Cartesian to Cyclindrical Coordinate

destroyer130
Messages
18
Reaction score
0
Problem
problem.PNG

Solution answer
answer.PNG

For this one, my upper bound of z in cylindrical's is sqrt(4-r^2) instead of (4-r^2). Which one is right, mine or the solution? Thanks for helping me out.
 
Physics news on Phys.org
destroyer130 said:
Problem
View attachment 54032
Solution answer
View attachment 54033
For this one, my upper bound of z in cylindrical's is sqrt(4-r^2) instead of (4-r^2). Which one is right, mine or the solution? Thanks for helping me out.

I'd say you are right. Must be a typo.
 
You're right
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top