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

Class 10, chapter permutation & combination ex :4.6

chapter permutation & combination ex :4.6

Negative skewness-measure of central tendency, Negative Skewness It i...

Negative Skewness It is an asymmetrical curve whether the long tail extends to the left NB: In developed countries this frequency curve for the age distribution is charact

Example of product moment correlation, Example of Product moment correlatio...

Example of Product moment correlation The given data was acquired during a social survey conducted in a described urban area regarding the yearly income of described families

Calculus level 2, the first question should be done using the website given...

the first question should be done using the website given (www.desmos.com/calculator )and another good example to explain using the graph ( https://www.desmos.com/calculator/ydimzr

Algebra, 25 algebraic equations that equal 36

25 algebraic equations that equal 36

Determine the other two sides of the triangle, The radius of the in circle ...

The radius of the in circle of a triangle is 4cm and the segments into which one side is divided by the point of contact are 6cm and 8cm.  Determine the other two sides of the tria

Determine the size of belt, On a piece of machinery, the centers of two pul...

On a piece of machinery, the centers of two pulleys are 3 feet apart, and the radius of each pulley is 6 inches. Determine the size of belt (in feet) is required to wrap around bot

Example of multiplying decimals, Example of Multiplying Decimals: Exa...

Example of Multiplying Decimals: Example:  0.45 x 10 = 4.5.  Same, while multiplying a decimal through 100, 1000, and 10,000, move the decimal point to the right the similar

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