/*! 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 70 A car's rear windshield wiper ro... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 70

A car's rear windshield wiper rotates \(125^{\circ} .\) The total length of the wiper mechanism is 25 inches and wipes the windshield over a distance of 14 inches. Find the area covered by the wiper.

Short Answer

Expert verified
The area covered by the wiper is approximately 49.658 square inches.

Step by step solution

01

Compute the radius

Since the total length of the wiper mechanism is given as 25 inches and the wiper wipes a distance of 14 inches (which represents the diameter of the circle), the radius (r) of the circle is half the diameter. So, the radius is given by \(r = \frac{d}{2} = \frac{14}{2} = 7\) inches.
02

Compute the area of the sector

We use the formula for the area of a sector which is: \( Area = \frac{\theta}{360} \times \pi r^{2}\), where \(\theta\) is the central angle. Plugging in the values we have:\( Area = \frac{125}{360} \times \pi \times (7)^2 \).
03

Solve for the area

Carrying out the multiplication, we get that the area is approximately \(49.658\) square 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

Evaluate the expression without using a calculator. \(\sin ^{-1}\left(-\frac{\sqrt{2}}{2}\right)\)

Sketch a graph of the function and compare the graph of \(g\) with the graph of \(f(x)=\arcsin x .\) \(g(x)=\arcsin (x-1)\)

Evaluate the expression without using a calculator. \(\arctan \frac{\sqrt{3}}{3}\)

Use a graphing utility to graph the functions \(f(x)=\sqrt{x}\) and \(g(x)=6\) arctan \(x .\) For \(x>0,\) it appears that \(g>f .\) Explain why you know that there exists a positive real number \(a\) such that \(g< f\) for \(x>a .\) Approximate the number \(a\) .

Use a calculator to evaluate the expression. Round your result to two decimal places. \(\arctan 25\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

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.