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

Hi, can i get job of teaching maths here

can i get job of teaching maths here

Rational expressions, Now we have to look at rational expressions. A ration...

Now we have to look at rational expressions. A rational expression is a fraction wherein the numerator and/or the denominator are polynomials.  Here are some examples of rational e

Finding the inverse of a function , Finding the Inverse of a Function : Th...

Finding the Inverse of a Function : The procedure for finding the inverse of a function is a rather simple one although there are a couple of steps which can on occasion be somewh

Zero-day attack, What is Zero-Day Attack? Explain Zero-Day Attack

What is Zero-Day Attack? Explain Zero-Day Attack

Describe multiplication and division equations, Describe Multiplication and...

Describe Multiplication and Division Equations? Multiplication Equations :  To solve multiplication equations, divide both sides of the equation by the number being multiplie

Multiplication properties, write a definition for associative property of m...

write a definition for associative property of multiplication in your own words and explain how you use it to compute 4*25*27 mentally

Transportation problems vogel approximation method, if there is a tie betwe...

if there is a tie between two penalties then how to make allocations?

Calculate the value of expected value, The owner of TMH Hospital wants to o...

The owner of TMH Hospital wants to open a new facility in a certain area. He usually builds 25-, 50-, or 100-bed facilities, depending on whether anticipated demand is low, medium

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