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Fishing rods type 2 portfolio

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Introduction

Math Portfolio Type II: Fishing Rods

Introduction

A fishing rod can only work well if there are numerous "guides" along the blank of the rod to guide the fishing lines. Having numerous "guides" along the blank of the rod provides greater castability, greater hooking power, and most importantly prevents the line from twisting and tangling up. A fishing rod without the "guides" would have little use since the lines will most likely tangled up before it even enters the water.

In this portfolio, I would have to develop a mathematical model for the effective placement of line guides on a fishing rod. A mathematical model for the placement of line guides on a fishing rod has many applications in the real world. One of the main benefits would be helping fishing rod companies in placing their "guides" in the most optimal positions so the rod can function better than their competitors. The fishing rod that I would have to develop a model on would be Leo's fishing rod. Leo's fishing rod is 230cm long and has eight guides along it with a ninth at the very tip of the rod. The table below

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Middle

b = -3a + 13

Now substitute the value of B into the B variable in Eq.5 and simplify the entire equation until the variable A is found.

8a+2(-3a+13)+10= 38

8a + (-6a+26) +10= 38

8a-6a=38-10-26

2a =2

a=1

Now take the value of A and substitute it into an equation with 3 variables like Eq.4 to determine the value of B

3( 1 ) + b + 10 = 23

3 + b = 13

b = 10

Lastly substitute the value of both A and B back into one of the original equations like Eq. 1 to determine the value of C

a + b 4- c = 10 1 + 10 + c = 10 c - 10 - 10 - 1

In the end, the final values of the coefficients determined with the 3 equations are:

A= l B=10 C= -1

The model equation for this situation based on the 3 sets of points and equations is

y = x2+ 10x- 1

Graph 2: The quadratic relationship between the # of guides and the distance from tip (cm)

image01.png

Part C: Determining a cubic function that fits the situation

A cubic function has a standard form of ax3+ bx2+ cx + d and coefficients of a, b, c, and d where a must never be 0. The cubic function for the situation was determined using Excel 2007 by creating a cubic trend line.

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Conclusion

By using my original quadratic model to model Mark's rod it can be seen that my model does have many limitations. One of the limitations it has would be the fact that there are many different forms of rods and rods blanks out there in the world. That means that each individual rod would have to have "guides" that are optimized for its particular blank." On top of that, my model doesn't take into account the numerous parts that a fish rod has like the grips, handles, reel, and reel seats. This means that some of the placement of guides may not be possible due to the presence of other parts of the rod in that area. Lastly, this quadratic model again has the limitation of not having a y-intersect at 0 and instead at. This means it can never truly model the guide at the tip of the rod.

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Fishing Rods: Guides, (n.d.). Live Outdoors. Retrieved April 14, 2012, from www.iiveoutdoors.com/fishing/articles/166909-fishing-rods-guides

rings, u. s., profile, a. I., & Concept, F. N. (n.d.). Optimum Placement, Number & Size of Guides Maximises Rod Performance. Fishing tackle & fishing tackle components - Hopkins & Holloway Limited. Retrieved April 14, 2012, from '" Fishing Rods: Guides, (n.d.). Live Outdoors. Retrieved April 14, 2012, from www.liveoutdoors.com/fishing/articles/166909-fishing-rods-guides


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