$8\mathrm{.}9)$ A long rectangular channel $3\mathrm{.}0$ m wide with a flow rate of $11\mathrm{.}6\frac{m^3}{s}$ has a specific energy, $E=3\mathrm{.}40m.$

a$.)$ Determine two possible depths of flow and their corresponding Froude numbers.

b$.)$ What is the critical slope for this discharge if the channel is made of concrete with a Manning's $n=0\mathrm{.}014?$