anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
let me think
jim_thompson5910
  • jim_thompson5910
we basically have this picture going on |dw:1440116767058:dw|

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More answers

jim_thompson5910
  • jim_thompson5910
what is the circumference of circle A?
anonymous
  • anonymous
25.12
jim_thompson5910
  • jim_thompson5910
let's leave it in terms of pi
jim_thompson5910
  • jim_thompson5910
you should get 8pi
anonymous
  • anonymous
ok
jim_thompson5910
  • jim_thompson5910
how about the larger circle?
anonymous
  • anonymous
14pi
jim_thompson5910
  • jim_thompson5910
if we divide 14pi by 8pi, we get (14pi)/(8pi) = 14/8 = 7/4
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
ok
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
so 1 full revolution of circle A means circle B only does approx 0.57142857 of a full revolution
anonymous
  • anonymous
so how to answer part 1
jim_thompson5910
  • jim_thompson5910
well you simply multiply 0.57142857 by the number of degrees in a full rotation
anonymous
  • anonymous
oh ok
jim_thompson5910
  • jim_thompson5910
part 2 is pretty much answered when I said how many times A revolves as it rolls around B

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