Respuesta :

Answer: The length of the second arc is 12 feet.

Step-by-step explanation:

Since we know that

A rope is swinging in such a way that the length of the arc is decreasing geometrically,

Length of first arc = 18 feet

Length of third arc = 8 feet

Let the length of second arc be x

As we know that

[tex]\frac{a_2}{a_1}=\frac{a_3}{a_2}\\\\\frac{x}{18}=\frac{8}{x}\\\\x^2=18\times 8\\\\x^2=144\\\\x=\sqrt{144}\\\\x=12[/tex]

Hence, the length of the second arc is 12 feet.

abidemiokin

They are sequence that increases exponentially. The length of the second arc is 12 feet

Geometric sequence

They are sequence that increases exponentially. If a rope is swinging in such a way that the length of the arc is decreasing geometrically with  first arc 18 feet long and the third arc 8 feet long, then the sequence of numbers will be:

18, x,8....

Take the common ratio of the sequence to determine the value of "x"

x/18 = 8/x

Cross multiply

x² = 8 *18
x² = 144

x = √144

x = 12

Hence the length of the second arc is 12 feet

Learn more on geometric sequence here: https://brainly.com/question/1509142

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