/*! 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} Problem 75 Find a set of parametric equatio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 75

Find a set of parametric equations to represent the graph of the rectangular equation using (a) \(t=x\) and (b) \(t=2-x\). $$y=e^{x}$$

Short Answer

Expert verified
The set of parametric equations for (a) using \(t=x\) is \(x=t\), \(y=e^{t}\) and for (b) using \(t=2-x\) is \(x=2-t\), \(y=e^{2-t}\)

Step by step solution

01

Step 1:Initialize the general equation

We鈥檙e given a single equation in two variables \(x\) and \(y\), \(y=e^{x}\). Our goal is to rewrite it parametrically, which means we want a separate equation for each variable. The expressions will both be in terms of a new variable, often called the parameter and here denoted as \(t\).
02

Rewrite equation using parameter \(t=x\)

In this step, we substitute \(x\) with the parameter \(t\) in the given equation. Then we get a set of parametric equations. These are: \(x = t, y = e^{t}\)
03

Rewrite equation using parameter \(t=2-x\)

Now, we use parameter setting \(t=2-x\). To start we鈥檒l need to solve this equation for \(x\). Solving for \(x\), we'll get \(x=2-t\). Then we substitute \(2-t\) for \(x\) in the equation \(y=e^{x}\) to get \(y=e^{2-t}\). So our parametric equations in this case are: \(x = 2 - t, y = e^{2-t}\)

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

Path of a Softball The path of a softball is modeled by $$-12.5(y-7.125)=(x-6.25)^{2}$$ where the coordinates \(x\) and \(y\) are measured in feet, with \(x=0\) corresponding to the position from which the ball was thrown. A. Use a graphing utility to graph the trajectory of the softball. B. Use the trace feature of the graphing utility to approximate the highest point and the range of the trajectory.

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$x^{2}+y^{2}=a^{2}$$

Find the distance between the point and the line. Point \((2,1)\) Line \(y=x+2\)

In Exercises \(91-116\), convert the polar equation to rectangular form. $$r=3 \cos 2 \theta$$

Determine whether the statement is true or false. Justify your answer. Because the graphs of the parametric equations \(x=t^{2}, y=t^{2} \quad\) and \(\quad x=t, y=t\) both represent the line \(y=x,\) they are the same plane curve.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Logic and Functions

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.