Problem

A telephone line hangs between two poles $ 14 m $…

04:57

Problem 50 Easy Difficulty

A flexible cable always hangs in the shape of a centenary $ y = c + a \cosh (x/a), $ where $ c $ and $ a $ are constants and $ a > 0 $ (see Figure 4 and Exercise 52.) Graph several members of the family of functions $ y = a \cosh (x/a). $ How does the graph change as $ a $ varies?

Name: a flexible cable always hangs in the shape of a centenary y c a cosh xa where c and a are constants
Uploaded: 2021-01-22
Duration: 2 min 53 s
Channel: Numerade
Description: A flexible cable always hangs in the shape of a centenary $ y = c + a \cosh (x/a), $ where $ c $ and $ a $ are constants and $ a > 0 $ (see Figure 4 and Exercise 52.) Graph several members of the family of functions $ y = a \cosh (x/a). $ How does the graph change as $ a $ varies?

Answer

Check back soon!

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Joseph L.

Boston College

Watch More Solved Questions in Chapter 3

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

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Video Transcript

All right, So let's go through this question. It basically is asking you if I have the expression. A Times coach off X divided by A as a changes. What kind of pattern do you see in the graph? Easy. We're just going to drop it and see what happens. Mhm. So first I am going to simply start with coach. Coach of X is a glass that looks like this. We know that it's an even function. It's a mixture off E to the X and E to the negative X, and it's split it in half. So that's why we know that it's It's a very nice curve that kind of looks like a parabola, and it's also usually modeled as things like wires handing. Uh huh. Let's see what happens when y is equal to to coach off X development. As you can see, the pattern is that now the height is instead of at one. It's now starting at two. It's being stretched out horizontally a little bit more. Let's see what happens if it's equal to five. Why equals two five? Coach off X of a five can see that now. The height is a little bit higher. It starts at five. It's being stretched out even farther. So long Story short, this pattern continues. If why equals a who's off X over a anything on the value of A, you're gonna be able to see what's gonna happen. So if it goes like this, when a is a fraction, it becomes very small. When a is a large large number, it just gets taller and taller and it gets stretched out horizontally. So I want you to pay attention to my cursor if you imagine that this is a point that I can pull to the left and to the right. That's basically what happens with wires. If you pull the wire sideways far apart from the center, the graph is going to be stretched out even more like this, and the very bottom part of the wire starts getting taller and taller. Right? So this is one of the reasons why this graph is very useful for representing how wires case okay? And that answers the question of how a coach X divided by a behaves

Yuki H.

University of California, Berkeley

Topics

Derivatives

Differentiation

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 11

Hyperbolic Functions