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?
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- anonymous

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- anonymous

Would I divide 14pi/8pi?

- anonymous

So far I have arc length 25.133 for the smaller circle, and 43.982 for the bigger circle.
43.982 - 25.133 = 18.849?

- anonymous

circumference of smaller gear=2 pi r=2*pi*4=8 pi
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## More answers

- anonymous

I got 205.7 before I asked on here but I wasn't sure Thank You.

- anonymous

correct

- anonymous

Do I just divide the circumference of the smaller circle from the bigger circle to get the amount of rotations?

- anonymous

for part 2.
circumference of larger gear=2*pi*r=2*pi*7=14 pi
circumference of smaller gear=2*pi*4=8pi
no. of revolutions made by smaller gear\[=\frac{ 14 \pi }{ 8 \pi }=\frac{ 7 }{ 4 }\]

- anonymous

Wow this was way simpler than I previously imagined. I don't remember the unit circle very well haha.

- anonymous

yes you started correctly.

- anonymous

So 1.75 revolutions correct?

- anonymous

correct

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