An automobile computer gives a digital readout of fuel consumption in gallons per hous. During a trip, a passenger recorded the fuel consumption every 5 minutes for a full hour of travel.
time: 0 / gal/h: 2.5
time: 5 / gal/h: 2.4
time: 10 / gal/h: 2.3
time: 15 / gal/h: 2.4
time: 20 / gal/h: 2.4
time: 25 / gal/h: 2.5
time: 30 / gal/h: 2.6
time: 35 / gal/h: 2.5
time: 40 / gal/h: 2.4
time: 45 / gal/h: 2.3
time: 50 / gal/h: 2.4
time: 55 / gal/h: 2.4
time: 60 / gal/h: 2.3
(a) Use the Trapezoidal Rule to approximate the total fuel consumption during the hour.
(b) If the automobile covered 60 miles in the hour, what was its fuel efficiency (in miles per gallon) for that portion of that trip.
Answer: (a) 2.42 gal (b)24.83mpg
a)The trapezoidal rule is a way of doing numberical integration. Add up the middle 11 gal/h entires and add hlad of the first and last entries; then multiply by the time interval between entries, 0.0833 hours.
b) Divide 60 miles by the 2.42 gallons consumed. You should show only three significant figures
what do you mean add "hlad"?
Sorry about the typo. That word should be "half"
I need a better more indepth answer
To approximate the total fuel consumption during the hour using the Trapezoidal Rule, we can use the formula:
Total fuel consumption ≈ (h/2) * [f(x₀) + 2*f(x₁) + 2*f(x₂) + ... + f(xₙ)]
where h is the interval size (in this case, 5 minutes), f(x) is the fuel consumption rate at time x, and n is the number of intervals (in this case, 12).
Let's calculate the total fuel consumption:
Total fuel consumption ≈ (5/2) * [2.5 + 2*(2.4) + 2*(2.3) + (2.4) + (2.4) + (2.5) + (2.6) + (2.5) + (2.4) + (2.3) + (2.4) + (2.4) + (2.3)]
Now we can simplify the expression:
Total fuel consumption ≈ 2.5 + 4.8 + 4.6 + 2.4 + 2.4 + 2.5 + 2.6 + 2.5 + 2.4 + 2.3 + 2.4 + 2.4 + 2.3
Total fuel consumption ≈ 2.42 gallons (rounded to two decimal places)
Thus, the approximate total fuel consumption during the hour is 2.42 gallons.
To calculate the fuel efficiency (in miles per gallon), we can use the formula:
Fuel efficiency = Total distance traveled / Total fuel consumption
In this case, the automobile covered 60 miles in the hour. So, the fuel efficiency is:
Fuel efficiency = 60 miles / 2.42 gallons
Now we can calculate the fuel efficiency:
Fuel efficiency ≈ 24.79 miles per gallon (rounded to two decimal places)
Therefore, the fuel efficiency for that portion of the trip is approximately 24.79 miles per gallon.