Question 1164778: A particle sliding down an inclined plane travels 2 feet the first second. In any second after the first it slides 4 feet farther than it did in the preceeding second.
A.) How far will it slide in the 7th second?
B.) How far will it slide in 7 seconds?
C.) How long will it take to slide 128 feet?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the formula to use is An = A1 + (n-1) * d
A1 is equal to 2
d is equal to 4
n is equal to the number of seconds
using this formula, you will find that it will slide 26 feet in the 7th second.
the formula ia A7 = 2 + 6 * 4 = 2 + 24 = 26
the formula to find the sum of all the feet that it slid is Sn = n * (A1 + An) / 2.
n is the number of seconds
A1 is the first term.
An is the nth term.
using this formula, you will find that the total number of feet that it slid in 7 seconds is S7 = 7 * (2 + 26) / 2 = 98.
you can use this same formula to find out how many seconds it takes to slide a total of 128 feet.
the formula becomes Sn = n * (2 + An) / 2
since Sn is equal to 128, the formula becomes:
128 = n * (2 + An) / 2
multiply both sides of this formula by 2 to get:
256 = n * (2 + An)
you know that An = A1 + (n-1) * d
you also know that A1 = 2 and d = 4
the formula becomes:
An = 2 + (n-1) * 4
simplify this to get:
An = 2 + 4n - 4 which becomes:
An = 4n - 2
in the formula of 256 = n * (2 + An), replace An with 4n - 2 to get:
256 = n * (2 + 4n - 2)
simplify to get:
256 = 2n + 4n^2 - 2n
simplify this to get:
256 = 4n^2
divide both sides of this formula by 4 to get:
64 = n^2
solve for n to get:
n = sqrt(64) = 8
this tells you a total of 128 feet will have been slid in 8 seconds.
use the An formula to find A8 and then use the Sn formula o find the total number of feet that was slid.
A8 = 2 + 7 * 4 = 2 + 28 = 30
this makes sense since it slid 26 feet in the 7th second and it now slides 4 more feet in the 8th second.
S8 = 8 * (2 + 30) / 2 = 128
this says the particle slides a total of 128 feet in 8 seconds.
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