$5-5$ A $50,000-$W AM broadcast transmitter is being evaluated by means of a two$-$tone test. The transmitter is connected to a $50-$ load, and m$($t$)=$ A$1$ cos v$1$t $+$ A$1$ cos $2$v$1$t$,$ where f$1=500$ Hz$.$ Assume that a perfect AM signal is generated. $($a$)$ Evaluate the complex envelope for the AM signal in terms of A$1$ and v$1.($b$)$ Determine the value of A$1$ for $90\%$ modulation. $($c$)$ Find the values for the peak current and average current into the $50-$ load for the $90\%$ modulation case.