Answer :
(a)
In order to calculate the resistance of the air conditioner, we can use the formula below:
[tex]P=\frac{V^2}{R}[/tex]Where P is the power (in W), V is the voltage (in V) and R is the resistance (in ohms).
So, for P = 49500 W and V = 412 V, we have:
[tex]\begin{gathered} 49500=\frac{412^2}{R}\\ \\ R=\frac{412^2}{49500}\\ \\ R=3.429\text{ ohms} \end{gathered}[/tex](b)
If the air conditioner is used 8 hours per day for 30 days, the total number of hours is 240 h.
Multiplying the power (in kW) by the time (in h), we have the energy (in kWh):
[tex]\begin{gathered} E=P\cdot t\\ \\ E=49.5\cdot240\\ \\ E=11880\text{ kWh} \end{gathered}[/tex]each kWh of energy costs 9 cents, so the total cost is:
[tex]\begin{gathered} Cost=11880\cdot0.09\\ \\ Cost=\$1069.20 \end{gathered}[/tex]Therefore the cost is $1069.20.