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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7, Problem 4TYS
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Find the center and radius of the sphere whose equation is

x 2 + y 2 + z 2 − 20 x + 10 y − 10 z + 125 = 0.

To determine

To calculate: The centre and radius of the sphere x2+y2+z2−20x+10y−10z+125=0.

Explanation

Given information:

The provided equation of sphere x2+y2+z2−20x+10y−10z+125=0.

Formula used:

The procedure to calculate center and radius from general equation of sphere x2+y2+z2+ax+by+cz+d=0,

Step-1 Find the group the term with same variable,

Step-2 Find complete the square of (y2+by) add [12(b)]2 to each side,

Step-3 Write the above equation as (x−a)2+(y−b)2+(z−c)2=R2.

The center of sphere is (a,b,c) and radius is R.

Calculation:

Consider the equation of sphere

x2+y2+z2−20x+10y−10z+125=0

Now the group the term with same variable,

(x2−20x)+(y2+10y)+(z2−10z)=−125

Now complete the square of (x2−20x) add [12(−20)]2 to each side, complete the square of (y2+10y) add [12(10)]2 to each side, complete the square of (z2−10z) add [12(−10)]2 to each side,

(x2−20x+[12(−20)]2)+(y2+10y+[12(10)]2)+(z2−10z+[12(−14)]2)=−125+[12(−

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Sect-7.1 P-1CPSect-7.1 P-2CPSect-7.1 P-3CPSect-7.1 P-4CPSect-7.1 P-5CPSect-7.1 P-6CPSect-7.1 P-7CPSect-7.1 P-1SWUSect-7.1 P-2SWUSect-7.1 P-3SWU
Sect-7.1 P-4SWUSect-7.1 P-5SWUSect-7.1 P-6SWUSect-7.1 P-7SWUSect-7.1 P-8SWUSect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10ESect-7.1 P-11ESect-7.1 P-12ESect-7.1 P-13ESect-7.1 P-14ESect-7.1 P-15ESect-7.1 P-16ESect-7.1 P-17ESect-7.1 P-18ESect-7.1 P-19ESect-7.1 P-20ESect-7.1 P-21ESect-7.1 P-22ESect-7.1 P-23ESect-7.1 P-24ESect-7.1 P-25ESect-7.1 P-26ESect-7.1 P-27ESect-7.1 P-28ESect-7.1 P-29ESect-7.1 P-30ESect-7.1 P-31ESect-7.1 P-32ESect-7.1 P-33ESect-7.1 P-34ESect-7.1 P-35ESect-7.1 P-36ESect-7.1 P-37ESect-7.1 P-38ESect-7.1 P-39ESect-7.1 P-40ESect-7.1 P-41ESect-7.1 P-42ESect-7.1 P-43ESect-7.1 P-44ESect-7.2 P-1CPSect-7.2 P-2CPSect-7.2 P-3CPSect-7.2 P-1SWUSect-7.2 P-2SWUSect-7.2 P-3SWUSect-7.2 P-4SWUSect-7.2 P-5SWUSect-7.2 P-6SWUSect-7.2 P-1ESect-7.2 P-2ESect-7.2 P-3ESect-7.2 P-4ESect-7.2 P-5ESect-7.2 P-6ESect-7.2 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10ESect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 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Essentials Of Statistics

Ranking a group of cities in terms of "quality of life" would be an example of measurement on a(n)______scale o...

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

In Exercises 18, determine whether the equation defines y as a linear function of x. If so, write it in the for...

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

5556 Find the absolute maximum and minimum values of f on the set D. f(x,y)=ex2y2(x2+2y2); D is the disk x2+y24

Calculus (MindTap Course List)

Critical Thinking Consider a data set with at least three data values. Suppose the highest value is increased b...

Understanding Basic Statistics

16. IQ test scores are standardized to produce a normal distribution with a mean of µ = 100 and a standard devi...

Statistics for The Behavioral Sciences (MindTap Course List)

Find the domain and sketch the graph of the function. 40. g(t)=t21t+1

Single Variable Calculus

Solve the equations in Exercises 126. (x3+1)x+1(x3+1)2x+1=0

Finite Mathematics

For problems 15-26, simplify each numerical expression. Be sure to take advantage of the properties whenever th...

Intermediate Algebra

In problems 45-62, perform the indicated operations and simplify. 57.

Mathematical Applications for the Management, Life, and Social Sciences

Exactly one of the following equations is a valid inclusion-exclusion formula for the union of three finite set...

Mathematical Excursions (MindTap Course List)

Use the definition in Expression (3.13) to prove that V(aX + b) = a2 x2. [Hint: With h(X) = aX + b, E[h(X)] = ...

Probability and Statistics for Engineering and the Sciences

If 2x g(x) x4 x2 + 2 for all x, evaluate limx1g(x)

Single Variable Calculus: Early Transcendentals

Factor: 25a225b2

Elementary Technical Mathematics

Label each of the following statements as either true or false. The only ideal of a ring R that property contai...

Elements Of Modern Algebra

What condition must be satisfied for it to be possible to circumscribe a circle about kite ABCD?

Elementary Geometry For College Students, 7e

Verify each identity. cotx=sin4x+sin6xcos4xcos6x

Trigonometry (MindTap Course List)

Calculate the assessed value and the property tax due on the following properties. 11. Fair Market Value Asses...

Contemporary Mathematics for Business & Consumers

Finding an Indefinite Integral In Exercises 21-26, find the indefinite integral. lnxxdx

Calculus of a Single Variable

Finding the Distance Between Two Parallel Lines In Exercises 99 and 100, verify that the two lines are parallel...

Calculus: Early Transcendental Functions (MindTap Course List)

The cylindrical brush on a vacuum cleaner is powered by an electric motor. In the figure, the drive shaft is at...

Elementary Geometry for College Students

PARENTAL INFLUENCE ON CHILDRENS CAREER CHOICES In an online survey of 1962 executives from 64 countries conduct...

Finite Mathematics for the Managerial, Life, and Social Sciences

True or False: Let F(x, y) = 2x cos yi x2 sin yj and C be the cubic y = x3 curve for 0 ≤ x ≤ 2. Then is indep...

Study Guide for Stewart's Multivariable Calculus, 8th

Probability A car battery has an average lifetime of 48 months with a standard deviation of 6 months. The batte...

Calculus (MindTap Course List)

Motion of a Liquid In Exercises 85 and 86, the motion of a liquid in a cylindrical container of radius 4 is des...

Multivariable Calculus

Verifying a Limit by the Definition In Exercises 3-6, use the definition of the limit of a function of two vari...

Calculus

The interval of convergence of is: [−1, 1] [−1, 1) (−1, 1] (−1, 1)

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

A researcher reports survey results by stating that the standard error of the mean is 20. The population standa...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A machine fills containers with a particular product. The standard deviation of fillingweights is known from pa...

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

Use the information on birth weights for babies born in Canada given in the previous exercise to answer the fol...

Introduction To Statistics And Data Analysis

Assume that an object tossed vertically upward reaches a height of h feet after t seconds, where h=100t16t2. Wh...

College Algebra (MindTap Course List)

Read the settings on the following 0.001-inch micrometer scales.

Mathematics For Machine Technology

For each of the following, identify the section of a research report that would probably contain the desired in...

Research Methods for the Behavioral Sciences (MindTap Course List)

Go through a current newspaper or magazine and select one article that describes the results of a study. Summar...

Research Methods for the Behavioral Sciences (MindTap Course List)

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