An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Since d > 0"> b > d > 0 , we have 1"> d b > 1 and b d < 1 , thus \frac{d}{b}"> d b > b d .
Since b > c > d > 0"> a > b > c > d > 0 , we have d < c and b"> a > b , thus a d < b c .
Since b > d > 0"> a > b > d > 0 , we have \frac{b}{d}"> d a > d b , thus d b < d a .
The final answer is: \frac{d}{b}"> d b > b d , a d < b c , d b < d a . Therefore, the answer is , <, <}"> > , < , < .
Explanation
Understanding the Problem We are given four numbers a , b , c , d such that b > c > d > 0"> a > b > c > d > 0 . We need to compare the given fractions and fill in the blanks with , <,"> > , < , or = .
Comparing the First Pair of Fractions Let's analyze the first comparison: d b □ b d . Since d > 0"> b > d > 0 , we know that 1"> d b > 1 and b d < 1 . Therefore, \frac{d}{b}"> d b > b d .
Comparing the Second Pair of Fractions Now let's analyze the second comparison: a d □ b c . Since b > c > d > 0"> a > b > c > d > 0 , we have d < c and b"> a > b . Dividing the first inequality by a and the second inequality by b , we get a d < a c and b c < b c . Since b"> a > b , we have a 1 < b 1 . Multiplying both sides of d < c by a 1 and b 1 respectively, we get a d < a c and b d < b c . Since b"> a > b , it follows that a d < b d < b c . Therefore, a d < b c .
Comparing the Third Pair of Fractions Finally, let's analyze the third comparison: d b □ d a . Since b > d > 0"> a > b > d > 0 , we have \frac{b}{d}"> d a > d b . Therefore, d b < d a .
Final Answer In summary, we have:
\frac{d}{b}"> d b > b d
a d < b c
d b < d a
Examples
Understanding inequalities between fractions is crucial in various real-life scenarios. For instance, when comparing investment returns, if investment A yields a return of d b and investment B yields a return of b d , where d > 0"> b > d > 0 , knowing that \frac{d}{b}"> d b > b d helps you quickly determine that investment A is more profitable. Similarly, in resource allocation, comparing ratios like a d and b c can help optimize distribution strategies, ensuring resources are allocated efficiently based on relative needs or demands. These comparisons are fundamental in making informed decisions in finance, economics, and resource management.
The total charge flowing through the device is 450 coulombs, which corresponds to approximately 2.81 x 10^21 electrons flowing through it in 30 seconds.
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