Need help regarding polynomial equations

[grim1234]

Need urgent help regarding polynomial equations

I am having trouble with three questions and was requiring your help
1/ I was wondering how would u find the length of a cubic curve if it was straightened? (Is the only way to use trapezoidal approximation and add the lengths of the lines touching the curve or is there a better way)?
2/ Regarding q1, a ball bearing is dropped down a tube which is moudled to the shape of a cubic curve, and i have calculated the theoretical launch velocity, but how would i calculate friction? I have other trials where the cubic equation (shape of tube) is altered and calculated the launch velocity in those trials but vannot seem to calculate friction to find the actual launch velocity?
3/Another question, i was wondering apart from a logistic equation, what equatons could be made to predict population growth with a table of data i have?

Thanks for your help

 

[rock.freak667]

The only thing I can tell is to find the length of the arc of a curve y between 2 points ,x₁ and x₂, you use the formula

$$S=\int_{x_1} ^{x_2} \sqrt{1 + \left( \frac{dy}{dx} \right) ^2} dx$$

 

[grim1234]

But how am i supposed to use that equation?

 

[snipez90]

Well as rockfreak mentioned, you find the endpoints of the segment of the graph you want to find the length and also take the derivative of the polynomial you are considering and use the formula.

 

[Defennder]

For q2, the retarding frictional force is due to the coefficient of kinetic friction as well as the magnitude of the normal force exerted on the cubic-graph-shaped tube. Find an expression which gives you the normal force exerted by the ball on the tube. Are you given the value of the coefficient of kinetic friction?

For 3, your question is too broad. There are many models which you can invoke depending on the circumstances, which you can clarify by being more specific as to what kind of living organisms and under which conditions your population data was taken from.

http://en.wikipedia.org/wiki/Population_modeling

 

[HallsofIvy]

grim1234, the problem with simply stating problems while not showing any work of your own is that we then have no idea of your mathematical knowledge about the problem and so can't know what kind of answers will help you. Have you taken calculus? If so then Rockfreak667's answer is exactly what you need. If you do not understand his answer and have not taken calculus, you probably not have the mathematics necessary to do an arclength problem.

As for the second problem, you will need to know something about the "coefficient of friction" of the tube. Do you have that information?

 

[grim1234]

Yes i have taken calculus. I was not provided with a value for friction.

 

[Defennder]

What then are you given? What is the statement of the problem?

 

[grim1234]

Dw thanks for ur help guys, I've found the answer. I need help with a projectile motion question with i and j components, if the object is already displaced 0.64j how would i calculate its maximum height?

 

[Defennder]

You need to provide more information. Knowing the vertical displacement of the object at one time doesn't tell you anything about the vertical velocity at the point in time, which you need to calculate max height.

 

[grim1234]

Im actually calculating the max heights at dffierent angles(0 degrees to 90 degrees in increments of 5). One other question, i am making a logistic function to predict the population of the USA by 2050 but i am getting approximately 385 which is far below the predicted value of 420-440, how would i be able to refine my equation using some statistics and altering the population limit? Thanks

 

[Defennder]

You need to be far more explicit about what exactly you are given and how you have worked through them. For the calculation of max heights, what information are you given? On your population modeling, what modeling assumptions have you made? What are your logistic equation parameters? How do you expect anyone to help if you do not tell us how you have done it or what data you are given?

 

[grim1234]

For the max height equation, the value of gravity provided is 9.9m/s and the initial speed is 4.025472891 m/s. I need to do a graph showing in increments of 5 degrees the max height reached by the object when launched from 0.64j. For the population 1, this is the info i am provided (in decades, 0=1790, 21.8=2008 etc) and in millions

0 3.9
1 5.3
2 7.2
3 9.6
4 12.9
5 17.1
6 23.2
7 31.4
8 38.6
9 50.2
10 62.9
11 76
12 92
13 105.7
14 122.8
15 131.7
16 150.7
17 179.3
18 203.2
19 226.5
20 248.7
21 281.4
21.8 304.6

I have created logistic function however, the capacity is too small, being around 470 whereas predictions for 2100 are much larger (570.94). Using this value for M (capacity), how would i create a logistic function that would predict a population of around 438 in 2050? Thanks