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Lubov Fominskaja [6]
4 years ago
7

Pls help

Mathematics
1 answer:
N76 [4]4 years ago
5 0
A. 45/100 = 9/20
B. 9/20 = 27/x
9x=540
x = 6
She was assigned 60 problems (showing your work is practically justification in its on right)
C. 60-27
Yolanda still has 33 problems to do.
Hope this helped
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8 0
3 years ago
How do I solve this?
Verdich [7]

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 8\pi 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 \theta. 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 2\pi radians:

\dfrac{14\pi\,\mathrm{in}}{2\pi\,\mathrm{rad}}=\dfrac{8\pi\,\mathrm{in}}\theta\implies\theta=\dfrac{8\pi}7\,\mathrm{rad}\approx205.7^\circ

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 14\pi in, and so does the point P on the smaller gear.

\dfrac{8\pi\,\mathrm{in}}{2\pi\,\mathrm{rad}}=\dfrac{14\pi\,\mathrm{in}}\theta\implies\theta=\dfrac{7\pi}2\,\mathrm{rad}=630^\circ

A full rotation is 360 degrees, so the smaller gear would have rotated \dfrac{630^\circ}{360^\circ}=1.75 times.

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6 0
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