To identify relationships where each independent variable is paired with its own unique dependent variable, we can consider the following examples:
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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.
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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).
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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.
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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.
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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.
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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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