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 plow 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

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03-07-2018
Mathematics

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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 plow 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

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jdoe0001 jdoe0001 · Answer 1 · 2018-07-03T23:27:21+02:00

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".

[tex]\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}[/tex]