1. ## miscellaneous questions

Yes,
I do know i should start a new thread for every question but I would end up with 4 threads in several forums each containing a (probably) silly question, so I think it is ok to post here.

1. To show given the lengths of a triangle this triangle exists, what do I have to do?
I thought of the inequality (a+b<c) and the sides being positve, what else?

2. Given a cubic function, do the ends always point in different directions(+ and -)?

3.Given 0<a<b is it sufficient to say sqrt(a)<sqrt(b) just by something like it is monotone?

4. A graph without circles is a tree. Does this apply to directed graphs, too?

2. Originally Posted by Sam1992
Yes,
I do know i should start a new thread for every question but I would end up with 4 threads in several forums each containing a (probably) silly question, so I think it is ok to post here.

1. To show given the lengths of a triangle this triangle exists, what do I have to do?
I thought of the inequality (a+b<c) and the sides being positve, what else?

2. Given a cubic function, do the ends always point in different directions(+ and -)?

3.Given 0<a<b is it sufficient to say sqrt(a)<sqrt(b) just by something like it is monotone?

4. A graph without circles is a tree. Does this apply to directed graphs, too?

Dear Sam1992,

For the first one use the cosine rule to find the three angles. If the three angles add up to 180 degrees the traingle exists.

3. Hello, Sam1992!

1. To show given the lengths of a triangle this triangle exists, what do I have to do?

I thought of the inequality (a+b < c) and the sides being positve, what else?

I assume you mean the Triangle Inequality.

Given the three sides of a triangle,
. . the sum of any two sides must be greater than the third side.

If the three sides are $a,b,c$, the following must be true:

. . . . . . $\begin{array}{ccc}a + b &>& c \\ a+c &>& b \\ b+c &>& a \end{array}$