/*! 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} Q 37 Describe the graphs of the equat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Q 37 (page 1066)

Describe the graphs of the equations and provide alternative equations in the specified coordinate systems.

. Change 蠒=蟺2to the rectangular and cylindrical systems.

Short Answer

Expert verified

The equation in rectangular coordinatesz=0

The equation in cylindrical coordinatesz=0

Step by step solution

01

Step 1:Given information

The given expression is蠒=蟺2

02

Simplification 

The objective is to convert the equation 蠒=蟺2into rectangular system.

Here,width="49">蠒=蟺2

width="217">鈬�cos-1zx2+y2+z2=蟺2

width="200">鈬�zx2+y2+z2=cos蟺2

localid="1653033836537" 鈬�zx2+y2+z2=0

鈬�z=0

Hence, The given equation in rectangular coordinates is z=0

Now,

To convert to the equation 蠒=蟺2into cylindrical system.

Substituting 蠒=tan-1r2in the equation 蠒=蟺2

So 蠒=蟺2

width="114">鈬�tan-1rz=蟺2

width="97">鈬�rz=tan蟺2

localid="1653034873552" 鈬�rz=10

鈬�z=0

Hence,The equation in cylindrical coordinates z=0

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

Find the masses of the solids described in Exercises 53鈥�56.

The solid bounded above by the plane with equation 2x + 3y 鈭� z = 2 and bounded below by the triangle with vertices (1, 0, 0), (4, 0, 0), and (0, 2, 0) if the density at each point is proportional to the distance of the point from the

xy-plane.

Evaluate each of the double integrals in Exercises37-54as iterated integrals.

localid="1650380493598" 鈭�鈭�Rsin2x+ydA,

wherelocalid="1650380496793" R=x,y|0鈮�x鈮�蟺2and0鈮�y鈮�蟺2

Let f(x, y, z) and g(x, y, z) be integrable functions on the rectangular solid R=x,y,z|a1猢�x猢�a2,b1猢�y猢�b2,c1猢�z猢�c2. . Use the definition of the triple integral to prove that :

鈭�Rf(x,y,z)+g(x,y,z)dV=鈭�Rf(x,y,z)dV+鈭�Rg(x,y,z)dV.

In the following lamina, all angles are right angles and the density is constant:

Discuss the similarities and differences between the definition of the double integral found in Section 13.1and the definition of the triple integral found in this section.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

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.