Water fills a bathtub at a rate of r(t) liters per minute (where t is the time in minutes). What does int_(2)^(3)r(t)dt=6 mean? Choose 1 answer: (A) The rate of the water filling the bathtub increased by 6 liters per minute between minutes 2 and 3 . (B) The bathtub fills with an additional 6 liters of water every minute. (C) There were 6 liters of water in the bathtub by the end of 3 minutes. (D) The water in the bathtub increased by 6 liters during the third minute.

Question

Water fills a bathtub at a rate of  r(t) liters per minute (where  t is the time in minutes). What does  int_(2)^(3)r(t)dt=6 mean? Choose 1 answer: (A) The rate of the water filling the bathtub increased by 6 liters per minute between minutes 2 and 3 . (B) The bathtub fills with an additional 6 liters of water every minute. (C) There were 6 liters of water in the bathtub by the end of 3 minutes. (D) The water in the bathtub increased by 6 liters during the third minute.

Bytelearn · Accepted Answer

Understand the integral: Understand the integral in the context of the problem. The integral of a rate function over a time interval gives the total amount of change over that interval. In this case, $ \int_{2}^{3} r(t) \, dt $ represents the total amount of water that fills the bathtub from minute 2 to minute 3.Interpret the value: Interpret the value of the integral. Since $ \int_{2}^{3} r(t) \, dt = 6 $, this means that 6 liters of water were added to the bathtub between minutes 2 and 3.Match interpretation to choices: Match the interpretation to the given choices. The correct interpretation is that the bathtub's water level increased by 6 liters during the time interval from minute 2 to minute 3. This matches choice (D) and not the other choices, as they imply different meanings that are not consistent with the integral's interpretation.

Full solution

More problems from Interpreting Linear Expressions

Related topics