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The minute hand of a clock is 1.7 centimeters long. How far does the tip of the minute hand travel in 35 minutes? (Round your answer to two decimal places.) cm Need Help? Read It Watch It​

User Shintaro
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Explanation:

To find the distance traveled by the tip of the minute hand in 35 minutes, we need to determine the circumference of the circular path covered by the tip of the minute hand and then multiply it by the fraction of the circle covered in 35 minutes.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the length of the minute hand serves as the radius of the circular path.

Given that the length of the minute hand is 1.7 centimeters, the radius (r) is also 1.7 centimeters.

So, the circumference (C) is:

C = 2πr

C = 2π(1.7)

C ≈ 10.68 centimeters

Now, we can determine the fraction of the circle covered in 35 minutes. In 60 minutes, the minute hand covers a full circle. Therefore, in 35 minutes, the fraction of the circle covered is 35/60 or 7/12.

Finally, we can calculate the distance traveled by the tip of the minute hand in 35 minutes by multiplying the circumference by the fraction of the circle covered:

Distance = C × (35/60)

Distance ≈ 10.68 × (35/60)

Distance ≈ 6.22 centimeters

Therefore, the tip of the minute hand travels approximately 6.22 centimeters in 35 minutes.

User Covadonga
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