/*! 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 60 The illumination from a light so... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 60

The illumination from a light source varies inversely as the square of the distance from the light source. If you raise a lamp from 15 inches to 30 inches over your desk, what happens to the illumination?

Short Answer

Expert verified
When the lamp is raised from 15 inches to 30 inches, the illumination on the desk will get quartered.

Step by step solution

01

Identify the relationship

In this kind of problem where the illumination varies inversely as the square of the distance from the light source, the mathematical representation can be \[ I = \frac{k}{d^2} \] where \(I\) represents the illumination, \(d\) is the distance from the source, and \(k\) is the constant of variation which remains consistent throughout the problem.
02

Determine the relation between the original distance and the new distance

According to the problem, the lamp is raised from 15 inches to 30 inches. So, the distance is doubled.
03

Apply the inversely proportional principle

As the illumination \(I\) is inversely proportional to the square of distance, when the distance is doubled, the illumination will get cut to a quarter because the new illumination \(I'\) would be \[ I' = \frac{k}{(2d)^2} = \frac{k}{4d^2} = \frac{I}{4}\]. So, the illumination is quartered.

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 a graphing utility to graph $$f(x)=\frac{x^{2}-4 x+3}{x-2} \quad \text { and} \quad g(x)=\frac{x^{2}-5 x+6}{x-2}$$ What differences do you observe between the graph of \(f\) and \(g ?\) How do you account for these differences?

Write the equation of a rational function \(f(x)=\frac{p(x)}{q(x)}\) having the indicated properties, in which the degrees of \(p\) and \(q\) are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. \(f\) has a vertical asymptote given by \(x=1,\) a slant Esymptote whose equation is \(y=x, y\) -intercept at \(2,\) and \(x\) -intercepts at \(-1\) and 2.

In Exercises \(78-79,\) use a graphing utility to graph \(f\) and \(g\) in the same viewing rectangle. Then use the \(200 \mathrm{M} \text { OUT }]\) feature to show that \(f\) and g have identical end behavior. $$f(x)=x^{3}-6 x+1, \quad g(x)=x^{3}$$

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. $$f(x)=-3(x-1)^{2}\left(x^{2}-4\right)$$

Use a graphing utility to graph \(y=\frac{1}{x^{2}}, y=\frac{1}{x^{4}},\) and \(y=\frac{1}{x^{6}}\) in the same viewing rectangle. For even values of \(n,\) how does changing \(n\) affect the graph of \(y=\frac{1}{x^{n}} ?\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.