/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 90 The minute hand of a clock is 6 ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 90

The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of \(\pi\) and then round to two decimal places.

Short Answer

Expert verified
The tip of the minute hand travels approximately \(12.56\) inches.

Step by step solution

01

Understanding the movement of the minute hand

The minute hand of the clock moves from 12 to 4. This is one third of a full circle (since a full circle would involve 12 hours).
02

Calculating the circumference of the full circle

The formula for the circumference of a circle is \(C= 2\pi r\), where \(r\) is the radius of the circle. Given that the length of the minute hand, which acts as the radius, is 6 inches, we find the full circumference as \(C= 2\pi * 6 = 12\pi\) inches.
03

Calculating the distance the tip of the minute hand travels

Since 12 to 4 is one third of a full circle, the distance the tip of the minute hand travels is one third of the full circumference, which is \(12\pi /3 = 4\pi\) inches.
04

Rounding

Finally, we express our answer in decimal form rounded to two decimal places. One can calculate the numerical value of \(\pi\) as being approximately 3.14. Multiply this by 4 to get \(4\pi = 12.56\) inches.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve for \(x:\) $$2 \sin ^{-1} x=\frac{\pi}{4}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I convert degrees to radians, I multiply by \(1,\) choosing \(\frac{\pi}{180^{\circ}}\) for 1

Explain what is meant by one radian.

Use a sketch to find the exact value of each expression. $$ \sec \left[\sin ^{-1}\left(-\frac{\sqrt{2}}{2}\right)\right] $$

Solve \(y=2 \sin ^{-1}(x-5)\) for \(x\) in terms of \(y\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.