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nirvana33 [79]
2 years ago
5

What is the common ratio of the geometric sequence (-3,-9, -27,-81.....}*

Mathematics
2 answers:
Marianna [84]2 years ago
5 0
Divide any term by the term before it, and you'll get the common ratio of the geometric series.

-81/-27=3
The common ratio is 3.
8090 [49]2 years ago
4 0

Answer:

The common ratio is 3

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

-9/-3 = 3

We can check by dividing the third term by the second term

-27/-9 =3

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The fish population in a certain lake rises and falls according to the formula F = 3000(23 + 11t − t2). Here F is the number of
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a) On January 1, 2017 the fish population will be the same as the initial population.

b) On September 18th, 2018 the fish population will be zero.

Step-by-step explanation:

Hi there!

a) First, let´s write the function:

F(t) = 3000(23 + 11t − t²)

The population on January 1, 2006 is the population at t = 0. Then:

F(0) = 3000(23 + 11· 0 - 0²)

F(0) = 3000 · 23 = 69000

This will be the population every time at which t² - 11t = 0. Then let´s find the other value of t (besides t = 0) that makes that expression to be zero:

t² - 11t = 0

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and

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On January 1, 2017 (2006 + 11), the fish population will be the same as the initial population.

b) We have to obtain the value of t at which F(t) = 0

F(t) = 3000(23 + 11t − t²)

0 = 3000(23 + 11t − t²)

divide both sides of the equation by 3000

0 = 23 + 11t − t²

Let´s solve this quadratic equation using the quadratic formula:

a = -1

b = 11

c = 23

x = [-b ± √(b² - 4ac)] / 2a

x = 12.8  ( the other value of x is negative and therefore discarded).

After 12.8 years all the fish in the lake will have died.

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0.8 years · 12 months/year = 9.6 months

If 1 month is 30 days, 0.6 month will be:

0.6 month · 30 days / month = 18 days

All the fish will have died after 12 years, 9 months and 18 days from January 1, 2006. That is, on September 18th, 2018.

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