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CalculusCalculus10th Edition

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Chapter 10, Problem 26RE
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Using an Ellipse Consider the ellipse x 2 25 + y 2 9 = 1 .

(a) Find the area of the region bounded by the ellipse.

(b) Fund the volume of the solid generated by revolving the region about its major axis.

To determine

To calculate:

(a) The area of the region bounded by the ellipse whose equation is x225+y29=1.

(b) The volume of the solid generated by revolving the region around the major axis of the ellipse x225+y29=1.

Explanation

Given:

The equation of ellipse is x225+y29=1.

Calculation:

(a)

Consider the equation.

x225+y29=1

Compare the equation x225+y29=1 with the standard equation of an ellipse

(x−h)2a2+(y−k)2b2=1

So, a2=25, b2=9

Then,

a=5.

b=3

As a>b so the ellipse is of the type horizontal major axis and the graph of ellipse is

The area of the region bounded by the ellipse is given by

A=πab

Then,

A=π×5×3=15π

(b)

The equation of the ellipse is: x225+y29=1

Here, the major axis is along the x –- axis.

Rearrange the equations as:

y29=(1−x225)y2=9(1−x225)=925(25−x2)

The required volume is double the volume of the solid obtained by revolving the area in the first quadrant

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Sect-10.1 P-1ESect-10.1 P-2ESect-10.1 P-3ESect-10.1 P-4ESect-10.1 P-5ESect-10.1 P-6ESect-10.1 P-7ESect-10.1 P-8ESect-10.1 P-9ESect-10.1 P-10E
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In Problems 7-10, solve the systems of equations by substitution.

Mathematical Applications for the Management, Life, and Social Sciences

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Convert the expressions in Exercises 6584 to power form. 1(x2+1)334(x2+1)3

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For each general triangle, a. determine the number of solutions and) b. solve the triangle, if possible, using ...

Elementary Technical Mathematics

True or False Label each of the following statements as either true or false. Let and such that is onto. Then ...

Elements Of Modern Algebra

For the following sample data, construct five different interval estimates of the population mean, one each for...

Essentials Of Statistics

Recent research has demonstrated that music-based physical training for elderly people can improve balance, wal...

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John Rock has narrowed down his selection of a new cell phone to two models with similar features. Model 800 is...

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For Questions 12 through 14, determine if the statement is true or false. Every complex number is either a real...

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Planetary Motion In Exercises 61-64, use Exercise 60 to find the polar equation of the elliptical orbit of the ...

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QUALITY CONTROL Jansen Electronics has four machines that produce identical components for use in its DVD playe...

Finite Mathematics for the Managerial, Life, and Social Sciences

A regular hexagonal pyramid has a base whose sides are of length 63 in. each. If the slant height is 12 in., fi...

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Finding an Equation for a Surface of RevolutionIn Exercises 3136, find an equation for the surface of revolutio...

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The polar coordinates of the point P in the figure at the right are:

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Let limxaf(x)=L. For 0 pictured at the right, what is the best choice for in the limit definition? a) p b) q c...

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

Finding a Trigonometric Integral In Exercises 1726, find the trigonometric integral. tansec4d

Calculus (MindTap Course List)

Explain why the main effects in a factorial study may not provide an accurate description of the results?

Research Methods for the Behavioral Sciences (MindTap Course List)

Determine the value z that a. Separates the largest 3 % of all z values from the others (Hint: See Example 7.26...

Introduction To Statistics And Data Analysis

Find the unknown area, base, or height for each of the parallelograms 49 through 60. Where necessary, round the...

Mathematics For Machine Technology

Registered nurses in 2007 made an average hourly wage of 30.04. In 2011, their hourly wage had risen to 33.23. ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Applications Use a calculation to solve each problem. Depreciation In business, equipment is often depreciated ...

College Algebra (MindTap Course List)

In addition to the key words, you should be able to define each of the following terms: literature search title...

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A poll conducted by Zogby International showed that of those Americans who said music plays a very important ro...

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

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