An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Distribute the 2 into the parenthesis.
Convert mixed numbers to improper fractions.
Combine like terms for x.
Combine like terms for y.
Simplify the expression: 10 7 x + 2 2 1 y + 6
Explanation
Understanding the Problem We are asked to simplify the expression 2\[\frac{3}{5} x+2 \frac{3}{4} y-\frac{1}{4} x-1 \frac{1}{2} y+3\] . This involves distributing the 2, combining like terms, and simplifying the result.
Distributing the 2 First, distribute the 2 into the parenthesis:
2 ( 5 3 x + 2 4 3 y − 4 1 x − 1 2 1 y + 3 ) = 2 ( 5 3 x ) + 2 ( 2 4 3 y ) − 2 ( 4 1 x ) − 2 ( 1 2 1 y ) + 2 ( 3 )
Converting to Improper Fractions Next, convert mixed numbers to improper fractions: 2 4 3 = 4 11 and 1 2 1 = 2 3 . So the expression becomes:
5 6 x + 4 22 y − 4 2 x − 2 6 y + 6
Combining x terms Now, combine like terms (x terms): 5 6 x − 4 2 x = 5 6 x − 2 1 x . To subtract these, we need a common denominator, which is 10. So, 5 6 x − 2 1 x = 10 12 x − 10 5 x = 10 7 x
Combining y terms Combine like terms (y terms): 4 22 y − 2 6 y = 2 11 y − 3 y . To subtract these, we need a common denominator, which is 2. So, 2 11 y − 3 y = 2 11 y − 2 6 y = 2 5 y
Final Simplification Write the simplified expression: 10 7 x + 2 5 y + 6
Convert the improper fraction to a mixed number: 2 5 y = 2 2 1 y
So, the final simplified expression is: 10 7 x + 2 2 1 y + 6
Examples
This type of simplification is useful in many real-world scenarios. For example, suppose you are calculating the total cost of materials for a project. You might have an expression that includes variables for the amount of each material needed. Simplifying the expression allows you to easily calculate the total cost by plugging in the values for the variables. This is also applicable when calculating areas or volumes in geometry, where simplifying expressions can make calculations more straightforward.
In 30 seconds, a device with a current of 15.0 A allows approximately 2.81 x 10^21 electrons to flow through it. This is calculated using the relationship between current, charge, and the charge of a single electron. Ultimately, the total charge of 450 coulombs leads to this large number of electrons.
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