/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 22 Given a vector-valued function r... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Q. 22 (page 860)

Given a vector-valued function r(t) with domain 鈩�, what is the relationship between the graph of r(t) and the graph of kr(t), where k > 1 is a scalar?

Short Answer

Expert verified

The relationship between the graph of r(t) and the graph of kr(t), where k > 1 is a scalar is that the arc length of the function will become ktimes.

Step by step solution

01

Step 1. Given Information. 

The given vector-valued functionr(t) has a domain鈩�.

02

Step 2. Explanation. 

Let a vector-valued function r(t) in鈩�isr(t)=cost,sint,t,t鈭�0,2蟺.

So, the graph of r(t)is

The arc length of the curve we get by the graph isl=22蟺.

03

Step 3. Explanation. 

Now, multiply by scalar k,so kr(t)=kcost,ksint,kt,t鈭�0,2蟺.

Take k=7,sokr(t)=7cost,7sint,7t.

So, the graph is

Now, the arc length of the curve by the graph is l=142蟺.

So, we can depict by the graphs and arc lengths that the arc length of the function will becomek times.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For each of the vector-valued functions, find the unit tangent vector.

r(t)=(t,t2,t3)

Let r(t) be a differentiable vector function. Prove that role="math" localid="1649602115972" ddt鈥�r鈥�=1鈥�r鈥�r路rr路 (Hint: role="math" localid="1649602160237" 鈥�r鈥�2=r路r

Given a vector-valued function r(t) with domain 鈩�,what is the relationship between the graph of r(t) and the graph of r(kt), where k > 1 is a scalar?

Find parametric equations for each of the vector-valued functions in Exercises 26鈥�34, and sketch the graphs of the functions, indicating the direction for increasing values of t.

r(t)=(sin3t,cos3t)fort鈭�[0,2蟺]

Find parametric equations for each of the vector-valued functions in Exercises 26鈥�34, and sketch the graphs of the functions, indicating the direction for increasing values of t.

r(t)=(sint,cos2t)fort鈭�[0,2蟺]
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.