Download the App!

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

Question

Answered step-by-step

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

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Yiming Zhang

Numerade Educator

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

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 4

Work

Missouri State University

Oregon State University

Idaho State University

Boston College

Lectures

04:47

Show how to approximate th…

01:02

Show how to approximate …

01:52

07:45

01:14

03:59

02:20

$13-22$ Show how to approx…

0:00

02:33

04:24

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,

View More Answers From This Book

Find Another Textbook

01:00

A firm is offered trade credit of 1/5, net 15. If the firms payson 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) > 0Set one side equal to zero and list the interval e…

03:21

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

01:23

If the depth of water in a basin is x cm, the volume is30x(10+2x)cm^3. …

01:40

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

A ferris wheel is 35 meters in diameter and boarded from aplatform 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 theprincipal P is invested at the in…