An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Substitute y = 1 into the equation 4 x − 4 y = 8 .
Simplify the equation to 4 x − 4 = 8 .
Add 4 to both sides: 4 x = 12 .
Divide by 4 to find x : x = 3 . The missing coordinate is 3 .
Explanation
Understanding the Problem We are given the equation 4 x − 4 y = 8 and the ordered pair ( ? , 1 ) . Our goal is to find the missing x -coordinate so that the ordered pair satisfies the equation.
Substituting the value of y To find the missing x -coordinate, we substitute y = 1 into the equation 4 x − 4 y = 8 . This gives us: 4 x − 4 ( 1 ) = 8
Simplifying the equation Now, we simplify the equation: 4 x − 4 = 8
Isolating the x term Next, we add 4 to both sides of the equation to isolate the term with x :
4 x − 4 + 4 = 8 + 4
4 x = 12
Solving for x Finally, we divide both sides of the equation by 4 to solve for x :
4 4 x = 4 12
x = 3
Finding the missing coordinate Therefore, the missing coordinate is 3, and the ordered pair is ( 3 , 1 ) .
Examples
Understanding how to solve for missing coordinates in linear equations is useful in various real-world scenarios. For example, when designing a bridge, engineers use linear equations to ensure that the load is evenly distributed. If one coordinate of a support is known, they can calculate the other coordinate to maintain structural integrity. Similarly, in economics, if you know the quantity of a product demanded at a certain price, you can use a linear equation to find the price at a different quantity level.
The total charge transferred through an electric device delivering a current of 15.0 A for 30 seconds is 450 C . This results in approximately 2.81 × 1 0 21 electrons flowing through the device. The calculations are based on the relationship between current, charge, and the charge of a single electron.
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