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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 3.9, Problem 47E
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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
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

A plane flying with a constant speed of 300 km/h passes over a around radar station at an altitude of 1 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later?

To determine

To find: The rate of change of the distance from the plane to the radar station.

Explanation

Formula used:

Chain rule: dydx=dydu⋅dudx.

Calculation:

Let us assume that at any time t, A be the position of top of radar station on the ground and P be the position of the plane 1 minute later after crossing the radar and B be the position of the radar on the ground.

Let x be the distance between the top of the radar and plane and y be the distance between the ground point of the radar and the plane as shown in the Figure 1 given below.

Since x and y changes with the time t, x and y are the function of the time t.

Since the plane climbs at an angle of 30° from the horizontal, the total angle between the plane and radar is 120°.

Obtain dydt when t=1 min later.

From the cosine rule in the ΔAPB.

y2=12+x2−2(1)(xcos(120))=1+x2−2x(−12)=1+x+x2

Differentiate y2=1+x+x2 with respect to the time t.

ddt(y2)=ddt(x2+x+1)2ydydt=(2x+1)dxdt             &#

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Chapter 3.9,
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Calculus: An Applied Approach (MindTap Course List)

Find the area of the part of the spherex2+y2+ z2 = a2 that lies inside the cylinderx2+y2=ax.

Multivariable Calculus

In a sample of n 6 scores, five of the scores are each above the mean by one point. Where is the sixth score l...

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

SOC Data on several variables measuring overall health and well-being for 11 nations are reported here for 2010...

Essentials Of Statistics

In Exercises 4143, find the distance between the two points. 42. (9, 6) and (6, 2)

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

If a function of one variable is continuous on an interval and has only one critical number, then a local maxim...

Calculus (MindTap Course List)

Recent research has shown that creative people are more likely to cheat than their less creative counterparts (...

Statistics for The Behavioral Sciences (MindTap Course List)

Critical Thinking Consider these types of graphs: histogram, bar graph. Pareto chart, pie chart, stem-and-leaf ...

Understanding Basic Statistics

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard funct...

Single Variable Calculus

For Problems 1-10, identify each statement as true or false. Objective 1 Every rational number is a real number...

Intermediate Algebra

The sample data x1, x2,...., xn sometimes represents a time series, where xt = the observed value of a response...

Probability and Statistics for Engineering and the Sciences

In Exercises 53 to 62, find the cardinality of each of the following sets. For some exercises you may need to c...

Mathematical Excursions (MindTap Course List)

In Problems 27 and 28, find the slope of the line that passes through each pair of points. 28. and

Mathematical Applications for the Management, Life, and Social Sciences

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

Finite Mathematics

Evaluate the difference quotient for the given function. Simplify your answer. 28. f(x)=x3,f(a+h)f(a)h

Single Variable Calculus: Early Transcendentals

Use y-y1=mx-x1to find the equation of the line that contains a,b and is perpendicular to the line y=-1cx+d. Lea...

Elementary Geometry For College Students, 7e

Give the exact value of each of the following. cos6

Trigonometry (MindTap Course List)

Let H be a normal subgroup of finite group G. If the order of the quotient group G/H is m, prove that gmH for a...

Elements Of Modern Algebra

Calculate the assessed value and the property tax due on the following properties. FairMarketValueAssessmentRat...

Contemporary Mathematics for Business & Consumers

Perform the indicated operations and simplify: 383516

Elementary Technical Mathematics

Finding an Equation of a Line In Exercises 1924, find an equation of the line that passes through the point and...

Calculus of a Single Variable

Finding Numbers In Exercises 5-10, find two positive numbers that satisfy the given requirements. The sum of th...

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercise 5 to 12, plan and write the two-column proof for each problem. Given: MNQR MNQR Prove: MNPRQP

Elementary Geometry for College Students

In Exercises 6568, determine whether the statement is true or false. If it is true, explain why it is true. If ...

Finite Mathematics for the Managerial, Life, and Social Sciences

0 1 2 ∞

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

For the vector function r(t) with unit tangent T, the principal unit normal vector is:

Study Guide for Stewart's Multivariable Calculus, 8th

Sraphing Level Curves Using Technology In Exercises 59- 62, use a graphing utility to graph six level curves of...

Calculus (MindTap Course List)

Finding the Distance Between Two Parallel PlanesIn Exercises 9194, verify that the two planes are parallel and ...

Multivariable Calculus

Using a Theorem In Exercises 6164, (a) use Theorem 9.5 to show that the sequence with the given n th term conve...

Calculus

As part of a study of the effects of timber management strategies (Ecological Applications [2003]: 11101123), i...

Introduction To Statistics And Data Analysis

The following data give the percentage of women working in five companies in the retail and trade industry. The...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Evaluate 734(916+212) .

Mathematics For Machine Technology

Self Check Graph: 3x2y=6.

College Algebra (MindTap Course List)

If o(E)=5:9, find o(E).

Mathematics: A Practical Odyssey

On the basis of data provided by a Romac salary survey, the variance in annual salaries for seniors in public a...

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

Describe the basic concern with measuring inter-rater reliability and explain how Cohens kappa addresses this c...

Research Methods for the Behavioral Sciences (MindTap Course List)

Construct a frequency distribution histogram or polygon for the set of scores presented in the following freque...

Research Methods for the Behavioral Sciences (MindTap Course List)

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