Question

a rope is swinging in such a way that the length of the arc is decreasing geometrically. If the first arc is 27 feet long and the fourth arc is 8 feet long, what is the length of the second arc?

Answer 1

@jim_thompson5910

Answer 2

my equation i came up with this 27(2/4)^n-1 is that not right?

Answer 3

`length of the arc is decreasing geometrically`

so if 27 is the first arc length then 27*r is the second arc length where r is some value in the interval 0 < r < 1

the third arc is 27*r*r = 27*r^2

the fourth arc is 27*r^2*r = 27*r^3, and we're given it's equal to 8, so

27r^3 = 8

making r = ???

Answer 4

is it .6666

Answer 5

or 2/3

Answer 6

so 27*r = 27*(2/3) = ???

Answer 7

12

Answer 8

no

Answer 9

oh i did it squared to find the second

Answer 10

18

Answer 11

yep the second arc is 18 ft

Answer 12

wait wouldn't it be 12 because it is squared for 2nd

Answer 13

Common ratio: r = 2/3



first arc = 27 ft .... given



second arc = (first arc)*(r)
second arc = (27)*(2/3)
second arc = 18 ft



third arc = (second arc)*(r)
third arc = (18)*(2/3)
third arc = 12



fourth arc = (third arc)*(r)
fourth arc = (12)*(2/3)
fourth arc = 8 ... also given and this confirms what we're given

Answer 14

oh i see but idk why 18 isn't one of my answer choices

Answer 15

there's a typo somewhere I'm assuming

Answer 16

oh maybe. but u seem correct

Answer 17

The only thing you can do is bring it up with the teacher

Answer 18

yeah i'll ask. thank you!

Answer 19

no problem