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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 3.9, Problem 20E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

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Problem 1E
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Problem 3E
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Problem 7E
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Problem 20E
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Problem 47E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s.

(a) At what rate is his distance from second base decreasing when he is halfway to first base?

(b) At what rate is his distance from third base increasing at the same moment?

Chapter 3.9, Problem 20E, A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base

(a)

To determine

To find: The rate at which his distance from the second base decreasing when he is halfway to the first base.

Explanation

Given:

Let given that a baseball diamond is a square with side 90 ft.

A batter hits the ball and the ball run towards first base with a speed of 24 ft/s, that is dxdt=24  ft/s .

Formula used:

(1) Chain rule: dydx=dydu⋅dudx

(2) Pythagorean Theorem.

Calculation:

Let x be the distance of the batter from the base point H, and y be the distance between the batter and the point from baseball at which it dropped.

Since both x and y changes with the time t

Therefore, x and y both are function of the time variable t

The position of the batter and the baseball as shown in the figure-1 given below

Apply Pythagoras Theorem in the right side Right angle triangle,

y2=(90−x)2+902

Obtain the value of y when x=45,

y2=(90−45)2+902=452+902=2,025+8,100=10,125

On further simplification the value of y is as follows.

y=10,125  =45×45×5=455  ft .

Obtain dydt   when he is halfway to first base

(b)

To determine

To find: The rate at which his distance from the third base increasing when he is halfway to the first base.

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Calculus: Early Transcendentals

In Exercises 5-8, graph the given function or equation. y={12xif1x1x1if1x3

Finite Mathematics and Applied Calculus (MindTap Course List)

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Applied Calculus

Determine the set of points at which the function is continuous. 30. F(x,y)=cos1+xy

Multivariable Calculus

Sketching a Graph by Point Plotting In Exercises 7-16, sketch the graph of the equation by point plotting. y=1x...

Calculus: Early Transcendental Functions

Instead of showing the actual number of individuals in each category, a population frequency distribution graph...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Professional athletes are threatening to strike because they claim that they are underpaid. The team owners hav...

Essentials Of Statistics

Use the given graph of f to state the value of each quantity, if it exists. If it does not exist, explain why. ...

Calculus (MindTap Course List)

DECLINING NUMBER of pay PHONES As cell phones proliferate, the number of pay phones continues to drop. The numb...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Terminology If a histogram is skewed left, more of the data falls which side: right or left?

Understanding Basic Statistics

Find each value requested for the distribution of scores in the following table. X Y 5 1 4 3 3 4 2 5 1 2 n X X2

Statistics for The Behavioral Sciences (MindTap Course List)

The manager of a furniture factory finds that it costs 2200 to manufacture 100 chairs in one day and 4800 to pr...

Single Variable Calculus

Let X = the number of nonzero digits in a randomly selected 4-digit PIN that has no restriction on the digits. ...

Probability and Statistics for Engineering and the Sciences

In Exercises 47 to 54, find the number of subsets of the given set. {1, 7, 11}

Mathematical Excursions (MindTap Course List)

True or false:

Mathematical Applications for the Management, Life, and Social Sciences

Simplify each expression in Exercises 1730, expressing your answer in positive exponent form. xy1x1

Finite Mathematics

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. Objectives 2 3xyx2y...

Intermediate Algebra

Find the domain of the function. 37. F(p)=2p

Single Variable Calculus: Early Transcendentals

Solve each equation and check: x+2=8

Elementary Technical Mathematics

Simplify each expression as much as possible. tan45+cot45

Trigonometry (MindTap Course List)

In Exercise 17 to 20, first prove that triangles are congruent then use CPCTC. Given: P and R are right s M is ...

Elementary Geometry For College Students, 7e

In Exercises 16, H is a normal subgroup of the group G. Find the order of the quotient group G/H. Write out the...

Elements Of Modern Algebra

12. Riverside Industries had cost of goods sold of $359,700 for the year. The beginning inventory at cost was $...

Contemporary Mathematics for Business & Consumers

Finding Tangential and Normal Components of Acceleration In Exercises 35-40, find the tangential and normal com...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding Vertical Asymptotes In Exercises 17-32. find the vertical asymptotes (if any) of the graph of the funct...

Calculus of a Single Variable

In Review Exercises 14 to 17, sketch and describe the locus in space. Find the locus of points equidistant from...

Elementary Geometry for College Students

FOREIGN EXCHANGE Mason has just returned to the United States from a Southeast Asian trip and wishes to exchang...

Finite Mathematics for the Managerial, Life, and Social Sciences

The surface given by z = −r2 in cylindrical coordinates is a(n): elliptic cone hyperboloid of one sheet hyperbo...

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: If , then converge absolutely.

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

Evaluating a Double Integral Using a Change of Variables In Exercises 17-22, use the indicated change of variab...

Multivariable Calculus

Using Formulas In Exercises 77-82, find the indefinite integral by using the appropriate formula from Exercises...

Calculus

Population In Exercises 51-54, the population (in millions) of a country in 2015 and the expected continuous an...

Calculus (MindTap Course List)

In a January 2016 Harris Poll, each of 2252 American adults was asked the following question: If you had to cho...

Introduction To Statistics And Data Analysis

Identify and describe the steps in the research process.

Research Methods for the Behavioral Sciences (MindTap Course List)

A researcher would like to compare two methods for teaching math to third-grade students. Two third-grade class...

Research Methods for the Behavioral Sciences (MindTap Course List)

Find the horizontal asymptotes, if any, of each rational function. f(x)=x+1x34x

College Algebra (MindTap Course List)

Read the settings on the following 0.0001-inch micrometer scales. The vernier, thimble, and barrel scales are s...

Mathematics For Machine Technology

Disneys Hannah Montana: The Movie opened on Easter weekend in April 2009. Over the three-day weekend, the movie...

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

Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let A =...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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