$4.$ Given the following vertical alignment. Grade $\backslash (1=2\mathrm{.}5\backslash \%\backslash )$ upgrade to a point of vertical intersection $($PVI$)$ at station $\backslash (340+00\backslash )$ at elevation $200$ feet. From the PVI Grade $2$ is $\backslash (3\backslash \%\backslash )$ downgrade. Determine the following for a $50-$mph design speed:

a$)$ The vertical curve K value that satisfies minimum stopping sight distance.

b$)$ Determine the length of the vertical curve.

c$)$ Determine the station and elevation of the highest point of the curve.

d$)$ Determine the station and elevation at $\backslash (339+00\backslash ).$