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

What is the diameter of the pipe along with the insulation, A pipe has a di...

A pipe has a diameter of 2.5 inches. Insulation which is 0.5 inches thick is placed around the pipe. What is the diameter of the pipe along with the insulation around it? The i

Congruences, Suppose m be a positive integer, then the two integer a and b ...

Suppose m be a positive integer, then the two integer a and b called congurent modulo m ' if a - b is divisible by m i.e.  a - b = m where is an positive integer. The congru

Differential equation.., 3.6Find the general solution of the differential e...

3.6Find the general solution of the differential equation Y" + 4y = Sec2 2x

Direction field for the differential equation, We require to check the deri...

We require to check the derivative thus let's use v = 60. Plugging it in (2) provides the slope of the tangent line as -1.96, or negative. Thus, for all values of v > 50 we will ha

Hypothesis testing procedure, Hypothesis Testing Procedure Whenever a b...

Hypothesis Testing Procedure Whenever a business complaint comes up here is a recommended procedure for conducting a statistical test. The reason of such a test is to establish

External division of section formula, give me the derivation of external di...

give me the derivation of external division of sectional formula using vectors

Find the least number that is divisible by all numbers, Find the  leas...

Find the  least  number that  is  divisible by all  numbers between 1  and  10  (both inclusive). Ans: The required number is the LCM of 1,2,3,4,5,6,7,8,9,10 ∴ LCM = 2  × 2

Spurious correlations, Spurious Correlations - in several rare situati...

Spurious Correlations - in several rare situations when plotting the data for x and y we may have a group indicating either positive correlation or negative (-ve) correlation

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