$(20$ points$)-$The signal y$($t$)=10$ sin $100$t $+$ sin $384$rt Vis to be sampled at $200$ Hz$.$ The signal is passed through a third$-$order Butterworth low$-$pass anti$-$aliasing filter with a cutoff frequency of $100$ Hz$.$ Suppose we are only interested in the low$-$frequency signal component. Will the higher frequency component be attenuated to under $15\%$ of its original amplitude? What is the level of attenuation this filter provides in decibels $($dB$)?$

What is the amplitude of the filtered high$-$frequency component as a percentage of the amplitude of the low$-$frequency component? c$.$ At what frequency will this new amplitude appear? NOTE: It is quite common to set the sample rate such that the Nyquist frequency is equal to the anti$-$ aliasing filter cut$-$off frequency.