An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the ratio of the photograph's sides: 5 4 = 0.8 .
Calculate the ratios of the canvas sizes: 10 8 = 0.8 , 20 16 = 0.8 , 24 18 = 0.75 , 36 24 = 0.666... .
Identify canvases with the same ratio as the photograph: 8 by 10 and 16 by 20.
State the prices of the proportional canvases: $6.43 and $11.65 .
Explanation
Understanding the Problem The problem asks us to find which canvases have dimensions proportional to a 4 inch by 5 inch photograph. This means the ratio of the sides of the canvas must be equal to the ratio of the sides of the photograph.
Calculating the Ratio of the Photograph First, let's find the ratio of the sides of the photograph. The ratio is 5 4 = 0.8 .
Calculating Ratios of Canvas Sizes Now, let's calculate the ratio of the sides for each canvas size:
8 by 10: 10 8 = 0.8
16 by 20: 20 16 = 0.8
18 by 24: 24 18 = 0.75
24 by 36: 36 24 = 0.666... = 3 2
Comparing Ratios Comparing the ratios, we see that the 8 by 10 and 16 by 20 canvases have the same ratio as the photograph (0.8). Therefore, these canvases are proportional to the photograph.
Identifying Canvas Prices The prices for the proportional canvases are:
8 by 10: $6.43
16 by 20: $11.65
So, the artist could use canvases at $6.43 and $11.65 to make a painting that is proportional to the photograph.
Examples
Understanding proportions is useful in many real-life situations. For example, when scaling a recipe, you need to maintain the correct proportions of ingredients to ensure the dish tastes as expected. Similarly, in architecture, blueprints are scaled drawings that maintain the proportions of the actual building. By understanding proportions, we can accurately resize and scale objects or quantities while preserving their relative relationships.
A current of 15.0 A flowing for 30 seconds results in a total charge of 450 C. This charge corresponds to approximately 2.81 x 10^21 electrons flowing through the device. Thus, about 2.81 quintillion electrons flow in that time frame.
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