An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The problem provides a formula P = 1 + ( n − 1 ) ( 2 ) to calculate the number of notebooks P based on the place n .
Calculate P for each place n from 1 to 5.
The calculated pairs are ( 1 , 1 ) , ( 2 , 3 ) , ( 3 , 5 ) , ( 4 , 7 ) , ( 5 , 9 ) .
The correct option is C: ( 1 , 1 ) , ( 2 , 3 ) , ( 3 , 5 ) , ( 4 , 7 ) , ( 5 , 9 ) .
C
Explanation
Understanding the Problem Let's analyze the problem. We are given a formula that determines the number of notebooks a student receives based on their place in a competition. The formula is P = 1 + ( n − 1 ) ( 2 ) , where P is the number of notebooks and n is the place (1st, 2nd, 3rd, 4th, or 5th). We need to find the correct series of pairs ( n , P ) that represents the number of notebooks for each place.
Calculating Notebooks for Each Place Now, let's calculate the number of notebooks for each place using the formula:
For 1st place ( n = 1 ): P = 1 + ( 1 − 1 ) ( 2 ) = 1 + ( 0 ) ( 2 ) = 1 + 0 = 1
For 2nd place ( n = 2 ): P = 1 + ( 2 − 1 ) ( 2 ) = 1 + ( 1 ) ( 2 ) = 1 + 2 = 3
For 3rd place ( n = 3 ): P = 1 + ( 3 − 1 ) ( 2 ) = 1 + ( 2 ) ( 2 ) = 1 + 4 = 5
For 4th place ( n = 4 ): P = 1 + ( 4 − 1 ) ( 2 ) = 1 + ( 3 ) ( 2 ) = 1 + 6 = 7
For 5th place ( n = 5 ): P = 1 + ( 5 − 1 ) ( 2 ) = 1 + ( 4 ) ( 2 ) = 1 + 8 = 9
So, the series of pairs ( n , P ) is ( 1 , 1 ) , ( 2 , 3 ) , ( 3 , 5 ) , ( 4 , 7 ) , ( 5 , 9 ) .
Finding the Correct Option Comparing the calculated series with the given options, we find that option C matches our calculated series: ( 1 , 1 ) , ( 2 , 3 ) , ( 3 , 5 ) , ( 4 , 7 ) , ( 5 , 9 ) . Therefore, option C is the correct answer.
Examples
This type of problem, where a formula determines the outcome based on a rank or position, is common in many real-life scenarios. For example, consider a sales competition where salespeople are awarded bonuses based on their sales ranking. The bonus amount could be determined by a formula similar to the one in this problem, ensuring that higher-ranked salespeople receive larger bonuses. Understanding how to use and interpret such formulas is valuable in analyzing and predicting outcomes in various competitive situations.
Approximately 2.81 × 1 0 21 electrons flow through an electric device delivering a current of 15.0 A for 30 seconds. This was calculated by finding the total charge in coulombs and then converting that charge to the number of electrons. Understanding the relationship between current, charge, and the charge of an electron is key to solving this problem.
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