Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Chapter 10.1, Problem 88E

(a)

To determine

To find: The equation of the sphere.

(a)

Expert Solution
Check Mark

Answer to Problem 88E

The equation of the sphere is (x−0)2+(y−0)2+(z−0)2=(3963)2 .

Explanation of Solution

Given information:

The given sphere of Earth is 4000 miles and the center of the Earth is placed at the origin of a tree dimensional coordinate system.

  Precalculus with Limits: A Graphing Approach, Chapter 10.1, Problem 88E , additional homework tip 1

Calculation:

Calculate the general equation of a sphere.

  (x−a)2+(y−b)2+(z−c)2=r2

Where,

  • (a,b,c) is a center of a sphere.
  • r is a radius of sphere.

So, the centre of sphere is (0,0,0) and radius is 3963 .

Thus the equation is (x−0)2+(y−0)2+(z−0)2=(3963)2 .

Therefore, the equation of the sphere is (x−0)2+(y−0)2+(z−0)2=(3963)2 .

(b)

To determine

To find: The shape of each of traces form on longitude.

(b)

Expert Solution
Check Mark

Answer to Problem 88E

The trace is of planes containing the z−axis , and shape of a circle of a radius of 3963 miles.

Explanation of Solution

Given information:

The given sphere of Earth is 4000 miles and the center of the Earth is placed at the origin of a tree dimensional coordinate system.

  Precalculus with Limits: A Graphing Approach, Chapter 10.1, Problem 88E , additional homework tip 2

Calculation:

Consider the traces form.

Let North Pole and South Pole lie on z−axis . Then lines of longitude that rum from north-south are the trace of planes containing z−axis and shape f a trace is a circle of radius of 3963 miles.

Therefore, the trace is of planes containing the z−axis , and shape of a circle of a radius of 3963 miles.

(c)

To determine

To find: The shape of each of traces form on latitude.

(c)

Expert Solution
Check Mark

Answer to Problem 88E

The trace of planes perpendicular to z−axis and shape of is circle.

Explanation of Solution

Given information:

The given sphere of Earth is 4000 miles and the center of the Earth is placed at the origin of a tree dimensional coordinate system.

  Precalculus with Limits: A Graphing Approach, Chapter 10.1, Problem 88E , additional homework tip 3

Calculation:

Consider the traces form.

The lines of latitude that run from East-West are the trace of planes perpendicular to z−axis and shape of is circle.

Therefore, the trace of planes perpendicular to z−axis and shape of is circle.

(d)

To determine

To find: The trace of equation of the sphere when the prime meridian represents.

(d)

Expert Solution
Check Mark

Answer to Problem 88E

The prime meridian represents trace of the plane containing the z−axis , and y−axis .

Explanation of Solution

Given information:

The given sphere of Earth is 4000 miles and the center of the Earth is placed at the origin of a tree dimensional coordinate system.

  Precalculus with Limits: A Graphing Approach, Chapter 10.1, Problem 88E , additional homework tip 4

Calculation:

Consider the figure.

The prime meridian represents trace of the plane containing the z−axis , and y−axis .

Therefore, the prime meridian represents trace of the plane containing the z−axis , and y−axis .

(e)

To determine

To find: The trace of equation of the sphere when the equator represents.

(e)

Expert Solution
Check Mark

Answer to Problem 88E

The equator represents trace of the plane containing the z−axis , and y−axis .

Explanation of Solution

Given information:

The given sphere of Earth is 4000 miles and the center of the Earth is placed at the origin of a tree dimensional coordinate system.

  Precalculus with Limits: A Graphing Approach, Chapter 10.1, Problem 88E , additional homework tip 5

Calculation:

Consider the figure.

The equator represents trace of the plane containing the x−axis , and y−axis .

Therefore, the equator represents trace of the plane containing the x−axis , and y−axis .

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Chapter 10.1, Problem 87E
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Chapter 10.1, Problem 89E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
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