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serg [7]
3 years ago
8

a street that is 116 meters long is covered in snow city workers are using a snow plow to clear the street a tire on the snow pl

ow has to turn 29 times and traveling the length of the street what is the diameter of the tire use the value 3.144 pi
Mathematics
1 answer:
Yuri [45]3 years ago
4 0
So, we know the snow plow tire turned or went around 29 times, namely 29 revolutions, and recall that one revolution is a 2π angle in radians.

since the tire went around 29 times, so it made an angle of 29 * 2π, or 58π.

we know the street is 116 meters long, namely "an arc made by that 58π angle is 116".

\bf \textit{arc's length}\\\\
s=r\theta ~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad radians\\
------\\
s=116\\
\theta =58\pi 
\end{cases}\implies 116=r58\pi \implies \cfrac{116}{58\pi }=r
\\\\\\
\cfrac{2}{\pi }=r\qquad \qquad\qquad \qquad  \stackrel{\textit{a \underline{d}iameter is twice the radius}}{2\left( \cfrac{2}{\pi } \right)=d\implies \cfrac{4}{\pi }=d}
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