- #1
pooka
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I am new to the forum,so if i posted the question not according to some specific format, i apologize.
Power companies typically bill customers based on the number of kilowatt-hours used during a single billing period. A kilowatt is a measure of how much power (energy) a
customer is using, while a kilowatt-hour is one kilowatt of power being used for one hour.
For constant power use, the number of kilowatt-hours used is calculated by kilowatt-hours=kilowatts * time (in hours). Thus, if customers use 5 kilowatts for 30 minutes, they'll have used 5 kilowatts * (1/2)hrs =2.5 kilowatt-hours.
Suppose the power use of a customer over a 30-day period is given by the continuous
function P(t) where P is kilowatts, t is time in hours, and t =0 corresponds to the
beginning of the 30 day period.
A.
Approximate, with a Riemann sum, the total number of kilowatt-hours used by the customer in the 30 days.
B.
Derive an expression representing the total number of kilowatt-hours used by the
customer in the 30-day period. (This expression should not be an approximation.)
for A:
I did R=720 sigma t=0 to t=720 f(t)
for B: i just did T(t)= integral sign 0 to 720 f(t)dt
Could someone confirm my answers? Thanks in advance.
Power companies typically bill customers based on the number of kilowatt-hours used during a single billing period. A kilowatt is a measure of how much power (energy) a
customer is using, while a kilowatt-hour is one kilowatt of power being used for one hour.
For constant power use, the number of kilowatt-hours used is calculated by kilowatt-hours=kilowatts * time (in hours). Thus, if customers use 5 kilowatts for 30 minutes, they'll have used 5 kilowatts * (1/2)hrs =2.5 kilowatt-hours.
Suppose the power use of a customer over a 30-day period is given by the continuous
function P(t) where P is kilowatts, t is time in hours, and t =0 corresponds to the
beginning of the 30 day period.
A.
Approximate, with a Riemann sum, the total number of kilowatt-hours used by the customer in the 30 days.
B.
Derive an expression representing the total number of kilowatt-hours used by the
customer in the 30-day period. (This expression should not be an approximation.)
for A:
I did R=720 sigma t=0 to t=720 f(t)
for B: i just did T(t)= integral sign 0 to 720 f(t)dt
Could someone confirm my answers? Thanks in advance.