An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Solve the equation for y in terms of x : y = ± 4 − x .
Observe that for a single value of x , there are two possible values for y (positive and negative square roots).
Conclude that the equation does not define y as a function of x because a function must have a unique y for each x .
The final answer is: is not a function
Explanation
Understanding the Problem We are given the equation x + y 2 = 4 and asked to determine if it defines y as a function of x . In simpler terms, we want to see if each value of x corresponds to exactly one value of y .
Isolating y^2 To figure this out, let's solve the equation for y in terms of x . We start by isolating y 2 :
y 2 = 4 − x
Solving for y Now, we take the square root of both sides to solve for y :
y = ± 4 − x
Analyzing the Result Notice the ± sign? This means that for a single value of x , we can have two different values of y . For example, if x = 0 , then y = ± 4 − 0 = ± 4 = ± 2 So, when x = 0 , y can be either 2 or − 2 .
Conclusion Since a single value of x can correspond to two different values of y , the equation x + y 2 = 4 does not define y as a function of x .
Examples
Imagine you're designing a curved road. The equation x + y 2 = 4 can describe the curve's shape. If y were a function of x , each point along the road (defined by x ) would have only one corresponding vertical position ( y ). However, since it's not a function, some x values have two y values, meaning the road could loop back on itself vertically. This understanding is crucial in design to avoid overlaps and ensure a safe, single path for vehicles.
The total charge passed is calculated using the formula Q = I ⋅ t , resulting in 450 C . Dividing this total charge by the charge of a single electron ( 1.6 × 1 0 − 19 C ) gives approximately 2.81 × 1 0 21 electrons. Thus, about 2.81 × 1 0 21 electrons flow through the device in 30 seconds.
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