An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The equation y = 1.5 x − 2 is a linear equation.
Linear equations represent functions where each x value has only one y value.
Calculating the missing values confirms the unique mapping.
Therefore, each input x would have exactly one output y . yes
Explanation
Analyzing the Problem The problem provides a table representing the equation y = 1.5 x − 2 . We are asked to determine if each input x would have exactly one output y if the table were completed. This is essentially asking whether the given equation represents a function where each x value maps to a unique y value.
Understanding the Equation The equation y = 1.5 x − 2 is a linear equation. Linear equations are functions, meaning that for every x value, there is only one corresponding y value. To further illustrate, let's calculate the missing y values for x = 3 and x = 6 .
Calculating Missing Values For x = 3 , we have: y = 1.5 ( 3 ) − 2 = 4.5 − 2 = 2.5 For x = 6 , we have: y = 1.5 ( 6 ) − 2 = 9 − 2 = 7 So, when x = 3 , y = 2.5 , and when x = 6 , y = 7 .
Concluding the Answer Since the equation is linear, each x value will always produce a unique y value. Therefore, if the table were completed, each input would indeed have exactly one output.
Examples
In real life, this concept is used in various scenarios, such as converting temperatures from Celsius to Fahrenheit using a linear equation. For every Celsius temperature, there is only one corresponding Fahrenheit temperature. Similarly, if you are calculating the cost of a taxi ride based on distance, the equation ensures that for every distance traveled, there is a unique cost.
The total charge delivered by a device with a current of 15.0 A for 30 seconds is 450 coulombs. This charge corresponds to approximately 2.81 × 1 0 21 electrons. Therefore, about 2.81 × 1 0 21 electrons flow through the device during this time period.
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