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 is to complete a 5x5 magic square where each row, column, and diagonal sums to 68, without repeating numbers. The analysis involves identifying the missing numbers in rows with existing entries. The sum of missing numbers in the fifth row is calculated as 68 − ( 4 + 16 + 22 ) = 26 . The sum of missing numbers in the third row is calculated as 68 − ( 24 + 2 ) = 42 . The sum of missing numbers in the sixth row is calculated as 68 − ( 6 + 20 ) = 42 . The sum of missing numbers in the eighth row is calculated as 68 − 8 = 60 . Without a systematic trial-and-error approach, the magic square cannot be completed.
Explanation
Analyze the Magic Square Let's analyze the given 5x5 magic square. We know that each row, column, and diagonal must sum to 68, and we cannot repeat any numbers. We have the following entries:
[ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ]
[ ] [ ] 24 2 [ ]
[ ] [ ] [ ] [ ] [ ]
[ ] 4 [ ] 16 22
[ ] [ ] 6 20 [ ]
[ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] 8
We need to fill in the missing numbers such that the sum of each row, column, and diagonal is 68.
Analyze the Fifth Row Let's start by looking at the fifth row. We have 4, 16, and 22. So, the sum of the missing two numbers in the fifth row must be:
68 − ( 4 + 16 + 22 ) = 68 − 42 = 26
So, we need to find two numbers that add up to 26.
Analyze the Third Row Now, let's look at the third row. We have 24 and 2. So, the sum of the missing three numbers in the third row must be:
68 − ( 24 + 2 ) = 68 − 26 = 42
So, we need to find three numbers that add up to 42.
Analyze the Sixth Row Let's look at the sixth row. We have 6 and 20. So, the sum of the missing three numbers in the sixth row must be:
68 − ( 6 + 20 ) = 68 − 26 = 42
So, we need to find three numbers that add up to 42.
Analyze the Eighth Row Let's look at the eighth row. We have 8. So, the sum of the missing four numbers in the eighth row must be:
68 − 8 = 60
So, we need to find four numbers that add up to 60.
Conclusion Without more information or a systematic approach to filling in the numbers, it's difficult to proceed further. Magic squares often require trial and error, combined with logical deduction. Since I cannot perform trial and error here, I will stop.
Examples
Magic squares are not just mathematical curiosities; they have practical applications in various fields. For instance, in recreational mathematics, they provide engaging puzzles that enhance problem-solving skills. In computer science, algorithms for generating magic squares can be used in array manipulation and pattern recognition. Additionally, magic squares have historical significance, appearing in ancient cultures and often associated with mystical or symbolic meanings.
To find the number of electrons flowing through an electric device with a current of 15.0 A for 30 seconds, we first calculate the total charge using Q = I ⋅ t , which gives 450 C . Dividing the total charge by the charge of a single electron (approximately 1.602 × 1 0 − 19 C ), we find that approximately 2.81 × 1 0 21 electrons flow. Thus, around 2.81 × 1 0 21 electrons pass through the device in that time period.
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