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anonymous

  • one year ago

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 inches, and the larger gear has a radius of 7 inches. two circles touching at one point. Larger circle has radius of 7 inches. Smaller circle has radius of 4 inches. Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation? Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear? Show all work.

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  1. anonymous
    • one year ago
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    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
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    let me think

  3. jim_thompson5910
    • one year ago
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    we basically have this picture going on |dw:1440116767058:dw|

  4. jim_thompson5910
    • one year ago
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    what is the circumference of circle A?

  5. anonymous
    • one year ago
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    25.12

  6. jim_thompson5910
    • one year ago
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    let's leave it in terms of pi

  7. jim_thompson5910
    • one year ago
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    you should get 8pi

  8. anonymous
    • one year ago
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    ok

  9. jim_thompson5910
    • one year ago
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    how about the larger circle?

  10. anonymous
    • one year ago
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    14pi

  11. jim_thompson5910
    • one year ago
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    if we divide 14pi by 8pi, we get (14pi)/(8pi) = 14/8 = 7/4

  12. jim_thompson5910
    • one year ago
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    convert 7/4 to a decimal to get 7/4 = 1.75 basically this number tells us that the smaller circle will do 1.75 full rotations as it rolls around the larger circle. Basically the smaller circle does 1.75 rotations per 1 rotation of the larger circle

  13. anonymous
    • one year ago
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    ok

  14. jim_thompson5910
    • one year ago
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    take this ratio 1.75 rotations of A: 1 rotation of B and divide both parts by 1.75 to get (1.75/1.75) rotation of A: (1/1.75) rotation of B 1 rotation of A: 0.57142857 rotation of B

  15. jim_thompson5910
    • one year ago
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    so 1 full revolution of circle A means circle B only does approx 0.57142857 of a full revolution

  16. anonymous
    • one year ago
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    so how to answer part 1

  17. jim_thompson5910
    • one year ago
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    well you simply multiply 0.57142857 by the number of degrees in a full rotation

  18. anonymous
    • one year ago
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    oh ok

  19. jim_thompson5910
    • one year ago
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    part 2 is pretty much answered when I said how many times A revolves as it rolls around B

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