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Chapter 4: Problem 83

Find the absolute value of the radian measure of the angle that the second hand of a clock moves through in the given time. 55 seconds

Short Answer

Expert verified
The absolute value of the radian measure of the angle that the second hand of a clock moves through in 55 seconds is \( \frac{11\pi}{6} \) radians

Step by step solution

01

Identify Key Information

The second hand of a clock completes a full revolution, which is \(2\pi\) radians, in 60 seconds.
02

Set up a Proportion

We know the number of radians covered in 60 seconds, but we want to find out the number of radians covered in 55 seconds. We can describe this relationship with the following proportion: \(\frac{2\pi}{60} = \frac{x}{55}\). Where x is the number of radians covered in 55 seconds.
03

Solve for x

We can now solve the previously mentioned equation for x. After cross-multiplication, we get \(x = \frac{55 \times 2\pi}{60}\)
04

Simplify x

We simplify x to get the final answer.\( x = \frac{11\pi}{6} \)

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