# - Fishing Rods Type 2

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Hey, there pls i need some help in ma math portfolio due in 2 days!! Its about a fishing rod, we're given points to plot on the graph and then we have to find a quadratic and cubic function modelling it. Then we have to find the equation of the original curve. I pretty much stuck and would really appreciate some help. Thanks in advance!

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How to model your qaudratic and equation using GDC or any other math software capable of matrix operations:

1.) Consider general form of cubic and quadratic equations (where a,b,c,d are coefficients and where a is never zero):

y=ax3 +bx2 +cx+d (cubic)

2.) Insert points from the graph (x,y coordinates) into general from of the equation to get a system of equations (example):

4a+2b+c=7 (point 2,7 in quadratic equation)

9a+3b+c=8 (point 3,8 in quadratic equation)

16a+4b+c=5 (point 4,5 in quadratic equation)

3.) For three points, quadratic equation equation is a polynomial fit, for four or more, it is a polynomial regression (hence, at least three points are required). For four points, cubic eqaution is a polynomial fit, for five or more, it is a polynomial regression (hence, at least four points are required). Remember, that polynomial fit means, that a polynomial passes through these points and that polynomial regression means that polynomial fits to the general shape that points form, but never actaully passes through any of the points. In any case, finding an equation of the original curve is pointless, because the most accurate regressions are the ones from 4th degree polynomials and up and you have to deal with 2nd and 3rd degree polynomials. Be more specific about the task you're working on.

4.) Having made system of equations, rewrite them in matrix:

Apply rref command in your TI-84 GDC (2nd -> Matrix -> Math -> rref). I used Maple 12 for clarity.

5.) All you are now left with is the read the coefficients of your equation:

a=-2, b=11, c=-7

and write the regression equation: y=-2x2 +11x-7

6.) Finally, to visually check the correctness of your results, you can plot regression equation and points you used all of them. I used my three points and obtained equation (note that this is a polynomial fit):

(I used Autograph to create this graph)

This should be it. Hope it helped.

Edited by Jernej
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well, the assignment is about a fishing rod with 8 guides on it. And one assignment on the paper is: "...Discuss the implication of adding a ninth guide to the rod", but I cant see what possibly could be an implication on adding a ninth guide?

Any other views?

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hi I just got assigned an sl type 2 paper and I REALLY need help. The table below is for a fishing rod with eight guides plus a guide at the tip of the rod.

guide # from tip- 1 2 3 4 5 6 7 8

distance from tip (cm)- 10 23 38 55 74 96 120 149

I have to define suitable variables, discuss parameters/constraints. Also, using the matrix method (which i dont know) or otherwise, i have to find a quadratic and cubic function to model the situation. Graph this and original. Then, find a polynomial function which passes though every data point while explaining the chice of function and reasonableness. Graph this and original. Find another function that fits the data. Graph this and original. Which of the fuctions best models the situation. Use the quadratic model to decide where you would place the ninth guide. discuss implications of adding ninth guide to rod.

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I now understand how to get the quadratic and cubic functions using regression on a graphing calculator but I am still confused about the polynomial function. I dont understand how to get that. Thank You.

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Our teacher didn't teach us matrices either so I solved using elimination.

So basically, use the general formula for a Septic formula since that would use all 8 points and so be a fit for all points.

The work through elimination is really tedious but a friend of mine recommended excel for calculations.

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To find the quadratic function, you can simply type in the values of the fishing rod into a graphing calculator (which I am assuming you have!) into the table and hit the quadratic function button and it will give you the equation! The same goes for the cubic function, you just have to hit the cubic function button!

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can someone tell me what it means by suitable variables and parameters/constraints are?

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I also need help understanding the parameters/constraints. Im not sure what they mean by that.

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I asked my teacher about it and he said that they are limitations to the information that you gain....not quite sure how to figure out limitations to an equation...

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You have to make reference to the fact that you are dealing with a Fishing Rod and you can't add infinite guides as the Rod has to have a certain length. I'm doing the same portfolio and I guess that this is what they mean by limitations.

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I'm also doing the maths portfolio about fishing rods and i have no idea how to use technology to find a new function to fit the data?

Any ideas?

I need to give it in tommorow:(

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All I can say is rough times...

Mine's due tomorrow and it's already 1am, I'm not even halfway through. The worst is finding a polynomial function which passes through all of the data points... I've figured it out (with the help of this thread) but it's going to take me an age to actually do it.

Future reference: regardless of EE being due next week... or any other IB related excuse you can come up with-- start these ridiculous portfolios at least a week in advance.

one thing I forgot...

.... looks like this isn't getting handed in tomorrow

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Hello!. Im doing my math portfolio about fishing rods...first I'll give you the data.

guide # from tip- 1 2 3 4 5 6 7 8

distance from tip (cm)- 10 23 38 55 74 96 120 149

so what i have to do is..find a quadratic and cubic function through matrices for this data. I already did that..it is the next part I am confused about. It says find a polynomial function that passes through every data point and explain this choice of function and its reasonableness. C

Can anyone tell me how to find this polynomial function that passes through all the data points??

Thank You!

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First of all, we will not do your work for you. That means providing tips but nothing more than that. The tips will not be obvious but more or less illusive. So you have to work out most things yourself!

http://www.ibsurvival.com/forum/index.php?showtopic=4293

http://www.ibsurvival.com/forum/index.php?showtopic=3286

http://www.ibsurvival.com/forum/index.php?showtopic=4516

http://www.ibsurvival.com/forum/index.php?showtopic=4080

http://www.ibsurvival.com/forum/index.php?showtopic=3286

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Maybe I am not translating it correctly, but this is the type 2 hw, where they say that a fishing hook has 8 rings to hold the string. They give you the distance from the top of the fishing hook of each ringlet. You graph it and then you're supposed to find a quadratic and cubic function that goes the nearsest possible to the results. If it sounds familiar to you... please help!!! I am lost... I tried to use matrices to find the function but I think I am not doing it correctly. Any tips???

Edited by Merit Cullen

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I have a question about the best function for this data. I did all of the functions, but wouldn't the best one automatically be the one where we made it fit all of the data?

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To find the quadratic function, you can simply type in the values of the fishing rod into a graphing calculator (which I am assuming you have!) into the table and hit the quadratic function button and it will give you the equation! The same goes for the cubic function, you just have to hit the cubic function button!

With the calculator is it very easy, however the portfolio will lost all its purpose. I used the calculator and I got the exact values of a, b and c... the quadratic fuction fitted almost perfectly with the original graph, and then my teacher told me that I should be solving that in a manual manner. How is it exactly that you do a regression? I am stuck in that step.

Edited by Merit Cullen

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I have a question about the best function for this data. I did all of the functions, but wouldn't the best one automatically be the one where we made it fit all of the data?

Nope. If you don't know why, think hard.

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Hey,

I was the given the following points, .

Guide number (from tip) 1 2 3 4 5 6 7 8

Distance from the tip (cm) 10 23 38 55 75 96 120 149

part of the task asks me to find a polynomial function, which passes through each point. I was thinking of using a polynomial function to the power of 8, this way when I use matrices in order to find the equation I take all points into account, which will give me the most accurate model. Is this right? or is there another polynomial which models the data better.

Oh yea, before I forget, does anyone know what the function of guides are on a fishing rod. How does it affect the rod.

Thanks

Edited by hazemm

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