Asked by HELLO
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.)
C. Consider the following data for the function.
t f(x)
0 2.3
1 2.5
2 2.1
3 3.9
4 3.6
5 5.5
6 4.5
7 5.6
8 1.2
9 1.0
10 1.8
Recall that f(t) represents the number of kilowatts being used by a customer at time t hours from the beginning of the billing period. Estimate the number of kilowatt-hours the customer uses in this 10-hour period, and explain your method.
I am trying and don't think i am getting the right answer.
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.)
C. Consider the following data for the function.
t f(x)
0 2.3
1 2.5
2 2.1
3 3.9
4 3.6
5 5.5
6 4.5
7 5.6
8 1.2
9 1.0
10 1.8
Recall that f(t) represents the number of kilowatts being used by a customer at time t hours from the beginning of the billing period. Estimate the number of kilowatt-hours the customer uses in this 10-hour period, and explain your method.
I am trying and don't think i am getting the right answer.
Answers
Answered by
Damon
well, you could choose a left Riemann sum or a right Riemann sum or an in between Riemann sum. For simplicity I will take the left
each day is 24 hours * 30 days = 720 hours
so
area = kw hr = p(0) + p(1) + p(2) ...+ p(719) [ each times one hour ]
B)
KwHr = integral from t = 0 to t = 720 of f(t) dt
your table I assume should show f(t) not f(x)
area = 2.3*1 + 2.5* 1 + 2.1*1 etc to 1.0 *1
because I am using the left sum option, I am not using (10, 1.8)
so add the first ten numbers to get your answer
I get 31.7 kw hr
which is about an average power of 3.17 kw during the ten hours.
It would be more accurate to then do a right sum using 1 to 10 and not using (0,2.3) then use the average of the right method and left method.
each day is 24 hours * 30 days = 720 hours
so
area = kw hr = p(0) + p(1) + p(2) ...+ p(719) [ each times one hour ]
B)
KwHr = integral from t = 0 to t = 720 of f(t) dt
your table I assume should show f(t) not f(x)
area = 2.3*1 + 2.5* 1 + 2.1*1 etc to 1.0 *1
because I am using the left sum option, I am not using (10, 1.8)
so add the first ten numbers to get your answer
I get 31.7 kw hr
which is about an average power of 3.17 kw during the ten hours.
It would be more accurate to then do a right sum using 1 to 10 and not using (0,2.3) then use the average of the right method and left method.
Answered by
Damon
By the way
POWER IS NOT ENERGY
look in physics book NEVER in math book ! (mathematics text writers do not get this stuff. They do not know the difference between bearing and heading in navigation either)
Energy = power * time
in this problem
Energy is in KW HR
and Power is in KW
This sentence should be:
A kilowatt is a measure of how much power (******* leave that energy word OUT ***** ) a customer is using ...........
POWER IS NOT ENERGY
look in physics book NEVER in math book ! (mathematics text writers do not get this stuff. They do not know the difference between bearing and heading in navigation either)
Energy = power * time
in this problem
Energy is in KW HR
and Power is in KW
This sentence should be:
A kilowatt is a measure of how much power (******* leave that energy word OUT ***** ) a customer is using ...........