A gaseous fuel mixture comprising 3 moles of methane and 2 moles of ammonia is combusted in \( X \) moles of pure oxygen in stoichiometric amount. Assuming complete combustion, with only \( {CO}_2 \), \( {H}_2{O} \), and \( {N}_2 \) in the product gases, the value of \( X \) is ____________. \[ 3 \, {CH}_4 + 2 \, {NH}_3 + X \, {O}_2 \rightarrow {Products (CO}_2, \, {H}_2{O}, \, {N}_2{)} \]
An ideal two-stage rocket has identical specific impulse and structural coefficient for its two stages. For an optimized rocket, the two stages have identical payload ratio as well. The payload is 2 tons and the initial mass of the rocket is 200 tons. The mass of the second stage of the rocket (including the final payload mass) is ___________ tons.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.