Question

Mars has a maximum temperature of 27℃ at the equator and a minimum temperature of -133℃ at the winter pole. a.) Write and solve a compound inequality that describes the possible temperatures (in degrees Fahrenheit) on Mars. Use the formula C=59(F-32).

Answer 1

To solve this problem, we first need to convert the temperatures from Celsius to Fahrenheit. We use the formula F = C * 9/5 + 32, where F represents temperature in Fahrenheit and C represents temperature in Celsius.

Step 1: Convert the maximum temperature

Plugging the maximum temperature of Mars, which is 27℃, into the formula, we have:

F = 27 * 9/5 + 32

This gives F = 80.6F.

So, the maximum temperature on Mars is 80.6℉.

Step 2: Convert the minimum temperature

We also plug in the minimum temperature of Mars, which is -133℃, into the formula:

F = -133 * 9/5 + 32

This gives F = -207.4F.

Therefore, the minimum temperature on Mars is -207.4℉.

Step 3: Write the inequality

Now we want to write a compound inequality that includes all possible temperatures on Mars in Fahrenheit i.e. -207.4F <= temp <= 80.6F.

This inequality means that the temperature on Mars is always greater than or equal to -207.4F and less than or equal to 80.6F.

Interpretation: The range of temperatures on Mars in Fahrenheit is from -207.4℉ to 80.6℉. Any temperature on Mars will likely fall within this range.