An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Define the variables: Let h be the height and x be the width.
Express the height in terms of the width: h = 2.5 x − 0.6 .
Substitute the given height: 4.9 = 2.5 x − 0.6 .
The equation to determine the width is: 2.5 x − 0.6 = 4.9 .
Explanation
Problem Analysis Let's analyze the given information. The height of the window is 0.6 feet less than 2.5 times its width. We also know that the height of the window is 4.9 feet. We need to find the equation that represents this situation, where x is the width of the window.
Expressing Height in Terms of Width Let h represent the height of the window and x represent the width of the window. According to the problem, the height h can be expressed as: h = 2.5 x − 0.6
Substituting the Given Height We are given that the height of the window is 4.9 feet, so h = 4.9 . Substitute this value into the equation: 4.9 = 2.5 x − 0.6
Matching the Equation Now, we need to find the equation that matches one of the given options. The equation we derived is: 2.5 x − 0.6 = 4.9
Final Answer Comparing this equation with the given options, we see that it is equivalent to 2.5 x − 0.6 = 4.9 . Therefore, the correct equation is 2.5 x − 0.6 = 4.9 .
Examples
Understanding how to set up equations from word problems is crucial in many real-life situations. For instance, if you're designing a rectangular garden where the length is a certain amount longer or shorter than a multiple of the width, you can use similar equations to determine the dimensions of the garden based on the available space or desired area. This skill is also useful in financial planning, where you might need to calculate expenses or investments based on certain conditions or constraints.
The electric device transfers approximately 2.81 × 1 0 21 electrons when delivering a current of 15.0 A for 30 seconds. This calculation is derived using the relationship between current, charge, and the charge of an electron. Ultimately, you multiply the current by the time to find charge and then divide by the charge of a single electron to find the total number of electrons.
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