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) ?

A. all multiples of 8
B. all whole numbers from 0 to 8
C. all real numbers from 0 to 60
D. all real numbers less than 60

Answer 1

The domain of D(t), representing the distance Helen's boat travels at maximum speed, is all real numbers from 0 to 60 seconds, which matches choice (C).

Step-by-step explanation:

The function D(t) represents the distance the boat has traveled at maximum speed after t seconds. Since Helen's boat reaches a maximum speed of 8 meters per second and she drives the boat at this speed for 1 minute, the function D(t) will apply for the duration of time the boat is at maximum speed.

One minute is equivalent to 60 seconds, so the domain for D(t), which represents all possible values of t for which the function is defined, will be all real numbers from the time Helen starts driving the boat at maximum speed (0 seconds), to the time she finishes that interval (60 seconds).

Therefore, the correct domain for the function D(t) is all real numbers from 0 to 60, making the answer (C) all real numbers from 0 to 60.