Electric energy units are often expressed in "kilowatt-hours." ($a$) Show that one kilowatt-hour (kWh) is equal to 3.6 $\times$ 10$^6$ J.($b$) If a typical family of four uses electric energy at an average rate of 580 W, how many kWh would their electric bill show for one month, and ($c$) how many joules
would this be? ($d$) At a cost of \$0.12 per kWh, what would their monthly bill be in dollars? Does the monthly bill depend on the $rate$ at which they use the electric energy?