/*! 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} Q 8 Beth has 3000 feet of fencing av... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q 8 (page 165)

Beth has 3000 feet of fencing available to enclose a rectangular field.

(a) Express the area A of the rectangle as a function of x, where x is the length of the rectangle.

(b) For what value of x is the area largest?

(c) What is the maximum area?

Short Answer

Expert verified

(a) The area A of the rectangle as a function of x is A(x)=-x2+1500x

(b) For the area to be the largest x should be 750

(c) Maximum area is 562500

Step by step solution

01

Part (a) Step 1. Given information

Beth has 3000 feet of fencing available to enclose a rectangular field

02

Part (a) of Step 2. Area A of the rectangle as a function of x. 

Beth has 3000 feet of fencing

Let, x be the length and w be the width

Therefore

2x+2w=3000x+w=1500w=1500-x

The area of the rectangle is A=xw

Substitute the value of w in the equation of the area.

localid="1649807567794" A=x1500-x

A as a function of x will be.

localid="1649807877743" A=-x2+1500x

03

Part (b) of Step 1.  value of x .

The value of the area is the largest in the vertex.

A=-x2-2路750路x+7502-7502=-x2-2路750路x+7502+7502=-x-7502+7502

So, the area is the largest when x=750.

04

Part (c) of Step 1.  Maximum area 

Substitute x=750 in the equation A=-x2+1500x

A(750)=-7502+1500路750A(750)=562500

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

Maximizing Revenue: The price p (in dollars) and the quantity x sold of a certain product obey the demand equation

p=-13x+100

(a) Find a model that expresses the revenue R as a function of x.

(b) What is the domain of R?

(c) What is the revenue if 100 units are sold?

(d) What quantity x maximizes revenue? What is the maximum revenue?

(e) What price should the company charge to maximize revenue?

True or False If the average rate of change of a linear function is 23, then if yincreases by 3,xwill increase by2.

A parabolic arch has a span of 120ftand a maximum height of25ft. Choose suitable rectangular coordinate axes and find an equation of the parabola. Then calculate the height of the arch at points 10ft,20ft,40ft from the center.

Raisins The following data represent the weight (in grams) of a box of raisins and the number of raisins in the box.

(a) Draw a scatter diagram of the data treating weight as the independent variable.

(b) What type of relation appears to exist between the weight of a box of raisins and the number of raisins?

(c) Select two points and find a linear model that contains the points.

(d) Graph the line on the scatter diagram drawn in part (b).

(e) Use the linear model to predict the number of raisins in a box that weighs 42.5 grams.

(f) Interpret the slope of the line found in part (c).

Constructing Rain Gutters A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges 90. See the illustration.

(a) What depth will provide maximum cross-sectional area and hence allow the most water to flow?

(b) What depths will allow at least 16 square inches of water to flow?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Pure 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.