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2 years ago

A rope is swinging In such a way that the length of the arc traced by a knot at its bottom end is

Mathematics

1 answer:

Sati [7]2 years ago

3 0

Answer:

13.6 ft

Step-by-step explanation:

The geometric sequence of arc lengths can be described by ...

f(n) = a·b^n

We have (n, f(n)) = (3, 20) and (7, 12). Using these values, we can find the common ratio (b):

20 = a·b^3

12 = a·b^7

Then ...

12/20 = (a·b^7)/(a·b^3) = b^4 = 3/5

We want the 6th term, which we can get from the 7th term by multiplying by b^-1.

b^(-1) = (b^4)^(-1/4) = (3/5)^(-1/4) = √(√(5/3)) ≈ 1.13622

Then the 6th swing had an arc length of ...

f(6) = f(7)·b^-1

f(6) = (12 ft)(1.13622) ≈ 13.63 ft ≈ 13.6 ft

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$\huge\textsf{Hey there!}$

$\large\textsf{6!}\\\large\textsf{= 6}\times\large\textsf{5}\times\large\textsf{4}\times\large\textsf{3}\times\large\textsf{2}\times\large\textsf{1}\\\large\textsf{6(5) = \bf 30}\\\large\textsf{= 30}\times\large\textsf{4}\times\large\textsf{3}\times\large\textsf{2}\times\large\textsf{1}\\\large\textsf{30(4) = \bf 120}\\\large\textsf{= 120}\times\large\textsf{3}\times\large\textsf{2}\times\textsf{1}\\\large\textsf{120(3) = \bf 360}\\\large\textsf{= 360}\times\large\textsf{2}\times\large\textsf{1}$

$\large\textsf{360(2) = \bf 720}\\\large\textsf{720}\times\large\textsf{1}\\\large\textsf{= \bf 720}$

$\boxed{\boxed{\huge\textsf{Therefore, your answer is: \bf 720}\huge\textsf{ (option B)}}}\huge\checkmark$

$\large\textsf{Good luck on your assignment and enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

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3 years ago

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3 years ago

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2 years ago