Helen has a remote-control boat that she drives in a pond at Blake Park. The boat has a maximum speed of 8 meters per second. She accelerates the boat to its maximum speed and drives it for 1 minute around the pond before decelerating. The function D(t) represents the distance the boat has traveled at maximum speed after t seconds. What is the domain of D(t)? Choices: (A)all multiples of 8 (B)all real numbers less than 60 (C)all real numbers from 0 to 60 (D)all whole numbers from 0 to 8

Question

Helen has a remote-control boat that she drives in a pond at Blake Park. The boat has a maximum speed of 8 meters per second. She accelerates the boat to its maximum speed and drives it for 1 minute around the pond before decelerating. The function D(t) represents the distance the boat has traveled at maximum speed after t seconds. What is the domain of D(t)?   Choices: (A)all multiples of 8 (B)all real numbers less than 60 (C)all real numbers from 0 to 60 (D)all whole numbers from 0 to 8

Bytelearn · Accepted Answer

Define Domain of Function: The domain of a function is the set of all possible input values (in this case, time t in seconds) for which the function is defined. Since the boat accelerates to its maximum speed and drives for 1 minute (which is 60 seconds), we need to consider the time interval during which the boat is at its maximum speed.Identify Time Interval: The boat is at its maximum speed from the moment it finishes accelerating until it starts decelerating. Since the problem states that the boat drives at maximum speed for 1 minute, the time interval during which the boat is at maximum speed is from 0 seconds to 60 seconds.Determine Domain Range: The domain of D(t) is therefore all real numbers from 0 to 60, as the boat cannot travel at maximum speed for a negative amount of time, and it does not travel at maximum speed for more than 60 seconds.Match Correct Choice: Looking at the given choices, we can see that choice (C) ＂all real numbers from 0 to 60＂ matches our reasoning and is the correct domain for the function D(t).

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