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vagabundo [1.1K]
3 years ago
12

The product of two consecutive positive integers is 132. What are the integers?

Mathematics
1 answer:
alina1380 [7]3 years ago
5 0

Answer:

The integers are 11 and 12

Step-by-step explanation:

11 and 12 are consecutive positive integers, and 11 x 12 = 132.

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Ok, so the question is based on geometric progression. Remember, the formula for calculating the nth-term of a geometric progression is: a*r^{n-1}. The a in the expression stands for the 1st term of the sequence, and r is the common ratio of the elements of the sequence. Now let's take a look at the problem.

"A ping pong ball has a 75% rebound ration". We can infer that our common ratio, r, is 75% which is 0.75.

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Now going back to the expression, the nth-term = a*r^{n-1}, we can substitute our common ration, 0.75 with r, and our 1st term, k, with a. This becomes: k * 0.75^{n-1}. This becomes our expression.

a. The highest height achieved by the ball after six bounces. Our nth-term here is 6, so let's use our expression to find the 6th term. n_{6} = 235 * 0.75^{6-1} = 235*0.75^{5} = 235*0.2373 = 55.7655ft

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\frac{235(1-0.75^{12})}{(1-0.75)} = 910.2242ft

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