https://file.aiquickdraw.com/mathbot/file/1728165199933v3rbzlu1.jpg

The problem involves the relationship between temperature and the density of a gas under constant pressure. The specific temperatures and densities given are:

- Temperatures (in °C): \(0, 21, 50, 70, 120\)
- Densities (in \( \text{kg/m}^3 \)): \(1.479, 1.325, 1.244, 1.144, 1.046\)

Let me solve each part step by step:

### (a) Domain and Range
- **Domain**: The domain represents the set of all possible input values, which in this case is the set of temperatures at which the densities were measured.
  \[
  \text{Domain} = \{0, 21, 50, 70, 120\} \,^\circ\text{C}
  \]
  
- **Range**: The range represents the set of all possible output values, which in this case is the set of measured densities.
  \[
  \text{Range} = \{1.479, 1.325, 1.244, 1.144, 1.046\} \, \text{kg/m}^3
  \]

### (b) Mapping the relation
To express the relation as a mapping, we will map each temperature (domain element) to its corresponding density (range element). The mapping is:
\[
\begin{aligned}
    0^\circ\text{C} &\mapsto 1.479\, \text{kg/m}^3 \\
    21^\circ\text{C} &\mapsto 1.325\, \text{kg/m}^3 \\
    50^\circ\text{C} &\mapsto 1.244\, \text{kg/m}^3 \\
    70^\circ\text{C} &\mapsto 1.144\, \text{kg/m}^3 \\
    120^\circ\text{C} &\mapsto 1.046\, \text{kg/m}^3
\end{aligned}
\]

### (c) Expressing the relation as a set of ordered pairs
The relation can be written as a set of ordered pairs, where the first element is the temperature and the second element is the corresponding density:
\[
\{(0, 1.479), (21, 1.325), (50, 1.244), (70, 1.144), (120, 1.046)\}
\]

Let me know if you would like more details on any part of this solution! Here are 5 follow-up questions for deeper exploration:

1. How can this relation be represented graphically?
2. What type of function might describe the relation between temperature and density?
3. How does increasing temperature affect gas density under constant pressure?
4. Can you find a mathematical model (equation) that fits this data?
5. How would the relation change if the pressure were not constant?

**Tip**: The domain refers to the input or independent variable in a relation, while the range refers to the output or dependent variable.

The density of a gas under constant pressure depends on temperature. Holding pressure constant at 14.5 pounds per square inch, a chemist measures the density of a sample of an element at temperatures 0, 21, 50, 70, and 120°C and obtains densities of 1.479, 1.325, 1.244, 1.144, and 1.046 kg/m³, respectively. (a) What is the domain and range of the relation? (b) Express the relation using a mapping. (c) Express the relation as a set of ordered pairs.

Explore how the density of a gas changes with temperature under constant pressure. Given temperatures of 0, 21, 50, 70, and 120°C, and corresponding densities of 1.479, 1.325, 1.244, 1.144, and 1.046 kg/m³, learn to find the domain and range, express the relation using mappings, and represent it as a set of ordered pairs.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation