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Assuming that the hour hand on an analog clock does not move with the minute hand (in a real clock, it does), what is the arc length between the hour hand and minute hand of an analog clock at 10:10? State your answer in terms of r since we do not know the radius. Why might this be a common time for clock makers to use for images of their clocks?

Assuming that the hour hand on an analog clock does not move with the minute hand in a real clock it does what is the arc length between the hour hand and minut class=

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Solution

Given the hour-hand and minute hand of an analog clock:

Length of an arc =

[tex]l=\frac{\theta}{360}\times2\pi r[/tex]

where

r = radius

pi = 3.142

[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ l=\frac{120}{360}\times2\times3.142\times r \\ l=2.095r \end{gathered}[/tex]

Hence the arc length = 2.095r

Therefore the correct answer is 2.095r

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