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Math
CalculusCalculus (MindTap Course List)8th Edition

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Chapter 3.7, Problem 75E
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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

An observer stands at a point P, one unit away from a track. Two runners start at the point S in the figure and run along the track. One runner runs three times as fast as the other. Find the maximum value of the observer’s angle of sight θ between the runners. [Hint: Maximize tan θ .]

Chapter 3.7, Problem 75E, An observer stands at a point P, one unit away from a track. Two runners start at the point S in the

To determine

To find:

The maximum value of the observer’s angle of sight θ between the runners

Explanation

1) Concept:

If f'x<0 then fx is the absolute minimum value

Formula:

tan⁡α+θ=tanα+tanθ1-tanα·tanθ

2) Calculation:

An observer stands at a point P, one unit away from the track

We have to find value of θ

tan⁡α=Side opposite to αSide adjacent to α

=1t1

=t

tan⁡α+θ=Side opposite to α+θSide adjacent to α+θ

tan⁡α+θ=3t1

By using formula,

tanα+tanθ1-tanα·tanθ=3t

Substitute value of tanα

t+tanθ1-t·tanθ=3t

t+tanθ=3t1-t·tanθ

t+tanθ=3t-3t2·tanθ

tanθ+3t2·tanθ=3t-t

1+3t2

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Contemporary Mathematics for Business & Consumers

23. Let be a group that has even order. Prove that there exists at least one element such that and . (Sec. ) ...

Elements Of Modern Algebra

Reading Tables Use the functions defined in Tables 1 and 2 in Problem 43 to answer the following questions. a. ...

Trigonometry (MindTap Course List)

The graph of θ = 2 in polar coordinates is a: circle line spiral 3-leaved rose

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

Finding a Maclaurin Polynomial In Exercises 1324, find the nth Maclaurin polynomial for the function. f(x)=1x+1...

Calculus: Early Transcendental Functions (MindTap Course List)

The equation of the plane partially drawn in the figure is: x = 3 y = 3 z = 3 x + y = 3

Study Guide for Stewart's Multivariable Calculus, 8th

To construct a regular hexagon, what measure would be necessary for each interior angle? Construct an angle of ...

Elementary Geometry for College Students

CHOOSING A DRIVER Five friends are leaving a bar for home. Aside from the owner of the car, one other person is...

Finite Mathematics for the Managerial, Life, and Social Sciences

Continuity of a Vector-Valued Function In Exercises 71-76, determine the interval(s) on which the vector valued...

Multivariable Calculus

Writing A newspaper headline states that "The rate of growth of the national deficit is decreasing." What does ...

Calculus

Maximum Area A rancher plans to fence a rectangular pasture adjacent to a river. The rancher has 100 meters of ...

Calculus (MindTap Course List)

Describe the two general problems (observer influence and subjectivity) that can exist with behavioral observat...

Research Methods for the Behavioral Sciences (MindTap Course List)

Simplify each expression. Assume that all variables represent positive numbers. Give all answers with positive ...

College Algebra (MindTap Course List)

In Exercises 2128, express the given biconditionals as the conjunction of two conditionals. The quadratic equat...

Mathematics: A Practical Odyssey

The two largest cable providers are Comcast Cable Communications, with 21.5 million subscribers, and Time Warne...

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

Over a nine-month period, OutdoorGearLab tested hardshell jackets designed for ice climbing, mountaineering, an...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

What pattern of results is needed to provide convincing evidence that behavior changed when the phase was chang...

Research Methods for the Behavioral Sciences (MindTap Course List)

Data on x = poverty rate (%) and y = high school dropout rate (%) for the 50 U.S. states and the District of Co...

Introduction To Statistics And Data Analysis

Use a digital micrometer to measure the length and the thickness of a key such as a house key.

Mathematics For Machine Technology

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