A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the first arc is 18 feet long and th

Question

AleksAgata

2 months ago

11

A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the first arc is 18 feet long and th

e third arc is 8 feet long, what is the length of the second arc?

Mathematics

2 answers:

Zina [12.3K] · Answer 1 · 2026-03-18T18:16:51+03:00

The right response to this inquiry is this one:

In geometric sequences, you multiply by a certain factor to derive the subsequent number.
Commencing at 18
, the following number can be expressed as 18*K (where K represents the factor).
The third number correlates to 18*k*k.

However, we know that the third number is 8.

Hence, <span>x = 12.</span>

zzz [12.3K] · Answer 2 · 2026-03-18T18:18:50+03:00

Response: The length of the second arc measures 12 feet.

Step-by-step reasoning:

Considering that

A rope swings in a manner where the arc's length reduces geometrically,

The first arc measures 18 feet

and the third arc is 8 feet

Let the length of the second arc be x

As established,

$\frac{a_2}{a_1}=\frac{a_3}{a_2}\\\\\frac{x}{18}=\frac{8}{x}\\\\x^2=18\times 8\\\\x^2=144\\\\x=\sqrt{144}\\\\x=12$

Therefore, the second arc's length is 12 feet.