Identify the surface for the equation , Mathematics

Assignment Help:

Identify the surface for each of the subsequent equations.

(a) r = 5

(b) r2 + z2 = 100

(c) z = r

Solution

(a)  In two dimensions we are familiar with that this is a circle of radius 5.  As we are now in three dimensions and there is no z in equation this means it is permitted to vary freely.  Thus, for any specific z we will have a circle of radius 5 centered on the z-axis.

Alternatively, we will have a cylinder of radius 5 centered on the z-axis.

(b) This equation will be simple to identify one time we convert back to Cartesian coordinates.

r2 + z2 = 100

x2 + y2 + z2  = 100

Thus, this is a sphere centered at the origin along with radius 10.

(c) Once again, this one won't be too bad if we convert back to Cartesian.  For reasons that will be clear eventually, we'll first square both sides, after that convert.

z2 = r2

z2 = x2 + y2

From the part on quadric surfaces we familiar with that this is the equation of a cone.


Related Discussions:- Identify the surface for the equation

Euilibrium, What is partial market equilibrium

What is partial market equilibrium

Linear programming, I want to send to you a file for my question.How. Could...

I want to send to you a file for my question.How. Could you please send my a link for that.

Assumptions and application of t distribution, Assumptions and Application ...

Assumptions and Application of T Distribution Assumptions of t distribution 1. The sample observations are random 2. Samples are drawn from general distribution 3.

Basics of vectors - calculus, Vectors - The Basics Let us start this s...

Vectors - The Basics Let us start this section off with a quick discussion on what is the use of vector.  Vectors are utilized to present quantities that have both a magnitude

Markov chain, The Video Club Martin rents movies at "regular price" andat ...

The Video Club Martin rents movies at "regular price" andat "half price". Usually if the films are regularly priced one day, they will be at regular price the next day with probab

Excel, do you guys have excel math

do you guys have excel math

Quadratic equation whose roots are real, Write the quadratic equation whose...

Write the quadratic equation whose roots are real and non conjugate Ans)  x^2-x+6=0 ...roots are real and non conjugate

Angles, samuel left mauritius at 22:30 on saturday and travelled to london ...

samuel left mauritius at 22:30 on saturday and travelled to london (GMT) for 14h30min he had a stopover for 4 h in london and he continued to travel to toronto for another 6h20min

What is monomials and polynomials in maths, What is Monomials and Polynomia...

What is Monomials and Polynomials in maths? An expression like 7x is called a monomial. A monomial is an integer, a variable, or a product of integers and variables. Other e

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd