A $+2\%$ grade intersects with a $1\%$ grade at station $(535+24\mathrm{.}25)$ at an elevation of $300$ ft$.$ If thedesign speed is $65$ mi$/$h$,$ determine: $[15$ points$]($a$)$ the stations and elevations of the PVC and PVT $($b$)$ the elevations and stations at horizontal distances of $65\mathrm{.}25$ ft$,165\mathrm{.}25$ ft$,265\mathrm{.}25$ ft$,365\mathrm{.}25$ ft$,465\mathrm{.}25$ ft$,565\mathrm{.}25$ ft$,$ and $579$ ft from the PVC$.$