A standard flashlight battery can deliver about $\backslash (2\mathrm{.}9\backslash$mathrm$\{$~W$\}\backslash$cdot $\backslash$mathrm$\{$~h$\}\backslash )$ of energy before it runs down. $($a$)$ If a battery costs $80$ cents, what is the cost in dollars of operating a $100$ W lamp for $7\mathrm{.}4$ h using batteries? $($b$)$ What is the cost in dollars if power is provided at the rate of $6\mathrm{.}0$ cents per kilowatt$-$hour?