300 IS THE ESTIMATED ANSWER.
46% / 100% = ?/ 200 ⇒ you can say 100 ×2 = 200 so 46 ×2 = 92 so the answer is 92 :D
Answer:
<em>The larger gear will rotate through 156°</em>
Step-by-step explanation:
<u>Arc Length</u>
The arc length S of an angle θ on a circle of radius r is:
![S = \theta r](https://tex.z-dn.net/?f=S%20%3D%20%5Ctheta%20r)
Where θ is expressed in radians.
The smaller gear of r1=3.7 cm drives a larger gear of r2=7.1 cm. The smaller gear rotates through an angle of θ1=300°.
Convert the angle to radians:
![\displaystyle \theta_1=300*\frac{\pi}{180}=\frac{5\pi}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta_1%3D300%2A%5Cfrac%7B%5Cpi%7D%7B180%7D%3D%5Cfrac%7B5%5Cpi%7D%7B3%7D)
The arc length of the smaller gear is:
![\displaystyle S_1=\frac{5\pi}{3}\cdot 3.7](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_1%3D%5Cfrac%7B5%5Cpi%7D%7B3%7D%5Ccdot%203.7)
![\displaystyle S_1=\frac{18.5\pi}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_1%3D%5Cfrac%7B18.5%5Cpi%7D%7B3%7D)
The larger gear rotates the same arc length, so:
![\displaystyle S_2=\frac{18.5\pi}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_2%3D%5Cfrac%7B18.5%5Cpi%7D%7B3%7D)
![\displaystyle \theta_2\cdot r_2=\frac{18.5\pi}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta_2%5Ccdot%20r_2%3D%5Cfrac%7B18.5%5Cpi%7D%7B3%7D)
Solving for θ2:
![\displaystyle \theta_2=\frac{18.5\pi}{3r_2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta_2%3D%5Cfrac%7B18.5%5Cpi%7D%7B3r_2%7D)
![\displaystyle \theta_2=\frac{18.5\pi}{3*7.1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta_2%3D%5Cfrac%7B18.5%5Cpi%7D%7B3%2A7.1%7D)
![\theta_2=2.73\ radians](https://tex.z-dn.net/?f=%5Ctheta_2%3D2.73%5C%20radians)
![\displaystyle \theta_2=2.73*\frac{180}{\pi}=156](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta_2%3D2.73%2A%5Cfrac%7B180%7D%7B%5Cpi%7D%3D156)
The larger gear will rotate through 156°