Question

a new coal-burning power plant can generate 1.4 gigawatts (billion watts) of power. burning 1 kilogram of coal yields about 460 kilowatt-hours of energy. complete parts (a), (b), and (c) below.
a. how much energy, in kilowatt-hours, can the plant generate each month?
the plant can generate 1008 million kilowatt-hours of energy each month.
(type an integer.)
b. how much coal, in kilograms, is needed by this power plant each month?
the plant needs 2.2 million kilograms of coal each month.
(round to one decimal place as needed.)
c. if a typical home uses 998 kilowatts-hours per month, how many homes can this power plant supply with energy?
this power plant can supply \\(\square\\) homes with energy.
(round to the nearest whole number.)

Explanation:

Step1: Convert the energy generated per month to the same unit as home usage

The plant generates \(1008\) million kilowatt - hours per month. Since \(1\) million \( = 10^{6}\), the energy generated is \(E=1008\times10^{6}\) kilowatt - hours.

Step2: Calculate the number of homes

Let \(n\) be the number of homes. We know that the energy used per home is \(e = 998\) kilowatt - hours per month. Using the formula \(n=\frac{E}{e}\), we substitute \(E = 1008\times10^{6}\) and \(e=998\).

$$ n=\frac{1008\times 10^{6}}{998}=\frac{1008000000}{998}\approx1010020.04 $$

Answer:

\(1010020\)