Download the App!

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

(a) The figure shows a telephone wire hanging between two poles at $ x = -b $ and $ x = b $. It takes the shape of a catenary with equation $ y = c + a \cosh (\frac{x}{a}) $.Find the length of the wire.(b) Suppose two telephone poles are 50 ft apart and the length of the wire between the poles is 51 ft. If the lowest point of the wire must be 20 ft above the ground, how high up on each pole should the wire be attached?

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

a) Length of the wire $=2 a \sinh (b / a)$b) The wire should be attached 24.36 $\mathrm{ft}$ above the ground

Calculus 2 / BC

Chapter 8

Further Applications of Integration

Section 1

Arc Length

Applications of Integration

Missouri State University

Oregon State University

University of Nottingham

Lectures

08:04

$\begin{array}{l}{\text { …

03:40

The figure below shows a t…

00:02

(a) The figure shows a tel…

01:15

Height of a Cable An elect…

03:01

Length of a Cable An elect…

01:18

Electrical wires suspended…

04:57

A telephone line hangs bet…

04:46

he is clear. So when you read here, so we're given why is equal to Steve us. Any closure of X divided by a and the length of the wire we're integrating from negative B to be square root of one plus hyperbolic function of sign that's divine of fighting square defense. This is equal to from negative B to B square root of caution square that's divided but a defense This is equal to from my gonna be to be waas the next departing by a defense. This is equal to hey, sign hyperbolic function. Next Divided by Ang, we're finding from negative beat B because evil tu tu es the hyperbolic function of Sign E over a. That's part A. And for part B, we know the wire is start that X is equal to zero. That's when it's the lowest. So why a zero when we plug it and become C plus A. And since the wire is 20 feet high with the lowest, the lowest point, C plus eight is equal to 20 were given that the wire ISS 51 feet. So we get to a fine high public function being divided by a is equal to 51 since we calculated this in part A in the distance between the two poles is 50 so to be is equal to 50. That makes be equal to 25. You put this into our equation to a the high public function of sign 25 divided, but a is equal to 51. You need a find for a we could use a calculator and we get around 72.4. So to find how high the pole should be attached, begin why off B is equal to see less a caution, the divine a frightening. We just plug things in and it becomes 20 minus a less a caution. You divide it by any we may be equal 25 a equal 72 point fly. We plug these both values insight and we get 24 0.3 six feet approximately

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:25

'11. (5 pts) Teresa is 20 years old and wants to accumulate $1,000,000 …

02:28

'Find the area of the shaded region 2) The region is bounded by y =5x -…

01:48

'iii) The derivative of constant times function is equal to the constan…

01:29

"Assume that C(x) is in dollars and is the number of units produced and…

03:07

'From actuary tables Washington Insurance Company determined the likeli…

04:31

'EMPTYING THE FUNNELWater is running out of a conical funnel, at th…

04:10

'An open box has square base and volume of 864 in3 Find the dimensions …

02:15

'21. The fracture strength of tempered glass averages 14 (measured in t…

03:36

'Calculate the area under the curve: Estimate the area under the graph …

05:35

'Suppose that the random variables Y1 and Y2 have joint probability den…