# precal

posted by .

A pile driver pounds a steel column into the ground. On the first drive, the column is pounded 1.65 metres into the ground, and on each successive drive it moves 80% as far as it did on the previous drive. The least number of drives required to drive the column a total of 8.2 metres into the ground is _____.

• precal -

so you want
1.65 + 1.65(.8) + 1.65(.8)^2 + .. = 8.2

you could just keep adding until you reach 8.2 but that would be less elegant than using a geometric series

a = 1.65
r = .8
Sum(n) = 8.2
a(1 - r^n)/(1-r) = sum(n)
1.65(1 - .8^n)/(1-.8) = 8.2
(1-.8^n)/.2 = 8.2/1.65
1-.8^n = 8.2/1.65*.2
.8^n = 1 - 8.2/1.65*.2
n log .8 = log [1 - 8.2/1.65*.2]
n = log [1- 8.2/1.65*.2] / log .8 = 22.8

22 drives will not do it, so they will need 23 pile drivings

check:
Sum(22) = 1.65 (1-.8^22)/.2 = 8.189
sum(23) = 1.65(1-.8^23)/.2 = 8.2013

## Similar Questions

1. ### chemistry

Reaction 1: I2(aq)Cu^+2(aq) Ag^+(aq)Br2(aq) Column 1---Column 2---Column 3---Column 4---Column 5 I-(aq)---X---X---T---T Cu(s)---T---X---T---T Ag(s)---X---X---X---T Br-(aq)---X---X---X---X Reaction of metals and solution of ions Reaction …
2. ### physics

a pile drive has a 413 kg block that is lifted 1.4m and then dropped onto the pile being driven into the ground. suppose that it takes 24ms to stop when it hits the pile. what is the average force exerted on the pile by the pile driver?
3. ### physics.

: When the mass hits the pile, it has kinetic energy. This energy is transformed into other forms of energy as the speed of the falling mass rapidly reduces to zero. As this happens, the pile is forced a small distance into the ground. …
4. ### physic

A 2,300-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 3.00 m before coming into contact with the top of the beam, and it drives the beam 9.4 cm farther into the ground as it comes to rest. Using …
5. ### physics

Each vertical steel column of an office building supports a weight of 1.30 x 10^5 N and is compressed to 5.90 x 10^-3 A) Find the compression in each column if a wegith of 5.50 x 10^5 N is supported. B)If the compression of each steel …
6. ### Physics

a 2199 kg pile driver is used to drive a steel beam into the ground. the pile driver falls 8.8 m before contacting the beam, and it drives the beam 19 cm into the ground before coming to rest. using energy considerations, calculate …
7. ### Physics

Suppose the 480 lb pile driver that drops 20 ft drives the pile 2 in. every time it strikes the pile. What is the average resisting force of the ground where the pile is driven?
8. ### science

kendra was looking at recipes in a cookbook. she divided some of the steps of a recipe into two columns. How would you label each column?
9. ### Physics

A pile driver lifts a 450 kg weight and then lets it fall onto the end of a steel pipe that needs to be driven into the ground. A fall of 1.5 m drives the pipe in 45 cm. What is the average force exerted on the pipe?
10. ### Science

This is what the chart talks about. A Melt 1 cup of butter chop an onion mix ingredients in a large bowl B Brown the meat in a frying pan boil 6 eggs bake at 350 degrees kendra was looking at recipes in a cookbook. she divided some …

More Similar Questions