Question

a. Which is warmer: \(-3^{\circ} \mathrm{F}\) or \(0^{\circ} \mathrm{F} ?\) b. Which is farther below sea level: \(-20\) feet or \(-100\) feet?

Short answer

And between -20 feet and -100 feet below sea level, which depth is farther below sea level? Answer: 0°F is warmer and -100 feet is farther below sea level.

Step-by-step solution

a. Comparing temperatures

We need to compare two temperatures in Celsius: \(-3^{\circ} \mathrm{F}\) and \(0^{\circ} \mathrm{F}\). We will analyze which temperature is greater, and thus warmer.

Analyzing the Fahrenheit scale

In the Fahrenheit scale, the higher the number, the warmer the temperature. Therefore, we will compare the numbers \(-3\) and \(0\) to determine which temperature is warmer.

Comparing numbers

Comparing the numbers, we have \(-3 < 0\). Since \(-3\) is smaller than \(0\), we can determine that \(-3^{\circ} \mathrm{F}\) is colder than \(0^{\circ} \mathrm{F}\).

Answer to part a

Since \(-3^{\circ} \mathrm{F}\) is colder than \(0^{\circ} \mathrm{F}\), we can conclude that \(0^{\circ} \mathrm{F}\) is warmer.

b. Comparing depths below sea level

In this part, we need to determine which depth is farther below sea level: \(-20\) feet or \(-100\) feet.

Analyzing the concept of depth

When talking about depths below sea level, a more negative number indicates a greater depth or farther below sea level. Therefore, we will compare the numbers \(-20\) and \(-100\) to determine which depth is farther below sea level.

Comparing numbers

Comparing the numbers, we have \(-20 > -100\). In this context, however, a smaller number represents a greater depth. Thus, \(-100\) feet is farther below sea level than \(-20\) feet.

Answer to part b

Since \(-100\) feet represents a greater depth below sea level than \(-20\) feet, we can conclude that \(-100\) feet is farther below sea level.