I feel pretty good about my work for this problem, but I$\text{'}$m not so sure about my constant value being c $>=15.$ If this could be proved by induction, then I would greatly appreciate it$.($b$)$ Prove that the solution to the following recurrence is T $($n$)=\backslash$Theta $($n$).$ Assume T $(1)=1.$

T $($n$)=$ T $($n$/3)+$ T $(3$n$/5)+$ n$.$

$($Hint: One approach would be to ignore the floors and use a recursion tree. Another more formal

approach for the upper bound would be to use induction. Set your hypothesis to be that T $($n$)<=$ cn

for all n $<$ m$,$ for a constant c$.$ Then establish the induction step that T $($m$)<=$ cm and in the process

derive a bound on the constant c$.$ Both approaches are acceptable.$)$