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:
![\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](https://tex.z-dn.net/?f=%5Cdfrac%7B14%5Cpi%5C%2C%5Cmathrm%7Bin%7D%7D%7B2%5Cpi%5C%2C%5Cmathrm%7Brad%7D%7D%3D%5Cdfrac%7B8%5Cpi%5C%2C%5Cmathrm%7Bin%7D%7D%5Ctheta%5Cimplies%5Ctheta%3D%5Cdfrac%7B8%5Cpi%7D7%5C%2C%5Cmathrm%7Brad%7D%5Capprox205.7%5E%5Ccirc)
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.
![\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](https://tex.z-dn.net/?f=%5Cdfrac%7B8%5Cpi%5C%2C%5Cmathrm%7Bin%7D%7D%7B2%5Cpi%5C%2C%5Cmathrm%7Brad%7D%7D%3D%5Cdfrac%7B14%5Cpi%5C%2C%5Cmathrm%7Bin%7D%7D%5Ctheta%5Cimplies%5Ctheta%3D%5Cdfrac%7B7%5Cpi%7D2%5C%2C%5Cmathrm%7Brad%7D%3D630%5E%5Ccirc)
A full rotation is 360 degrees, so the smaller gear would have rotated
times.
Answer:
<h2>600 bottles </h2>
Step-by-step explanation:
Given that Top Hat Soda has 300,000 millilitres of cola to bottle and,
a bottle is 500 millilitres in capacity.
To find the amount of bottles that will fill the Top Hat Soda,
we have to divide Top Hat Soda by the 500 millilitres bottle
we have:
Number of bottles needed to fill Top Hat Soda= 300,000/500 = 600 bottles.
Hence 600 bottles will fill the Top Hat Soda
Answer:
28 in.^2
Step-by-step explanation:
A = bh
Use the triangle to find h.
3^2 + h^2 = 5^2
h^2 = 25 - 9
h = 4
A = (7 in.)(4 in.)
A = 28 in.^2
Answer:
<1 <2 and <1 <4
Step-by-step explanation:
A supplementary angle is a straight line with 180 degrees.