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CalculusCalculus10th Edition

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Chapter 11.2, Problem 42E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Calculus

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

Finding the Equation of a SphereIn Exercises 43–46, complete the square to write the equation of the sphere in standard form. Find the center and radius.

x 2 + y 2 + z 2 + 9 x − 2 y + 10 z + 19 = 0

To determine

To calculate: The center and radius of sphere x2+y2+z2+9x−2y+10z+19=0 rewrite in standard form.

Explanation

Given:

The equation is x2+y2+z2+9x−2y+10z+19=0.

Formula used:

The equation of sphere is (x−l)2+(y−m)2+(z−m)2=r2 where (l,m,n) are the center points and r is the radius.

The formula from algebra is:

(a−b)2=a2−2ab+b2(a+b)2=a2+2ab+b2

Calculation:

Consider the equation x2+y2+z2+9x−2y+10z+19=0.

Then, group the same variable terms.

x2+y2+z2+9x−2y+10z+19=0x2+9x+y2−2y+z2+10z+19=0

Then, try to make the complete square term of the same variables.

Then for that add and subtract (92)2 in the variable x terms, then 12 in the variable y term and similarly 52 in z term.

So,

x2+2⋅x⋅92+(92)2−(92)2+y2−2⋅y⋅1+12−12+z2+2⋅z⋅5+52−52+

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Mathematical Excursions (MindTap Course List)

Simplify the algebraic expressions in Problems 15-34 by removing parentheses and combining similar terms. Objec...

Intermediate Algebra

An integral equation is an equation that contains an unknown function y(x) and an integral that involves y(x). ...

Single Variable Calculus: Early Transcendentals

For the following investments, compute the amount of compound interest earned in 1 year and the annual percenta...

Contemporary Mathematics for Business & Consumers

Assume that is a binary operation on a non empty set A, and suppose that is both commutative and associative....

Elements Of Modern Algebra

Evaluate each expression without using a calculator and write your answer in radians. arccos(22)

Trigonometry (MindTap Course List)

In Exercises 9 to 24, find an equation of the line described. Leave the solution in the form Ax+By = C. The lin...

Elementary Geometry For College Students, 7e

From the sample space in Exercise 3, what is the probability that one ace will be drawn?

Elementary Technical Mathematics

Using the Root Test In Exercises 39-52, use the Root Test to determine the convergence or divergence of the ser...

Calculus: Early Transcendental Functions (MindTap Course List)

Rectangular-to-Polar Conversion In Exercises 15-24, the rectangular coordinates of a point are given. Plot the ...

Calculus of a Single Variable

What condition must be satisfied for it to be possible to circumscribe a circle about trapezoid RSTV?

Elementary Geometry for College Students

What is the future value of an annuity? Give an example.

Finite Mathematics for the Managerial, Life, and Social Sciences

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