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KengaRu [80]
4 years ago
10

Help! It's about and ratios and porportions

Mathematics
2 answers:
Elanso [62]4 years ago
6 0
I think snail D could travel 12 in an hour because you need to double it!
bulgar [2K]4 years ago
4 0
Good Afternoon, 

I will go over each one so you understand:
  
       First Question: How far can snail D travel in 1 hour?
Well, we know That snail D travels 6 inches in 30 minutes, and we also know that 30 minutes is \frac{1}{2} of an hour. Therefore, we can multiply 30 minutes by 2 to get an hour, and do the same with the amount of inches this snail travels. So 6 x 2 = 12. He travels 12 inches in an hour :)
   
      Second Question:  Here we do the same thing, except the snail travels 1 inch in 15 minutes and we want to know how much he travels in 30 minutes, so 2 x 1 = 2. The snail travels 2 inches in 30 minutes. Thats a slow snail!
   




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Step-by-step explanation:

Pick a function that is the same "family".  It needs to be a function that you know diverges or converges.  So p-series and geometric series are common choices.  Often we make the numerators the same so that it's easy to compare.

For example, if you have an = 1 / (n − 1), you would choose bn = 1 / n.  Since n − 1 is less than n, we know an is greater than bn.  And since we know bn diverges, that means the larger function an also diverges.

Or, if you have an = 1 / (n + 1), we again choose bn = 1 / n.  However, comparison test is inconclusive here (an < bn, bn diverges), so we use limit comparison test instead.

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1

The limit is greater than 0, and bn diverges, so an also diverges.

Let's try something more complicated.  Let's say an = e⁻ⁿ / (n + cos²n).  The numerator e⁻ⁿ is always less than 1, and the denominator is always greater than n.

If we again choose p-series bn = 1 / n, we know bn > an, and bn diverges, so comparison test is inconclusive.  Limit comparison test is possible, but tricky.

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