let r$($n$)=2$n$^2+5$nlog$($n$)+50.$ we claim that r$($n$)$ belongs to $\backslash$Omega $($n$^2).$ we need to prove this statement. for the pairs k and n$0$ given, which ones satisfy r$($n$)>=$ k $*$ n$^2$n $>=$ n$0$

k$=57,$ n$0=2$

k$=2,$ n$0=100$

k$=2,$ n$0=2$

k$=57,$ n$0=1$

k$=3,$ n$0=100$

k$=0\mathrm{.}5,$ n$0=5$