A crest vertical curve connects a $+4\mathrm{.}44\%$ grade and a $-6\mathrm{.}87\%$ grade. The PVI is at station

$43+50$ at an elevation of $1240\mathrm{.}00$ ft $.$ The design speed is $30m\frac{i}{h}r.$

Determine:

$($a$)$ The length of the vertical curve using the AASHTO $"$K$"$ factor method.

$($b$)$ The station of PVC

$($c$)$ The elevation of PVC

$($d$)$ The station of PVT

$($e$)$ The elevation of PVT$.$

$($f$)$ The station of the high point.

$($g$)$ The elevation of the high point.

$($h$)$ The elevation of station $44+23\mathrm{.}33$