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

Tangent, Tangent, Normal and Binormal Vectors In this part we want to ...

Tangent, Normal and Binormal Vectors In this part we want to look at an application of derivatives for vector functions.  In fact, there are a couple of applications, but they

How long will it take to dispense 330 gallons, A large pipe dispenses 750 g...

A large pipe dispenses 750 gallons of water in 50 seconds. At this rate, how long will it take to dispense 330 gallons? Find out the number of gallons per second by dividing 75

Smith keeps track of poor work, Smith keeps track of poor work. Often on af...

Smith keeps track of poor work. Often on afternoon it is 5%. If he checks 300 of 7500 instruments what is probability he will find less than 20 substandard?

Plot your data on a scatter plot, Devise data that link a certain relations...

Devise data that link a certain relationship OF YOUR CHOOSING between two variables. Write a rationale stating why you chose this particular data and what you are planning to STAT

Theorem, #question if two angles of a triangle are unequal in measure then ...

#question if two angles of a triangle are unequal in measure then the side opposite to greater angle is longer than the side opposite to the smaller angle

Round 14.851 to the nearest tenth, Round 14.851 to the nearest tenth? T...

Round 14.851 to the nearest tenth? The tenths place is the ?rst number to the right of the decimal. Here the number 8 is in the tenths place. To decide whether to round up or

Levels of significance - rejection and acceptance regions, Levels of signif...

Levels of significance A level of significance is a probability value which is utilized when conducting tests of hypothesis. A level of significance is mostly the probability

Explain multiples, Explain Multiples ? When a whole number is multiplie...

Explain Multiples ? When a whole number is multiplied by another whole number, the results you get are multiples of the whole numbers. For example,  To find the first four mult

Differentiate quotient rule functions, Example of quotient rule : Let's no...

Example of quotient rule : Let's now see example on quotient rule.  In this, unlike the product rule examples, some of these functions will require the quotient rule to get the de

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