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Math
CalculusCalculus (MindTap Course List)8th Edition

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Chapter 3.7, Problem 37E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is (a) a maximum? (b) A minimum?

To determine

To cut:

The wire into pieces of square and equilateral triangle so that the total area enclosed is (a) maximum (b) minimum

Explanation

1) Concept:

Divide the wire into a circle and square, and find dimensions of circle and square. Then, find the maximum and minimum area using the formula.

2) Formula:

1) Area of equilateral triangle 34 l2

Where l is a side of the triangle

2) Area of square l2 where l is side of square.

3) Calculation:

A piece of wire of length 10 m cut into two pieces.

One piece is bent into a square

Suppose length x is bent into a square

As the sides of squares are equal

Lengths of each side of squares are x4

Other is bent into an equilateral triangle

Area of the wire used = Area of square + Area of equilateral triangle

A(x)= x42+3410-x3.10-x3

A(x)=x216+310-x236

A'x=x8 +310-x18(-1)

A'x=x8-310-x18

A'x=18x-8310-x144

The total area enclosed is maximum or minimum, when A'(x)=0

0=18x-8310-x144

Multiply on both sides by 144

18x-8310-x=0

18x-803+83x=0

Combine like terms,

18+83x-803=0

Adding 803 from both sides,

18+83x=803

Divide by 18+83 on both sides,

x=80318+83

Factoring 80=2·40 and 18+83=29+43

x=2·40329+43

Cancelling out common factor,

x=4039+43=4

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Finding Equations of Tangent Lines In Exercises 27-30, find the equations of the tangent lines at the point whe...

Calculus of a Single Variable

A log 10 m long is cut at 1-meter intervals and its cross-sectional areas A (at a distance x from the end of th...

Single Variable Calculus: Early Transcendentals

Label each of the following statements as either true or false. If ab0(modn), then either a0(modn) or b0(modn).

Elements Of Modern Algebra

Let f(x)=2x5 and g(x)=x2+3x+4. Evaluate the following. f(2)

Trigonometry (MindTap Course List)

30. Among other ingredients, a recipe for linguini with red sauce calls for the following: 24 ounces linguini p...

Contemporary Mathematics for Business & Consumers

True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

If the predator population increases in a predator-prey model, the prey population will a) decrease b) increase...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Finding a Vector In Exercises 3 and 4, find the component form of v given its magnitude and the angle it makes ...

Calculus: Early Transcendental Functions (MindTap Course List)

OPTIMIZING ADVERTISING EXPOSURE As part of a campaign to promote its annual clearance sale, Excelsior Company d...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 9 to 28, use the drawings as needed to answer the following questions. Consider the figure for Exe...

Elementary Geometry for College Students

ProofIn Exercises 4752, prove the poverty of the cross product. u(vw)=(uv)w

Multivariable Calculus

Finding Partial DerivativesIn Exercises 1518, find w/s and w/t using the appropriate Chain Rule. Evaluate each ...

Calculus

Finding Volume In Exercises 21-26, use a double integral to find the volume of the indicated solid.

Calculus (MindTap Course List)

Consider the Costello Music Company problem in exercise 48. The quarterly sales data follow. Year Quarter I Qua...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Write these numbers as words using the alternative method for reading decimal fractions. 39. 12.104

Mathematics For Machine Technology

In Exercises125-132, match the logarithmic expression on the left with an equivalent logarithmic expression on ...

College Algebra (MindTap Course List)

It is common for baseball pitchers to use stretching to prepare for a game. But does this make a difference? Th...

Introduction To Statistics And Data Analysis

Describe the third-variable problem and the directionality problem, identify these problems when they appear in...

Research Methods for the Behavioral Sciences (MindTap Course List)

Define the concept of “stability” within a phase, and explain why it is important.

Research Methods for the Behavioral Sciences (MindTap Course List)

Pelican Stores Pelican Stores, a division of National Clothing, is a chain of womens apparel stores operating t...

Statistics for Business & Economics, Revised (MindTap Course List)

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