/*! 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 74 What does it mean to eliminate t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 74

What does it mean to eliminate the parameter? What useful information can be obtained by doing this?

Short Answer

Expert verified
Eliminating the parameter in a set of parametric equations means expressing the equations in non-parametric form, often in terms of x and y only. This can simplify the equations and make the properties of the function they represent easier to visualize and understand.

Step by step solution

01

Explanation of the Concept

Firstly, let's understand what eliminating the parameter means. In mathematics, you will often encounter parametric equations, especially in calculus and physics. These are a set of equations that express the coordinates of points in space as functions of a variable, often denoted as t.
02

The Process

Eliminating the parameter is to express these equations in a non-parametric form. If you have a function expressed in two variables x and y as functions of t such as \(x = f(t)\) and \(y = g(t)\), you eliminate the parameter by expressing y as a function of x.
03

Benefits of Elimination

Doing this can often simplify the equations and make them easier for us to visualize or work with. This might also make more evident certain properties of the function. For example, the function could be a line or a curve, and this would be easier to see in Cartesian form \(y = f(x)\) than in parametric form \(x = f(t)\) and \(y = g(t)\).

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

Use Cramer's Rule (determinants) to solve the system: $$ \left\\{\begin{aligned} x-y &=-5 \\ 3 x+2 y &=0 \end{aligned}\right. $$

Verify the identity: $$ \sin 2 x=2 \cot x \sin ^{2} x $$

What is an ellipse?

Exercises 105鈥�107 will help you prepare for the material covered in the next section. Simplify and write the equation in standard form in terms of \(x^{\prime}\) and \(y^{\prime}\) $$ \left[\frac{\sqrt{2}}{2}\left(x^{\prime}-y^{\prime}\right)\right]\left[\frac{\sqrt{2}}{2}\left(x^{\prime}+y^{\prime}\right)\right]=1 $$

Write an equation for the path of each of the following elliptical orbits. Then use a graphing utility to graph the two ellipses in the same viewing rectangle. Can you see why early astronomers had difficulty detecting that these orbits are ellipses rather than circles? \(\cdot\) Earth's orbit: Length of major axis: 186 million miles Length of minor axis: 185.8 million miles \(\cdot\) Mars's orbit: Length of major axis: 283.5 million miles Length of minor axis: 278.5 million miles
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.