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

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Chapter 7.1, Problem 44E
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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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Finding the Center and Radius of a Sphere In Exercises 39-44, find the center and radius of the sphere. See Example 6.

4 x 2 + 4 y 2 + 4 z 2 − 8 x − 16 y + 11 = 0

To determine

To calculate: The centre and radius of sphere whose equation is 4x2+4y2+4z2−8x+16y+11=0.

Explanation

Given Information:

The equation of sphere, 4x2+4y2+4z2−8x+16y+11=0.

Formula used:

The standard equation of a sphere with centre at (h,k,j) and radius r is,

(x−h)2+(y−k)2+(z−j)2=r2

Calculation:

The equation of sphere can be written as,

4x2+4y2+4z2−8x+16y+11=04(x2+y2+z2−2x+4y+114)=0x2+y2+z2−2x+4y+114=0

Convert the provided equation into the square by grouping the similar variable. So, the above equation can be written as:

(x2−2x)+(y2+4y)+z2+114=0(x2−2x)+(y2+4y)+z2=−114

To complete the square, add the half of square of each linear term of the equation

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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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Use a Pattern in Make Predictions Consider the following figures. Figure a1 consists of two line segments, and ...

Mathematical Excursions (MindTap Course List)

For Problems 11-14, find the absolute value. 6.2

Intermediate Algebra

Evaluate the integral and interpret it as the area of a region. Sketch the region. 0/2sinxcos2xdx

Single Variable Calculus: Early Transcendentals

Note: Exercises preceded by an asterisk are of a more challenging nature. In Exercises 39 and 42, refer to the ...

Elementary Geometry For College Students, 7e

Evaluate cos(sin123) without using a calculator.

Trigonometry (MindTap Course List)

Solve each formula for the given letter: P=WAforA

Elementary Technical Mathematics

25. (See Exercise 8.) Describe the units of . 8. For the given value of , find all the units in . a. ...

Elements Of Modern Algebra

Solve the following word problems. Round dollars to the nearest cent and percents to the nearest tenth of a per...

Contemporary Mathematics for Business & Consumers

Using Lagrange Multipliers In Exercises 1-8, use Lagrange multipliers to find the indicated extrema, assuming t...

Calculus: Early Transcendental Functions (MindTap Course List)

Determining Differentiability In Exercises 77-80, describe the x -values at which f is differentiable. f(x)=x2x...

Calculus of a Single Variable

In Exercise 1731, solve each linear programming problem by the simplex method. Maximize P=2x+6y+6z. Subject to ...

Finite Mathematics for the Managerial, Life, and Social Sciences

Use the Distributive Axiom to simplify each expression: a 6(94) c 7y2y b (12)6(4+8) d 16x+8x

Elementary Geometry for College Students

Even and Odd Functions and Zeros of Functions In Exercises 75-78, determine whether the function is even, odd, ...

Calculus (MindTap Course List)

Find a point c for the Mean Value Theorem for Integrals for f(x) = x2 2x on [2, 5]. a) 18 b) 6 c) 1+7 d) no su...

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

is a(n): ellipsoid elliptic cone elliptic paraboloid elliptic cylinder

Study Guide for Stewart's Multivariable Calculus, 8th

AreaIn Exercises 4146, use a double integral to find the area of the shaded region.

Multivariable Calculus

EXPLORING CONCEPTS Improper Integral Consider the integral 0310x22dx To determine the convergence or divergence...

Calculus

Define primary and secondary sources and explain how each plays a role in the process of finding a research ide...

Research Methods for the Behavioral Sciences (MindTap Course List)

The Coca-Cola Company reported that the mean per capita annual sales of its beverages inthe United States was 4...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Solve the following exercises. Compute angles to the nearer minute in triangles with customary unit sides. Comp...

Mathematics For Machine Technology

Refer again to the crosstabulation of household income by educational level shown in exercise 29. a. Compute co...

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

In Exercises 27-56, use a calculator to find each value. Give the entire display of your calculator. a. ln(2e3....

Mathematics: A Practical Odyssey

Explain the difference between a confidence interval and a prediction interval. How can a prediction level of 9...

Introduction To Statistics And Data Analysis

Describe the purpose of a dismantling design.

Research Methods for the Behavioral Sciences (MindTap Course List)

Let P(x)=5x3+2x2x+1. Use synthetic division to find each value. P(i)

College Algebra (MindTap Course List)

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