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:
13.72 cubic units
Step-by-step explanation:
The equation below shows the total volume (V), in cubic units, of 5 identical boxes with each side equal to s units: V = 5s3
If s = 1.4 units, what is the value of V?
Substitute s = 1.4 into V = 5s³ = 5(1.4)³ = 13.72 cubic units.
Answer:
![\frac{4^{21}}{5^6}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5E%7B21%7D%7D%7B5%5E6%7D)
Step-by-step explanation:
![\left(\frac{4^7}{5^2}\right)^3](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7B4%5E7%7D%7B5%5E2%7D%5Cright%29%5E3)
![=\frac{\left(4^7\right)^3}{\left(5^2\right)^3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cleft%284%5E7%5Cright%29%5E3%7D%7B%5Cleft%285%5E2%5Cright%29%5E3%7D)
![\left(4^7\right)^3](https://tex.z-dn.net/?f=%5Cleft%284%5E7%5Cright%29%5E3)
![=4^{21}](https://tex.z-dn.net/?f=%3D4%5E%7B21%7D)
![=\frac{4^{21}}{\left(5^2\right)^3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%5E%7B21%7D%7D%7B%5Cleft%285%5E2%5Cright%29%5E3%7D)
![\left(5^2\right)^3](https://tex.z-dn.net/?f=%5Cleft%285%5E2%5Cright%29%5E3)
![5^6](https://tex.z-dn.net/?f=5%5E6)
![=\frac{4^{21}}{5^6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%5E%7B21%7D%7D%7B5%5E6%7D)
Answer: a^3
Step-by-step explanation: Reduce the expression by cancelling the common factors
Hope this helps! :) ~Zane
A) 20sin (15)
B) 5/tan(15)
C) cos^-1 (10/11)
D) sqrt (180) <---- (a^2 + b^2 = c^2)
I just put what you should type into the calculator. Make sure you have your calculator in the right mode (radian or degree), Idk which you needed so...