Question

Analyze the situation. Identify a reasonable domain and range for the situation. The distance an airplane has traveled at any point during a flight is determined by the airplane’s speed, 565 mph.

Answer 1

The domain of the situation represents the possible time durations for which the airplane can fly. Since there's no specific starting time provided, we'll consider the domain as the time starting from
`\( t = 0 \) (start of the flight) to some maximum time \( t = t_{\text{max}} \)`. The maximum reasonable time for a non-stop flight could be around 18 hours, which is a typical duration for some of the longest commercial flights in the world.

Thus, the domain is:
`\( 0 \leq t \leq 18 \) hours.`

`\textbf{2. Range:}`

The range represents the possible distances the airplane can travel based on its speed and the time it has been flying. Given the speed
`\( v = 565 \)` mph and using the formula
`\( \text{Distance} = \text{Speed} * \text{Time} \)`, the minimum distance is 0 miles (at the start of the flight) and the maximum distance it can travel non-stop is 10,170 miles (calculated as
`\( 565 \) mph \( * 18 \) hours`).

Thus, the range is:
`\( 0 \leq d \leq 10,170 \)` miles.

`\textbf{Conclusion:}`

For an airplane traveling at a speed of 565 mph, the reasonable domain for the time of its flight is between 0 and 18 hours, and the range for the distance it can cover is between 0 and 10,170 miles.