Derive a recurrence for the number p(n) of ways to parenthesizing an expression with n atoms. compute the optimal parenthesis and optimal cost to multiply a l 10x20 b i 20x5 . l 5x40 d | 40x10.

16. in a reaction that has reached equilibrium, a. the forward and reverse reactions are occurring at the same rate. b. the reactants and products are in equal concentrations. c. the forward reaction has gone further than the reverse reaction. d. there are equal numbers of atoms on both sides of the equation. e. a, b, and d are correct.