/*! 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 55 The heat generated by a stove el... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 55

The heat generated by a stove element varies directly as the square of the voltage and inversely as the resistance. If the voltage remains constant, what needs to be done to triple the amount of heat generated?

Short Answer

Expert verified
The resistance needs to be divided by 3 to triple the amount of heat generated.

Step by step solution

01

Understanding the exercise

Study the problem and recognize that when one quantity varies directly as another, the variation can be described by an equation of the form y=kx, where k is constant. Similarly, inverse variation can be presented by an equation of the form y=k/x. Here it's said that the heat H varies directly as the square of the voltage v ( i.e., \(H鈭漹^2\) ) and inversely as the resistance r (H鈭�1/r). Combining these, we get \(H =k* (v^2/r)\), where k is the constant of variation.
02

Formulate the equation

Given that the voltage stays the same, but the heat triples, set up an equation. If H is replaced by 3H (triple the amount of heat) and r by r1 (the new resistance), we get \(3H = k*(v^2/r1)\).
03

Solve for the new resistance

Solve the new formula for r1. By using the original relationship \(H = k*(v^2/r)\), substitute for k in our new equation \(3H = k*(v^2/r1)\) which gives \(r1 = (v^2*r)/(3H)\). Hence, the resistance should be divided by 3 to triple the heat generated when the voltage is constant.

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 the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies inversely as \(x . y=12\) when \(x=5 .\) Find \(y\) when \(x=2\).

The perimeter of a rectangle is 180 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 800 square feet.

The average number of daily phone calls, \(C\), between two cities varies jointly as the product of their populations, \(P_{1}\) and \(P_{2}\) and inversely as the square of the distance, \(d\), between them. a. Write an equation that expresses this relationship. b. The distance between San Francisco (population: \(777,000\) ) and Los Angeles (population: \(3,695,000\) ) is 420 miles. If the average number of daily phone calls between the cities is \(326,000,\) find the value of \(k\) to two decimal places and write the equation of variation. c. Memphis (population: \(650,000\) ) is 400 miles from New Orleans (population: \(490,000\) ). Find the average number of daily phone calls, to the nearest whole number, between these cities.

Will help you prepare for the material covered in the next section. a. If \(y=k x^{2},\) find the value of \(k\) using \(x=2\) and \(y=64\) b. Substitute the value for \(k\) into \(y=k x^{2}\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=5\)

A company is planning to manufacture mountain bikes The fixed monthly cost will be \(\$ 100,000\) and it will cost \(\$ 100\) to produce each bicycle. a. Write the cost function, \(C\), of producing \(x\) mountain bikes. b. Write the average cost function, \(\bar{C},\) of producing \(x\) mountain bikes c. Find and interpret \(\bar{C}(500), \bar{C}(1000), \bar{C}(2000),\) and \(\bar{C}(4000)\) \- d. What is the horizontal asymptote for the graph of the average cost function, \(\bar{C}\) ? Describe what this means in practical terms.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Probability and 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.