago
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    @Vocaloid thanks

  33. Vocaloid
    • one year ago
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    yeah, sorry about interrupting, my mistake D:

  34. anonymous
    • one year ago
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    yes a little lol @Z4K4R1Y4

  35. Z4K4R1Y4
    • one year ago
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    @Vocaloid Np

  36. anonymous
    • one year ago
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    it's okay thanks :) @Vocaloid

  37. Z4K4R1Y4
    • one year ago
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    so what would be the area of the sector in the second part? @alexwaldorf

  38. anonymous
    • one year ago
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    19374.08? @Z4K4R1Y4

  39. Z4K4R1Y4
    • one year ago
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    not quite. area of full circle = 78.53982.. area of sector of angle 120 would be 1/3 of that.

  40. anonymous
    • one year ago
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    oh so is it 23.17994? @Z4K4R1Y4

  41. Z4K4R1Y4
    • one year ago
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    yes!... do you understand why it's 1/3 of full area?

  42. anonymous
    • one year ago
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    26*

  43. anonymous
    • one year ago
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    yes I do :) @Z4K4R1Y4

  44. Z4K4R1Y4
    • one year ago
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    good. finally we have...

  45. Z4K4R1Y4
    • one year ago
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    |dw:1433040636347:dw|

  46. Z4K4R1Y4
    • one year ago
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    area of sector of radius 20 (15+5) = 418.87.. and area of sector of radius 5 (white part) = 23.17...

  47. Z4K4R1Y4
    • one year ago
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    does that make sense?

  48. anonymous
    • one year ago
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    yes it does

  49. anonymous
    • one year ago
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    so is 23.17 the answer?

  50. anonymous
    • one year ago
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    @Z4K4R1Y4

  51. Z4K4R1Y4
    • one year ago
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    not quite. the area we need to find is the black part.

  52. Z4K4R1Y4
    • one year ago
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    |dw:1433041243267:dw|

  53. Z4K4R1Y4
    • one year ago
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    @alexwaldorf ??

  54. anonymous
    • one year ago
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    395.695? @Z4K4R1Y4

  55. Z4K4R1Y4
    • one year ago
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    that is correct but if you put all the decimals in from both calculations you will get 392.6990817.

  56. anonymous
    • one year ago
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    so is that the final answer lol @Z4K4R1Y4

  57. Z4K4R1Y4
    • one year ago
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    yes

  58. anonymous
    • one year ago
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    so we're done that's it?? @Z4K4R1Y4

  59. Z4K4R1Y4
    • one year ago
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    yes

  60. anonymous
    • one year ago
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    oh my goodness thank you so much you're the best @Z4K4R1Y4 I really really appreciate it

  61. Z4K4R1Y4
    • one year ago
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    no problem. you're welcome

  62. Z4K4R1Y4
    • one year ago
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    I've got to go now...bye

  63. anonymous
    • one year ago
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    have a great night, thanks a bunches!! @Z4K4R1Y4

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