Question
Work with partner to complete the following
List the relationships for which each independent variable is paired with its own unique dependent variable.
List the relationships for which each independent variable is paired with its own unique dependent variable.
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GPT-4o mini
To identify relationships where each independent variable is paired with its own unique dependent variable, we can consider the following examples:
1. **Temperature (°C) and Electrical Resistance (Ω)**:
- As temperature increases, resistance in a conductor may change. Each temperature can correspond to a unique resistance value under specific conditions.
2. **Age (years) and Maximum Heart Rate (bpm)**:
- Maximum heart rate can be uniquely calculated based on age (typically estimated with the formula 220 minus age).
3. **Length of a Pendulum (m) and Period of Swing (s)**:
- The period of a simple pendulum is determined by its length; each length of the pendulum corresponds to a unique period.
4. **Distance Traveled (m) and Time Taken (s) in a Constant Speed Scenario**:
- For a car moving at a constant speed, the distance is directly related to time, creating a unique pair for each distance.
5. **Depth of Water (m) in a Tank and Pressure (Pa)**:
- The pressure at the bottom of a tank of water is uniquely determined by the depth of water, following the formula P = ρgh where ρ is the density and g is the acceleration due to gravity.
6. **Number of Hours Studied (hours) and Grade on an Exam (%)**:
- Assuming other factors are controlled, a specific number of study hours can correspond to a unique expected grade on an exam.
In each of these relationships, you can see that the independent variable is directly related to a unique dependent variable, highlighting a one-to-one relationship.
1. **Temperature (°C) and Electrical Resistance (Ω)**:
- As temperature increases, resistance in a conductor may change. Each temperature can correspond to a unique resistance value under specific conditions.
2. **Age (years) and Maximum Heart Rate (bpm)**:
- Maximum heart rate can be uniquely calculated based on age (typically estimated with the formula 220 minus age).
3. **Length of a Pendulum (m) and Period of Swing (s)**:
- The period of a simple pendulum is determined by its length; each length of the pendulum corresponds to a unique period.
4. **Distance Traveled (m) and Time Taken (s) in a Constant Speed Scenario**:
- For a car moving at a constant speed, the distance is directly related to time, creating a unique pair for each distance.
5. **Depth of Water (m) in a Tank and Pressure (Pa)**:
- The pressure at the bottom of a tank of water is uniquely determined by the depth of water, following the formula P = ρgh where ρ is the density and g is the acceleration due to gravity.
6. **Number of Hours Studied (hours) and Grade on an Exam (%)**:
- Assuming other factors are controlled, a specific number of study hours can correspond to a unique expected grade on an exam.
In each of these relationships, you can see that the independent variable is directly related to a unique dependent variable, highlighting a one-to-one relationship.
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