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

Video games, Should video game companies continue to alter their products t...

Should video game companies continue to alter their products to include other functions, such as e-mail

Basic requirement for interpolation & extrapolation to work, What is the ba...

What is the basic requirement for both interpolation and extrapolation to work?  There must exist a functional relationship between an independent variable and a dependent variable

Equal matrices, Is this given matrices are called equal Matrices?

Is this given matrices are called equal Matrices?

Calculate the volume of rectangular piece of cardboard, 1. A rectangular pi...

1. A rectangular piece of cardboard measuring 15 inches by 24 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side

Shares and dividend, a man in rested rupee 800 is buying rupee 5 shares and...

a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit

Give an examples of simplifying fractions , Give an examples of Simplifying...

Give an examples of Simplifying Fractions ? When a fraction cannot be reduced any further, the fraction is in its simplest form. To reduce a fraction to its simplest form,

Calculate latest triangular area sail for his boat, Rick is order a latest ...

Rick is order a latest triangular sail for his boat. He needs knowing the area of the sail. Which formula will he use? The area of a triangle is 1/2 times the length of the bas

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