The flow$-$density relationship for a highway segment is given as with $q$ in $ve\frac{h}{h}$ and k in veh $\frac{?}{mi}.$

a$)$ What is the capacity of the highway segment? $[10$ points$]$

b$)$ What is the speed at capacity? $[5$ points$]$

c$)$ What is the density when the highway is at half of its capacity? $[10$ points$]$