Respuesta :
Answer:
[tex]\theta=156^0[/tex]
Step-by-step explanation:
The smaller gear rotates through an angle of 300°.
In radian, 300°= [tex]300X\frac{\pi}{180} =\frac{5\pi}{3}[/tex]
The arc length, s on the smaller gear(with a radius of 3.7 cm) is:
[tex]s=r\theta[/tex]
[tex]s= \frac{5\pi}{3} X 3.7=\frac{18.5\pi}{3}[/tex]
The larger gear moves through the same arc length.
Therefore:
Arc length of the larger gear, [tex]s=\frac{18.5\pi}{3}[/tex]
Radius of the larger gear =7.1cm
[tex]s=r\theta[/tex]
[tex]\frac{18.5\pi}{3}=7.1\theta\\\theta=\frac{18.5\pi}{3X7.1}\\\theta=\frac{18.5\pi}{21.3}[/tex]
To convert back to degrees
[tex]\theta=\frac{18.5\pi}{21.3}\\\theta=\frac{18.5\pi}{21.3}X\frac{180}{\pi} =156.33\\\\\theta=156^0[/tex]
The larger gear rotates through an angle of 156 degrees.
This question is based on the concept of radian and degree. Therefore, the larger gear rotates through an angle of 156 degrees.
Given:
The radius of the smaller gear is 3.7 cm and the radius of the larger gear is 7.1 cm.
If the smaller gear rotates through an angle of 300°.
According to the question,
The smaller gear rotates through an angle of 300°.
In radian = [tex]300^0 = 300 \times \dfrac{\pi}{180} = \dfrac{5 \pi}{3}[/tex]
Now, find the arc length, s on the smaller gear(with a radius of 3.7 cm) is:
[tex]s = r \theta \\s = \dfrac{5\pi}{3} \times 7 = \dfrac{18.5 \pi}{3}[/tex]
Hence, the larger gear moves through the same arc length.
Therefore, Arc length of the larger gear is [tex]s = \dfrac{18.5 \pi}{3}[/tex].
As we know that, radius of the larger gear = 7.1 cm
[tex]s = r \theta\\\\\dfrac{18.5}{3} = 7.1 \theta\\\\\theta = \dfrac{18.5}{3 \times 7.1 }[/tex]
Now, convert it into degree,
[tex]\theta = \dfrac{18.5}{3 \times 7.1 } \times \dfrac{180}{\pi} \\\\\theta = 156.33[/tex]
[tex]\theta = 156^o[/tex]
Therefore, the larger gear rotates through an angle of 156 degrees.
For more details, prefer this link;
https://brainly.com/question/9747298
