Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Show how to approximate the required work by a Ri…

01:52

Question

Answered step-by-step

Problem 14 Medium Difficulty

Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it.

A thick cable, 60 ft long and weighing 180 lb, hangs from a winch on a crane. Compute in two different ways the work done if the winch winds up 25 ft of the cable.
(a) Follow the method of Example 4.
(b) Write a function for the weight of the remaining cable after $ x $ feet has been wound up by the winch. Estimate the amount of work done when the winch pulls up $ \Delta x ft $ of cable.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Yiming Zhang
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Yiming Zhang

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 4

Work

Related Topics

Applications of Integration

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Join Course
Recommended Videos

04:47

Show how to approximate th…

01:02

Show how to approximate …

01:52

Show how to approximate th…

07:45

Show how to approximate th…

01:14

Show how to approximate …

03:59

Show how to approximate th…

02:20

$13-22$ Show how to approx…

0:00

Show how to approximate th…

02:33

Show how to approximate th…

04:24

Show how to approximate th…

Watch More Solved Questions in Chapter 6

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34

Video Transcript

So first, let's figure out what is Thea adamant about? We're reading some. No, the way this 1 80 pounds and the cable is the length of the cable of 60 feet. So the racial are is one A or 60 equals 223 And, uh so that is the weaker link is three times the X, and that's gonna be over elements, you know, weariness up and Barbie with a calculator work they're requires to get a label. Gotta get a cable wanting up for 25 feats. And that's the wedding by two whores. The first part is, you know, the work to want it up and the second poor is second part is actually, um, the weight of the 30 but remaining feet of the table. Just think of it. You wanted something up. You have to Hey, some energy to to want it up. And, uh, you have to live out way have lived out the rest of the cable that is on wondering. Right? So it's actually, um, that one plus two. And for double one simple and easy equals to deserve to 25 3 times played by minus X, the eggs. That's the work. We used to wonder up the cable from 0 to 25 seats up all right. And that particles too. 970 37 points, creepy feeds guns. And second for is sitting part is the work we gonna pay for the remaining 35 feet at the table. And we know from the first way we know from our aid at our inter grants and three X three times down the eggs so poor and integral, which is to transform driven some to a ribbon into girl. It's gonna be 3 30 to 35 33 the eggs 333 times 20. But the ends, That's Theo, the length of the cable that has been lifted up. And that part is fixes number, which is people's too 70 welcomes 25 in the that's 2625 feet guns. So until the whole work able student, everyone wants it to, which equals two 3562 going to be bit guns. That's a total work, too. T make the job done. Okay,

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
65
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
43
Hosted by: Alonso M
See More

Related Topics

Applications of Integration

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

Recommended Videos

04:47

Show how to approximate the required work by a Riemann sum. Then express the wo…

01:02

Show how to approximate the required work by a Riemann sum. Then express the …

01:52

Show how to approximate the required work by a Riemann sum. Then express the wo…

07:45

Show how to approximate the required work by a Riemann sum. Then express the wo…

01:14

Show how to approximate the required work by a Riemann sum. Then express the …

03:59

Show how to approximate the required work by a Riemann sum. Then express the wo…

02:20

$13-22$ Show how to approximate the required work by a Riemann sum. Then expre…

0:00

Show how to approximate the required work by a Riemann sum. Then express the wo…

02:33

Show how to approximate the required work by a Riemann sum. Then express the wo…

04:24

Show how to approximate the required work by a Riemann sum. Then express the wo…
Additional Mathematics Questions

01:00

A firm is offered trade credit of 1/5, net 15. If the firms pays
on day 2…

05:04

The temperature during a day can be modeled by a sinusoid.
Answer the fol…

02:21

x^2 (x+1) (x-8) > 0
Set one side equal to zero and list the interval e…

03:21

Write the equation 9𝑥 2 − 𝑦 2 − 14𝑦 − 58 = 0 in standard form
and determi…

01:23

If the depth of water in a basin is x cm, the volume is
30x(10+2x)cm^3. …

01:40

The population of a city is modeled by the equation
P(t)=249,246e0.15t wh…

03:21

A ferris wheel is 35 meters in diameter and boarded from a
platform that …

01:03

Write the following function in terms of its cofunction.
cos(π/8) Write y…

13:43


Find the x-intercepts of each of the following functions. Also, describe…

03:54

7: Find the accumulated amount A if the
principal P is invested at the in…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started