An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Set up the equation for the total number of pages read: y = 75 + 2 x .
Substitute the x values from each table into the equation and calculate the corresponding y values.
Compare the calculated y values with the y values in the table.
Identify the table where all pairs of ( x , y ) satisfy the equation: Table 2.
T ab l e 2
Explanation
Problem Analysis We are given four tables showing the relationship between the minutes of reading, x , and the total number of pages read, y . We know that Selma read 75 pages yesterday and reads 2 pages per minute today. Therefore, the total number of pages read can be modeled by the equation y = 75 + 2 x . We need to determine which table shows viable solutions for this equation.
Checking the Tables Let's analyze each table to see if the values satisfy the equation y = 75 + 2 x .
Calculations and Comparisons Table 1:
For x = 2 , y = 75 + 2 ( 2 ) = 75 + 4 = 79 . This matches the table.
For x = 14 , y = 75 + 2 ( 14 ) = 75 + 28 = 103 . The table shows y = 101 , so this table is incorrect.
Table 2:
For x = − 16 , y = 75 + 2 ( − 16 ) = 75 − 32 = 43 . This matches the table.
For x = 6 , y = 75 + 2 ( 6 ) = 75 + 12 = 87 . This matches the table.
For x = 27 , y = 75 + 2 ( 27 ) = 75 + 54 = 129 . This matches the table.
For x = 52 , y = 75 + 2 ( 52 ) = 75 + 104 = 179 . This matches the table. So, Table 2 is a viable solution.
Table 3:
For x = 0 , y = 75 + 2 ( 0 ) = 75 + 0 = 75 . The table shows y = 0 , so this table is incorrect.
Table 4:
For x = 0 , y = 75 + 2 ( 0 ) = 75 + 0 = 75 . This matches the table.
For x = 11 , y = 75 + 2 ( 11 ) = 75 + 22 = 97 . This matches the table.
For x = 2025 , y = 75 + 2 ( 2025 ) = 75 + 4050 = 4125 . The table shows y = 1155 , so this table is incorrect.
Conclusion Based on our analysis, only Table 2 shows viable solutions for the total number of pages Selma has read.
Examples
Understanding linear equations like y = 75 + 2 x is useful in many real-life situations. For example, if you are saving money, you might start with an initial amount (like the 75 pages Selma already read) and then add a certain amount each day (like the 2 pages Selma reads per minute). This equation helps you predict how much money you'll have saved after a certain number of days or how many pages you'll have read after a certain number of minutes. This kind of math is also used in calculating distances while traveling, figuring out costs, and even in science to predict outcomes based on constant rates.
An electric device with a current of 15.0 A for 30 seconds delivers approximately 450 coulombs of charge. This is equivalent to about 2.81 x 10^21 electrons flowing through the device. The calculation involves using the relationships between current, charge, and the charge of a single electron.
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