An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Convert all given measurements to a common unit (feet) using the provided conversion ratios.
Calculate the equivalent values in feet for each measurement.
Match the measurements based on their equivalent values in feet.
The equivalent measurements are: 372 feet → 124 yards, 352 yards → 0.2 miles, 124 yards → 372 feet, 1,016 yards → , 348 inches → 29 feet.
The final answer is: 372 feet → 124 yards 352 yards → 0.2 miles 124 yards → 372 feet 1,016 yards →
348 inches → 29 feet 372 feet → 124 yards , 352 yards → 0.2 miles , 124 yards → 372 feet , 1016 yards → , 348 inches → 29 feet
Explanation
Problem Analysis and Conversion Strategy We are given a conversion table and asked to match equivalent measurements. The key is to convert all measurements to a common unit, such as feet, to make comparisons easier.
Converting to Feet Let's convert the given measurements to feet using the provided ratios:
372 feet (already in feet)
352 yards = 352 yards × 3 yard feet = 1056 feet
124 yards = 124 yards × 3 yard feet = 372 feet
1016 yards = 1016 yards × 3 yard feet = 3048 feet
348 inches = $348 \text{ inches} \times \frac{1}{12} \frac{\text{feet}}{\text{inch}} = 29 \text{ feet}
Converting Matching Measurements to Feet Now, let's convert the measurements we need to match to feet as well:
29 feet (already in feet)
10,560 feet (already in feet)
2 miles = 0.2 miles × 1760 mile yards × 3 yard feet = 1056 feet
2 miles = $2 \text{ miles} \times 1760 \frac{\text{yards}}{\text{mile}} \times 3 \frac{\text{feet}}{\text{yard}} = 10560 \text{ feet}
Matching Equivalent Measurements Now we can easily match the equivalent measurements:
372 feet = 124 yards
352 yards = 1056 feet = 0.2 miles
124 yards = 372 feet
1016 yards = 3048 feet
348 inches = 29 feet
Final Answer and Summary Therefore, the equivalent measurements are:
372 feet → 124 yards
352 yards → 0.2 miles
124 yards → 372 feet
1,016 yards →
348 inches → 29 feet
Examples
Understanding unit conversions is crucial in many real-life situations. For instance, when planning a road trip, you might need to convert miles to kilometers to understand distances displayed on your car's odometer or road signs in different countries. Similarly, in construction, converting between feet, inches, and yards is essential for accurate measurements of materials and spaces. Mastering these conversions ensures precision and avoids costly errors in various practical applications.
To find the number of electrons flowing through an electric device that delivers a current of 15.0 A for 30 seconds, we calculate the total charge as 450 Coulombs. Dividing this charge by the charge of a single electron ( 1.602 × 1 0 − 19 C/electron ) gives approximately 2.81 × 1 0 21 electrons. So, 2.81 × 1 0 21 electrons flow through the device.
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