An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The domain of a function is the set of all possible input values (x-values).
Identify the x-values from the table: -2, -1, 0, and 1.
Express the domain as a set: { − 2 , − 1 , 0 , 1 } .
The domain of the function is { − 2 , − 1 , 0 , 1 } .
Explanation
Understanding the Domain The domain of a function is the set of all possible input values (x-values). In this case, we are given a table of x and y values, and we need to identify the domain of the function represented by the table.
Identifying the x-values The table provides the following x-values: -2, -1, 0, and 1.
Listing the Domain as a Set Therefore, the domain of the function is the set containing these x-values: { − 2 , − 1 , 0 , 1 } .
Selecting the Correct Option Comparing this set with the provided options, we see that option D matches our result.
Final Answer The domain of the function shown in the table is { − 2 , − 1 , 0 , 1 } .
Examples
In real life, understanding the domain of a function is crucial in various scenarios. For instance, if you're modeling the growth of a plant over time, the domain would represent the time interval during which you're observing the plant. You can't have negative time, so the domain would typically start at zero and extend to the duration of your observation. Similarly, if you're analyzing the trajectory of a ball, the domain would represent the time the ball is in the air. Knowing the domain helps you make sense of the function's output and ensures that your model is realistic and applicable to the situation.
In 30 seconds, an electric device delivering a current of 15.0 A allows approximately 2.81 × 10^{21} electrons to flow through it. This is calculated by first finding the total charge of 450.0 Coulombs and then converting that charge to the number of electrons using the charge of a single electron. Overall, understanding current and charge is crucial in electrical physics.
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