Consider the point P where the gears meet. When the smaller gear rotates clockwise, the larger one will rotate counterclockwise.
Through one rotation of the smaller gear, P will have traveled the circumference of the smaller gear, which is 
in.
At the same time, a point P' on the larger gear traverses the same distance along the larger gear's circumference. This point traces out an arc that is subtended by some angle 
. The arc is as long as the smaller gear's circumference.
The measure of a circle's interior angle subtended by an arc is proportional to a complete revolution, i.e. an angular displacement of 
radians:
For part 2, we apply the same reasoning to the larger gear. In one full rotation of the larger gear, the point P' traverses the circumference 
in, and so does the point P on the smaller gear.
A full rotation is 360 degrees, so the smaller gear would have rotated 
times.
Answer:
500x1.5
Step-by-step explanation:
Parallel: the lines have = slopes. We thus need 5/6 to equal 2/p. then 5p must equal 12, and p = 12/5. (answer)
Check: Is 5/6 = 2 / (12/5)? YES
Perp.: The lines have slopes that are negative reciprocals of one another.
Then -6/5 = 2/p, or
-6 2
---- = ----
5 p Thus, -6p = 10, and p = -5/3 (answer)
X = 13, Y = 10
I'm a bit tired right now, so I'm not going to explain my work, but hopefully this still helps.
Good luck with your schoolwork/homework!
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Apologies in advance for wrong answers or bad explanation.
Gym B should be cheaper by $20 if you go the same number of times.
