precal

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 _____.

1. 👍 0
2. 👎 0
3. 👁 1,011
1. 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

1. 👍 0
2. 👎 0

Similar Questions

1. Geometry

Write a two-column proof. Given: 7y=8x-14; y=6 Prove: x=7 I need help making a two-column proof with the statements and the reasons, please! Thank you! ( This is what I have so far) Statements | Reasons 1. 7y=8x-14;y=6 | Given 2.

2. Ed. Tech

After creating a column heading and/or typing text within a column, what must you do to move text to the next column? A. Add a column break B. Select the next column and start typing C. Highlight the next column D. Change the page

3. 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?

4. Calculating Rate Constants

I'm really stuck with this one. Here's the rate law and the data that is needed. I appreciate any help Rate= k[I2]X{[H+]Y[CH3COCH3]Z Column 1 - Trial Column 2 - Volume of 0.0010 M I2 Column 3 - Volume of 0.050 M HCl Column 4 -

1. solid mechanics

Find the Euler's crippling load for a hollow cylindrical steel column of 3.8 mm external diameter and 2.5 mm thick. Take length of the column as 2.3 m and hinged at its both ends crippling load by Rankine's formula. Using

2. computers

I need help with the follwing question: Give an example of a column A and a column B such that B is functionally dependent on A. Give an example of a column C and a column D such that D is not functionally dependent on C.

3. Elasticity (Physics)

A tunnel of length L=150m, height H=7.2m, and width w=5.8m (with a flat roof) is to be constructed at a distance d=60m beneath the ground. The tunnel roof is be entirely supported by square steel columns, each with a cross

4. Tech

4. after creating a column heading and or typing text within a column what must you do to move text to the next column? Add a column break select the next column and start typing** highlight the next column change the page

1. Chemistry

Why should a mixture to be separated by column chromatography be introduced onto the column in a minimum amount of solvent?

2. Physics

Water has a density of 1000kg/m^3. The depth of a swimming pool at the deep end is about 4m. A)What is the volume of a column of water 4m deep and 1m^3 in cross-sectional area? B)What is the mass of this column of water? C)What is

3. 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? A.) Column A shows sublimation; column B shows vaporization B.) Column A shows vaporization;

4. Statistics

A volunteer ambulance service handles 0 to 5 service calls on any given day. The probability distribution for the number of service calls is as follows: one column has number of service calls (X) those numbers are 0 1 2 3 4 5. The