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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Stacey Warren - Expert brainly.com
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let me think
we basically have this picture going on
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what is the circumference of circle A?
let's leave it in terms of pi
you should get 8pi
how about the larger circle?
if we divide 14pi by 8pi, we get
(14pi)/(8pi) = 14/8 = 7/4
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
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
so 1 full revolution of circle A means circle B only does approx 0.57142857 of a full revolution
so how to answer part 1
well you simply multiply 0.57142857 by the number of degrees in a full rotation
part 2 is pretty much answered when I said how many times A revolves as it rolls around B