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The amount of gasoline stored at a fuel station is decreasing at a rate of 
r(t) liters per hour (where 
t is the time in hours).
What does 
int_(20)^(21)r(t)dt=-450 mean?
Choose 1 answer:
(A) During the first 20 hours, the amount of gasoline at the fuel station decreased by 450 liters.
(B) During the 
21^("st ") hour, the amount of gasoline at the fuel station decreased by 450 liters.
(C) During the first 21 hours, the amount of gasoline at the fuel station decreased by 450 liters.
(D) During the 
20^("th ") hour, the amount of gasoline at the fuel station decreased by 450 liters.

The amount of gasoline stored at a fuel station is decreasing at a rate of r(t) r(t) liters per hour (where t t is the time in hours).\newlineWhat does 2021r(t)dt=450 \int_{20}^{21} r(t) d t=-450 mean?\newlineChoose 11 answer:\newline(A) During the first 2020 hours, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(B) During the 21st  21^{\text {st }} hour, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(C) During the first 2121 hours, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(D) During the 20th  20^{\text {th }} hour, the amount of gasoline at the fuel station decreased by 450450 liters.

Full solution

Q. The amount of gasoline stored at a fuel station is decreasing at a rate of r(t) r(t) liters per hour (where t t is the time in hours).\newlineWhat does 2021r(t)dt=450 \int_{20}^{21} r(t) d t=-450 mean?\newlineChoose 11 answer:\newline(A) During the first 2020 hours, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(B) During the 21st  21^{\text {st }} hour, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(C) During the first 2121 hours, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(D) During the 20th  20^{\text {th }} hour, the amount of gasoline at the fuel station decreased by 450450 liters.
  1. Interpret Integral: The integral of r(t)r(t) from 2020 to 2121 represents the total change in the amount of gasoline during the time interval from t=20t=20 to t=21t=21 hours.
  2. Calculate Change: Since the integral value is 450-450, this means the amount of gasoline decreased by 450450 liters during that time interval.
  3. Eliminate Wrong Answers: The correct answer is not (A) because it refers to the first 2020 hours, not the interval from 2020 to 2121 hours.
  4. Identify Correct Answer: The correct answer is not (B) because it specifies the 21st21^{st} hour only, but the integral covers the entire interval from 2020 to 2121 hours.
  5. Identify Correct Answer: The correct answer is not (B) because it specifies the 21st21^{st} hour only, but the integral covers the entire interval from 2020 to 2121 hours.The correct answer is not (C) because it refers to the first 2121 hours, which would include the time from 00 to 2121 hours, not just from 2020 to 2121 hours.
  6. Identify Correct Answer: The correct answer is not (B) because it specifies the 21st21^{st} hour only, but the integral covers the entire interval from 2020 to 2121 hours.The correct answer is not (C) because it refers to the first 2121 hours, which would include the time from 00 to 2121 hours, not just from 2020 to 2121 hours.The correct answer is (D) because it correctly identifies the interval from the 20th20^{th} to the 21st21^{st} hour, during which the fuel station's gasoline decreased by 202000 liters.

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