FISHING RODS                                                                                                            SL TYPE II

This portfolio deals with Leo’s fishing rod which has an overall length of 230 cm together with eight guides that are placed a certain distance from the tip of the fishing rod as shown in Table 1. The task therefore is to develop mathematical models for the placement of the line guides on the fishing rod using quadratic, cubic, polynomial and one other free function. In addition, the quadratic model function that is developed will be further tested by applying it to Mark’s fishing rod which has an overall length of 300 cm and eight guides.

Table 1. Number of guides, with respective distances from the tip, on Leo’s fishing rod

Before beginning the process of formulating different mathematical models, it is possible to mention certain constrains as well as variables. The two variables in this modeling are

                   g= Guide number (from tip)    and      X= distance from tip (cm)

One constrain of the data presented in Table 1 is that there cannot be negative number of guides or negative distances from the tip. As a result the plotted graph is limited to the first quadrant as seen below from    Graph 1. Also the placement of the guides (distance) from the tip does not follow a regular pattern. This might make it difficult to achieve a function that satisfies all the points.

Graph 1. Plotted graph of number of guides and their respective distances from the tip on Leo’s fishing rod

it can also be seen from Graph 1 that the plotted data of Leo’s fishing rod begins from (1, 10) and goes up to (8,149) forming an ascending pattern. Thus this pattern indicates that the constant of the highest index on each of the model functions must be positive.

The next step involves finding a quadratic function that can be used as a model. Keeping in mind the general expression of a quadratic function, which is in the form of X = Ag² + Bg + C, it is possible to apply the matrix method to find the unknown variables A, B, C. In this case g will represent guide number while X will be equivalent to the distance from the tip.

Join now!

To find the three unknowns A, B, C the matrix method requires three equations to be formed. This can be achieved by choosing three guide lines with their respective distance and forming three equations by substituting them in the place of g and X. So I have chosen to take the first, last guides and their respective distances from the tip since they are the beginning and the ending points of the problem. The fourth guide was also chosen since it is a middle point. The equations are as follows:-

Equation 1: 10 = A (1) + B (1) + C

...

This is a preview of the whole essay