$1.$ A combustor operates with a combustor inlet temperature of $724\mathrm{.}7$ K $,$ a combustor total temperature of $1389$ K $,$ a fuel heating value of $\backslash (41,400\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ),$ and a Cp of $\backslash (1143\backslash$mathrm$\{$~J$\}/\backslash$mathrm$\{$kg$\}-\backslash$mathrm$\{$K$\}\backslash ).$ What is the approximate fuel$-$to$-$air ratio if the burner efficiency is $0\mathrm{.}997$

$2.$ A nozzle with air as the operating fluid is converging$-$diverging with an expansion area ratio of $1\mathrm{.}1.$ The stagnation pressure is $4$ atm $.$ The surrounding atmosphere is $3$ atm $.$ What is the exit pressure of the nozzle? Show your work.

$3.$ An ideal ramjet operates with an ambient condition of sea level and a Mach number of $4|$The combustor maximum temperature of $\backslash (3000^\{\backslash$circ$\}\backslash$mathrm$\{$R$\}\backslash ).$ Calculate the nozzle exit velocity.