/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 38 Describe the solid satisfying th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 38

Describe the solid satisfying the condition. \(x^{2}+y^{2}+z^{2}>4\)

Short Answer

Expert verified
The solid is the region in 3D space outside a sphere of radius 2 centered at the origin.

Step by step solution

01

Identification of the Equation Form

The equation provided, \(x^{2}+y^{2}+z^{2}>4\), is of the form \(x^{2}+y^{2}+z^{2}=r^{2}\), where r is the radius of a sphere in a 3D space. Reading from the equation, we can see that r is equal to 2 (since 2 squared equals 4). As we are dealing with an inequality and not an equation, the radius is not exactly 2, but the sphere's expansion will be based on this value of 2.
02

Interpretation of the Inequality

Since we have \(x^{2}+y^{2}+z^{2}>4\), this conveys that we are dealing with a volume that is greater than the volume of the sphere with radius 2. This simply means that the solid that satisfies this condition is the region of the 3D space located outside of a sphere of radius 2, centered at the origin.
03

Final Conclusion

Having identified the inequality's nature and the type of solid it defines, we can therefore define the solid that satisfies the condition \(x^{2}+y^{2}+z^{2}>4\) as the region outside a sphere of radius 2 centered at the origin in a three-dimensional (3D) coordinate space.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Geography Because of the forces caused by its rotation, Earth is an oblate ellipsoid rather than a sphere. The equatorial radius is 3963 miles and the polar radius is 3950 miles. Find an equation of the ellipsoid. (Assume that the center of Earth is at the origin and that the trace formed by the plane \(z=0\) corresponds to the equator.)

A toy wagon is pulled by exerting a force of 25 pounds on a handle that makes a \(20^{\circ}\) angle with the horizontal. Find the work done in pulling the wagon 50 feet.

An object is pulled 10 feet across a floor, using a force of 85 pounds. The direction of the force is \(60^{\circ}\) above the horizontal. Find the work done.

What is the \(x\) -coordinate of any point in the yz-plane?

Consider the vectors \(\mathbf{u}=\langle\cos \alpha, \sin \alpha, 0\rangle\) and \(\mathbf{v}=\langle\cos \beta, \sin \beta, 0\rangle\) where \(\alpha>\beta\) Find the dot product of the vectors and use the result to prove the identity \(\cos (\alpha-\beta)=\cos \alpha \cos \beta+\sin \alpha \sin \beta\).
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.