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Unformatted text preview: Distance from Tip (cm) Guide Number (from tip) Let A represent, let B represent and let X represent . = A X B A- 1 = A X A- 1 B = I X A- 1 B = X A- 1 . B Guide Number (from Tip) Distance from the Tip (cm) Graph Distance from the Tip (cm) Graph Guide Number (from Tip) Distance from the Tip (cm) Guide Number (from tip) Graph Polynomial Function of the Fishing Rod Distance from the tip (cm) Graph Quartic Function of Fishing Rod Guide Number (from tip) Graph 6 Math Portfolio Type II: Fishing Rods Introduction A fishing rod requires guides for the line so that the line does not tangle, and that the line casts easily and efficiently. In this task we will be exploring and developing a mathematical model for the placement of line guides on a fishing rod. Aim: In this Type II Math Portfolio we will be developing a model function for placing line guides on a fishing rod. This fishing rod requires guides for the line so that it does not tangle and that the line casts easily and efficiently. In order to find these functions, we will need to interpret the data points given and plot them. In the first situation we have Leos fishing rod. Leos fishing rod is 230 cm in length has eight guides, and an additional guide on the tip of the fishing rod. Using the given information about the number of guides and their length from the tip we will be able to determine and identify variable suitable to the situation and define certain parameters and constraints. We will then explore different polynomial functions in relation to the data concerning the fishing rod and the guides. This investigation will include the general form of a quadratic, cubic, quadric and an 8 th degree polynomial. The data set will then be applied to these functions to find a common model function which fits the data points. Each function we find will have to be assessed reasonably and mathematically. In addition to the different model functions acquired through this investigation, it is then essential to comment on the reasonableness and differences of these models and how they compare to the data set. After calculating the different functions suitable for the data set we will then discuss which one of them best describes the situation, and then using our quadratic function decide whether or not we could place a ninth guide, as well as the implications of the addition of a ninth guide. After Leos fishing rod we will consider Marks fishing rod and determine if the derived quadratic function models the new data set. 1. Modelling the Data 1 The table provided shows us the distances for each of the line guide from the tip of the fishing rod. Table1: Leos Fishing Rod Guide number (from tip) 1 2 3 4 5 6 7 8 Distance from tip (cm) 10 23 38 55 74 96 120 149 A graph depicting the data set: Guide Number versus the Distance from the Tip....
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- Spring '10