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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 4.7, Problem 77E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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
Problem 81E
Problem 82E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Where should the point P be chosen on the line segment AB so as to maximize the angle θ?

Chapter 4.7, Problem 77E, Where should the point P be chosen on the line segment AB so as to maximize the angle ?

To determine

To find: The position of P on the line segment AB so that θ is maximum.

Explanation

Given:

Length of AB =3.

Calculation:

Let BC=2 and AD=5.

∠CPD=θ.

In Figure 1,

Let, ∠BPC=α and ∠APD=β.

Let BP=x.

Hence,

AP=3−x.

In triangle ΔPBC,

tanα=2xα=tan−1(2x)

In triangle ΔPAD,

tanβ=53−xβ=tan−1(53−x)

Now,

θ+α+β=180θ=180−α−β

Substitute α=tan−1(2x) and β=tan−1(53−x) in θ,

θ=180−tan−1(2x)−tan−1(53−x)

Differentiate θ with respect to x,

θ′=−(11+(2x)2×(−2x2))−(11+(53−x)2×5(3−x)2)=24+x2−5x2−6x+34

For critical points, θ′=0

24+x2−5</

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Chapter 4.7,
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Expand each expression in Exercises 122. x(4x+6)

Finite Mathematics

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or gi...

Single Variable Calculus: Early Transcendentals

Label each of the following statements as either true or false. 1. Mapping composition is a commutative operati...

Elements Of Modern Algebra

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Elementary Geometry For College Students, 7e

For the following investments, find the total number of compounding periods and the interest rate per period. T...

Contemporary Mathematics for Business & Consumers

Change each of the following to decimal degrees. If rounding is necessary, round to the nearest hundredth of a ...

Trigonometry (MindTap Course List)

Perform the indicated operations and simplify: 71613

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Finding a Derivative In Exercises 29-40, Find the derivative of the algebraic function. h(x)=1x2+5xx+1

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In Exercise 14, solve the linear programming problem by the simplex method. Minimize C=2x+4y+z Subject to x+2y+...

Finite Mathematics for the Managerial, Life, and Social Sciences

Find the number of sides of a regular polygon that has a central angle measuring a 90. c 60. b 45. d 24.

Elementary Geometry for College Students

True or False: converges if and only if .

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Evaluate dx using the Fundamental Theorem of Calculus. 6 12 18 24

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Selection bias and individual differences are both potential problems dealing with the participants in a study....

Research Methods for the Behavioral Sciences (MindTap Course List)

Referring to the previous exercise, use the result of Part (a) along with the fact that a carton contains 12 eg...

Introduction To Statistics And Data Analysis

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

Determine which, if any, of the three lines PQ, PR, and QR are perpendicular. Explain how to determine whether ...

College Algebra (MindTap Course List)

Create an example of a citation for each of the following: a. A single author cited in parentheses. b. Two or m...

Research Methods for the Behavioral Sciences (MindTap Course List)

Solve each of the following equations using the multiplication principle of equality. Check each answer. 4=y(78...

Mathematics For Machine Technology

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STATISTICS F/BUSINESS+ECONOMICS-TEXT

Finding a Jacobian In Exercises 35-40, find the Jacobian (x,y,z)(u,v,w) for the indicated change of variables. ...

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