Question

A pilot is flying a CRJ-900 from Phoenix, Arizona, to Louisville, Kentucky. The aircraft cannot take off or land if the temperature on the field is not within its operating limitations. The aircraft cannot operate if the temperature is at or below −40° F, or at or above 118° F.
Part A: Write an inequality to represent the temperatures the pilot can take off and land in. (2 points)


Part B: Describe the graph of the inequality completely from Part A. Use terms such as open/closed circles and shading directions. Explain what the solutions to the inequality represent. (4 points)


Part C: In June 1990, the temperature in Phoenix, Arizona rose to 122° F. Could the pilot have taken off on this day? Why or why not? (4 points)

Answer 1

We need to find an inequality that represents the possible landing or take of conditions of an aircraft, the required graph and one case where the inequality will be tested.

The required inequality is $-40$.

The graph represents the allowable temperature range in which the aircraft can takeoff or land.

The pilot could not have taken off on June 1990, the temperature in Phoenix, Arizona.

Let the temperature be denoted by $x$

The temperature cannot be at or below $-40^{\circ}\text{F}$, so

$x>-40$

The temperature cannot be at or above $118^{\circ}\text{F}$, so

$x$

The inequality will be $-40$.

In the graph it can be seen that all points between -40 and 118 falls in the shaded region but it will exclude the points -40 and 118.

The graph represents the allowable temperature range in which the aircraft can takeoff or land.

The temperature in June 1990 in Phoenix, Arizona was $122^{\circ}$ which is more than $118^{\circ}\text{F}$.

Hence, the pilot could not have taken off on this day.

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