An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The point-slope form of a line is y − y 1 = m ( x − x 1 ) .
Harold's equation is y = 3 ( x − 7 ) , which can be rewritten as y − 0 = 3 ( x − 7 ) .
Comparing the equations, we find the point ( x 1 , y 1 ) = ( 7 , 0 ) .
Therefore, the point Harold used is ( 7 , 0 ) .
Explanation
Understanding the Point-Slope Form The point-slope form of a linear equation is given by y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is a point on the line and m is the slope. Harold wrote the equation y = 3 ( x − 7 ) . We need to identify the point Harold used.
Identifying the Values Harold's equation is y = 3 ( x − 7 ) . We can rewrite this as y − 0 = 3 ( x − 7 ) . Comparing this to the point-slope form y − y 1 = m ( x − x 1 ) , we can see that m = 3 , x 1 = 7 , and y 1 = 0 .
Determining the Point Therefore, the point Harold used is ( x 1 , y 1 ) = ( 7 , 0 ) .
Examples
Understanding the point-slope form is useful in various real-life scenarios. For example, if you know the rate at which you are saving money (slope) and your current savings (a point), you can predict your future savings using this form. Similarly, in physics, if you know the velocity of an object (slope) and its position at a certain time (a point), you can determine its position at any other time.
The number of electrons flowing through a device delivering a current of 15.0 A for 30 seconds is approximately 2.81 x 10^21 electrons. This is calculated using the relationship between current, charge, and the charge of a single electron. Current is the rate of charge flow, and we find the total charge first, then divide by the electron charge to get the number of electrons.
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