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Alexeev081 [22]
3 years ago
11

A pendulum swings 80 cm on its first swing, 76 cm on its second swing, 72.2 cm on its third swing, and 68.59 cm on its fourth sw

ing. Complete parts a and b below.
a. If the pattern continues, what explicit formula can be used find the distance of the nth swing?
Mathematics
1 answer:
Kisachek [45]3 years ago
7 0

Answer:

a_{n} = 80*(0.95)^{n-1}

Step-by-step explanation:

Geometric sequences:

The nth term of a geometric sequence is given by the following equation.

a_{n+1} = ra_{n}

In which r is the common ratio.

This can be expanded for the nth term in the following way:

a_{n} = a_{1}r^{n-1}

In which a_{1} is the first term.

In this question:

a_{1} = 80, r = \frac{68.59}{72.2} = \frac{72.2}{76} = \frac{76}{80} = 0.95

a. If the pattern continues, what explicit formula can be used find the distance of the nth swing?

a_{n} = a_{1}r^{n-1}

a_{n} = 80*(0.95)^{n-1}

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Answer:

1. Their ages are:

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Step-by-step explanation:

1. We make the assumption that:

S = Steve's age

A = Anne's age

In four years, we are going to have:

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S = (3 * 8) – 6 = 24 – 6

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Steve's age = 18

Anne's age = 8.

2. We make the assumption that:

M = Max's age

B = Bert's age

Five years ago, we had:

M - 5 = (B - 5)2

M - 5 = 2B - 10 .......................... (3)

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Substitute M from (4) into (3) and solve for B, we have:

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If we substitute B = 11 into equation (4), we will have:

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Therefore, their ages are:

Max's age = 17

Bert's age = 11.

3. We make the assumption that:

S = Sury's age

B = Billy's age

Now, we have:

S = B + 10 ................................ (5)

Next year, it will be:

S + 1 = (B + 1)2

S + 1 = 2B + 2 .......................... (6)

Substituting S from equation (5) into equation (6) and solve for B, we will have:

B + 10 + 1 = 2B + 2

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Substituting B = 9 into equation (5), we have:

S = 9 + 10

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Therefore, their ages are:

Sury's age = 19

Billy's age = 9.

4. We make the assumption that:

M = The man's age

S = His son's age

Therefore, now, we have:

M = 3S ................................... (7)

Five years ago, we had:

M - 5 = (S - 5)5

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Substituting M = 3S from (7) into (8) and solve for S, we have:

3S - 5 = 5S – 25

3S – 5S = - 25 + 5

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S = -20 / -2

S = 10

Substituting S = 10 into equation (7), we have:

M = 3 * 10 = 30

Therefore, their ages are:

The man's age = 30

His son's age = 10

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