A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme

Question

Montano1993 [528]

2 years ago

10

A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme

temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F. Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form. (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 January 1989, the temperature in Nome, Alaska dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not? (4 points)
I need part b

Also I need it asap please and thanks

Mathematics

1 answer:

Andrews [41] · Answer 1 · 2023-05-28T06:14:12+03:00

The inequality to represent the temperatures at which the gas in the truck will remain in liquid form is -40 < x < 140

<h3>Part A: The inequality</h3>

Let the temperature of the gas be represented with x.

When the temperature hits −40° F (or below), the gas freezes.

This means that the gas temperature must always exceed −40° F to remain being a liquid

i.e x > −40

Also, when the temperature hits 140° F (or above), the gas evaporates.

This means that the gas temperature must always be less than 140° F to remain being a liquid

i.e x < 140

So, we have:

x > −40 and x < 140

Rewrite as:

-40 < x and x < 140

Combine both inequalities

-40 < x < 140

Hence, the inequality to represent the temperatures at which the gas in the truck will remain in liquid form is -40 < x < 140

<h3>Part B: The description of the graph</h3>

In (a), we have:

-40 < x < 140

The end points of the inequalities use a less than sign.

Less than signs are represented by open circle.

Hence, the graph would use an open circle, and intervals between -40 and 140 would be shaded

<h3>Part C: Would −49° F gas remained in liquid form?</h3>

We have:

-40 < x < 140

The number -49 is not in the range -40 < x < 140

Hence, the gas would not remain in liquid form (in fact, it would freeze because it is less than -40)