V$.[$total: $\backslash (15\backslash \%\backslash )]$ A gearbox transmits $30$ kW from a shaft rotating at $50$ rpm$,$ and the desired output speed is $2800$ rpm exactly. The overall gearbox size needs to be minimized so that a two$-$stage Compound Reverted Gear Train is used, as shown in Figure $3.($a$)$ State the gear ratio limitation of a pair of spur gears. $[2\backslash \%]($b$)$ Please specify the appropriate teeth numbers. Assuming $\backslash (20^\{\backslash$circ$\}\backslash )$ pressure angle and $5$ mm module spur gears are used so that the minimum number of teeth to avoid interference is $18.[10\backslash \%]($c$)$ Please estimate the distances between the two axes of your gear train. $[3\backslash \%]$