An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Approximately 2.81 × 1 0 21 electrons flow through an electric device delivering a current of 15.0 A for 30 seconds. This is calculated using the relationship between current, charge, and the charge of an electron. By using these formulas, we find that the total charge and number of electrons can be determined systematically.
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Calculate the area of each corral using the formula A re a = L e n g t h × Wi d t h .
Determine the area per animal for each corral using the formula A re a p er A nima l = N u mb er o f A nima l s A re a .
Compare the calculated area per animal for each corral to the minimum requirement of 20 square meters per animal.
Identify that only Corral 4 meets the requirement with exactly 20 square meters per animal, thus the answer is D .
Explanation
Problem Analysis and Solution Plan First, we need to calculate the area of each corral. The area of a rectangle is given by the formula: A re a = L e n g t h × Wi d t h Then, we will calculate the area per animal for each corral by dividing the total area by the number of animals in that corral: A re a p er A nima l = N u mb er o f A nima l s A re a Finally, we will compare the calculated area per animal with the given constraint of at least 20 square meters per animal to determine which corral meets the requirement.
Calculate Corral Areas Let's calculate the area for each corral:
Corral 1: A re a 1 = 50 m e t ers × 40 m e t ers = 2000 s q u a re m e t ers
Corral 2: A re a 2 = 60 m e t ers × 35 m e t ers = 2100 s q u a re m e t ers
Corral 3: A re a 3 = 55 m e t ers × 45 m e t ers = 2475 s q u a re m e t ers
Corral 4: A re a 4 = 65 m e t ers × 40 m e t ers = 2600 s q u a re m e t ers
Calculate Area per Animal Now, let's calculate the area per animal for each corral:
Corral 1: A re a p er A nima l 1 = 110 anima l s 2000 m 2 = 18.18 m 2 / anima l
Corral 2: A re a p er A nima l 2 = 115 anima l s 2100 m 2 = 18.26 m 2 / anima l
Corral 3: A re a p er A nima l 3 = 125 anima l s 2475 m 2 = 19.80 m 2 / anima l
Corral 4: A re a p er A nima l 4 = 130 anima l s 2600 m 2 = 20.00 m 2 / anima l
Compare with Requirement and Identify Solution Comparing the area per animal for each corral with the requirement of at least 20 square meters per animal:
Corral 1: 18.18 m 2 / anima l (Does not meet the requirement)
Corral 2: 18.26 m 2 / anima l (Does not meet the requirement)
Corral 3: 19.80 m 2 / anima l (Does not meet the requirement)
Corral 4: 20.00 m 2 / anima l (Meets the requirement)
Therefore, only Corral 4 meets the requirement of having at least 20 square meters per animal.
Final Answer Based on our calculations, Corral 4 provides exactly 20 square meters per animal, which meets the minimum requirement.
Examples
Understanding area calculations is crucial in various real-world scenarios. For instance, when planning a garden, you need to calculate the area to determine how much soil or fertilizer to buy. Similarly, architects use area calculations to design buildings and ensure that rooms are large enough for their intended purposes. In agriculture, farmers use area calculations to determine how much land is needed to grow a certain amount of crops or to provide adequate grazing space for livestock. These calculations help optimize resource use and ensure efficient planning.
