/*! 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 1 Write an equation that expresses... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 1

Write an equation that expresses each relationship. Use \(k\) as the constant of variation. \(g\) varies directly as \(h\)

Short Answer

Expert verified
The equation that expresses the relationship is \(g = kh\).

Step by step solution

01

Understanding direct variation

Firstly, get familiar with the concept of direct variation. If one quantity varies directly as another, it means they increase or decrease at a constant rate. The equation representing a direct variation is usually written in the form \(y = kx\), where \(k\) is the constant of variation.
02

Writing the equation for the given quantities

Knowing that the rule for direct variation is \(y = kx\), we can use this to form an equation using our variables \(g\) and \(h\). In this case, let \(g\) be the \(y\) variable and \(h\) be the \(x\) variable, with \(k\) remaining the constant of variation. Thus the equation that expresses the relationship is \(g = kh\).

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

In Exercises \(21-26,\) use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$f(x)=11 x^{4}-6 x^{2}+x+3$$

In Exercises \(35-50\) a. Use the Leading Coefficient Test to determine the graphs end behavior. b. Find \(x\) -intercepts by setting \(f(x)=0\) and solving the resulting polynomial equation. State whether the graph crosses the \(x\)-axis, or touches the \(x\)-axis and turns around, at each intercept. c. Find the \(y\) -intercept by setting \(x\) equal to 0 and computing \(f(0)\) d. Determine whether the graph has \(y\) -axis symmetry, origin symmetry, or neither. e. If necessary, find a few additional points and graph the function. Use the fact that the maximum number of turning points of the graph is \(n-1\) to check whether it is drawn correctly. $$f(x)=-2 x^{4}+2 x^{3}$$

In Exercises \(27-34,\) find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the \(x\) -axis, or touches the \(x\) -axis and turns around, at each zero. $$f(x)=2(x-5)(x+4)^{2}$$

The polynomial function $$ f(x)=-0.87 x^{3}+0.35 x^{2}+81.62 x+7684.94 $$ models the number of thefts, \(f(x),\) in thousands, in the United States \(x\) years after \(1987 .\) Will this function be useful in modeling the number of thefts over an extended period of time? Explain your answer.

In Exercises \(55-56,\) use a graphing utility to determine upper and lower bounds for the zeros of \(f .\) Does synthetic division verify your observations? $$ f(x)=2 x^{4}-7 x^{3}-5 x^{2}+28 x-12 $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.