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

Let $ f $ and $ g $ be linear functions with equa…

01:23

Question

Answered step-by-step

Problem 60 Hard Difficulty

The Heaviside function defined in Exercise 59 can also be used to define the ramp function $ y = ctH(t) $ , which represents a gradual increase in voltage or current in a circuit.

(a) Sketch the graph of the ramp function $ y = tH(t) $.
(b) Sketch the graph of the voltage $ V(t) $ in a circuit if the switch is turned on at time $ t = 0 $ and the voltage is gradually increased to 120 volts over a 60-second time interval. Write a formula for $ V(t) $ in terms of $ H(t) $ for $ t \le 60 $.
(c) Sketch the graph of the voltage $ V(t) $ in a circuit if the switch is turned on at time $ t = 7 $ seconds and the voltage is gradually increased to 100 volts over a period of 25 seconds. Write a formula for $ V(t) $ in terms of $ H(t) $ for $ t \le 32 $.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Carson Merrill
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Carson Merrill

Numerade Educator

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

More Answers

04:43

Clarissa Noh

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Related Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Discussion

You must be signed in to discuss.
ll

Leo L.

January 2, 2022

Nevermind. Got it 120 vols over 60 sec = slope of 2

ll

Leo L.

January 2, 2022

Looks like I am missing something basic. Both authors say c = 2t. Where is that 2 coming from? Could someone explain.

td

Tuv D.

August 16, 2020

Part c), when t=7, V(7)=0, so the slope of the graph should be from 0 to 100 for [7,32]

Top Calculus 3 Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 3 Courses

Lectures

Video Thumbnail

04:31

Multivariate Functions - Intro

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

Video Thumbnail

12:15

Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

Join Course
Recommended Videos

0:00

The Heaviside function def…

01:21

The Heaviside function def…

16:39

The Heaviside function def…

01:06

The Heaviside function def…

01:21

The Heaviside function $H$…

01:07

The Heaviside function $\m…

08:50

The Heaviside function $H$…

03:51

The Heaviside function $ H…

Watch More Solved Questions in Chapter 1

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
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66

Video Transcript

So for the given problem um we can use it to define the ramp function Y equals C. T. Hft. Um Which is going to represent a gradual increase in the voltage or current in a circuit. So we're going to sketch the graph of the ramp function. We see the voltage is going to be in this case C is going to be too so we'll have to t 3 50. And then given the ramp function we'll eventually end up getting um Since this is Changing turned on at seven seconds we'll have four Times T -7 yeah. of eight times at age 15 and seven. So that will be our final uh resulting function for the voltage.

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
142
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
Hosted by: Alonso M
See More

Related Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Top Calculus 3 Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 3 Courses

Lectures

Video Thumbnail

04:31

Multivariate Functions - Intro

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

Video Thumbnail

12:15

Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

Join Course
Recommended Videos

0:00

The Heaviside function defined in Exercise 59 can also be used to define the ra…

01:21

The Heaviside function defined in Exercise 57 can also be used to define the ra…

16:39

The Heaviside function defined in Exercise 59 can also be used to define the r…

01:06

The Heaviside function defined in Exercise 57 can also be used to define the r…

01:21

The Heaviside function $H$ is defined by $$H(t)=\left\{\begin{array}{ll} 0 & …

01:07

The Heaviside function $\mathrm{H}$ is defined by $$H(t)=\left\{\begin{array}{…

08:50

The Heaviside function $H$ is defined by $$H(t)=\left\{\begin{array}{ll}{0} & …

03:51

The Heaviside function $ H $ is defined by $ H(t) = \left\{ \begin{…
Additional Mathematics Questions

05:51

For certain item the demand curve is given by
P = D(z) = 1 +2
and the …

00:58

Determine if the graph is a function
Also give the domain and range.
I…

02:48

Question
points
Suve Ans
(Problem Set #6)
The sales of a grocery…

05:54

Assume the distribution of the amount of gravel (in tons) sold by a particul…

01:53

For cach year; the population of a forest of trees, call it Forest A_ is rep…

03:35

A 5 litre container must have a square base, vertical sides, and an open top…

07:06

Three coins are dropped on a table a. Let A be the event "exactly two h…

03:40

According
survey in country, 29% of adults do not have any credit cards. …

01:40

1. Statistical methods used to summarize or describe a collection of data ar…

01:19

[20 points] Consider a randomly selected group of 150 students. Suppose 36 s…

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