MHB Solving the Domain: sqrt(x^2+y^2-1)>0 and 1<= x^2+y^2 <=20

[Kris1]

Im trying to combine this domain into something of the form a>b and b<c however I cannot seem to convert this equation :/

Is it possible to convert this domain into a single expression??

The domain is

sqrt(x^2+y^2-1)>0 and 1<= x^2+y^2 <= 20

any ideas?? I've encountered this problem many times and I am unsure as to how to solve this. Is there a general formula to apply?

 

[MarkFL]

The first condition:

$$\sqrt{x^2+y^2-1}>0$$

implies:

$$1<x^2+y^2$$

Because both conditions must be true (as implied by the "and" between them), we find the intersection of the implication of the first condition with the second condition, to find we require:

$$1<x^2+y^2\le 20$$

in order for both conditions to be satisfied.

 

[Kris1]

Thanks this makes a lot of sense. Combining two like this makes a lot of sense. This will make all of my further calculations easier thank you :)