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 ∫2021r(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 21st 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 20th hour, the amount of gasoline at the fuel station decreased by 450 liters.
Q. 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 ∫2021r(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 21st 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 20th hour, the amount of gasoline at the fuel station decreased by 450 liters.
Interpret Integral: The integral of r(t) from 20 to 21 represents the total change in the amount of gasoline during the time interval from t=20 to t=21 hours.
Calculate Change: Since the integral value is −450, this means the amount of gasoline decreased by 450 liters during that time interval.
Eliminate Wrong Answers: The correct answer is not (A) because it refers to the first 20 hours, not the interval from 20 to 21 hours.
Identify Correct Answer: The correct answer is not (B) because it specifies the 21st hour only, but the integral covers the entire interval from 20 to 21 hours.
Identify Correct Answer: The correct answer is not (B) because it specifies the 21st hour only, but the integral covers the entire interval from 20 to 21 hours.The correct answer is not (C) because it refers to the first 21 hours, which would include the time from 0 to 21 hours, not just from 20 to 21 hours.
Identify Correct Answer: The correct answer is not (B) because it specifies the 21st hour only, but the integral covers the entire interval from 20 to 21 hours.The correct answer is not (C) because it refers to the first 21 hours, which would include the time from 0 to 21 hours, not just from 20 to 21 hours.The correct answer is (D) because it correctly identifies the interval from the 20th to the 21st hour, during which the fuel station's gasoline decreased by 200 liters.
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