• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Fishing Rods Portfolio

Extracts from this document...

Introduction

International Baccalaureate

IB Math Standard Level

Portfolio

Type II

Fishing Rods

Sagar Sood

IB Math SL

Ms. Ridley

Due: 15th Oct, 09

Introduction

A fishing rod requires guides for the line so that it does not tangle and so that the line casts easily and efficiently.

In this investigation, a mathematical model will be developed that will calculate functions from the given data points of two fishing rods of lengths 230cm and 300cm. This model will further determine the placement of the line guides on the fishing rod.

In mathematics, a function is a relation between a given set of elements and another set of elements that associate with each other, algebraically and graphically. In this investigation, an approach using matrices will be attempted to calculate functions for the given data and then be plotted to verify the results. Furthermore, there will be an effective use of technology so as to minimize errors and flaws.

Variable

Let x= Guide number (from tip)

Let y= Distance from tip (cm)

Middle Let  be equal to      Hence, the equation is  The graph below shows the calculated quadratic equation that goes through the data points of Table 2

Figure 3   This model is quite accurate as the curve of the function passes through all the points. Although the curve does not pass through the center of the data points on the graph.

One possible reason for flaw could be that only four data points were used to calculate the function, even though that was the only possibility. If there was a way to use all eight data points to calculate the function, the curve would go through all data points on the graph hence being more accurate.  To calculate this equation, the first, third, sixth and eighth data points will be used.

 Guide No. (from tip) Distance from tip (cm) 1 10 3 38 6 96 8 149

Table 3

Conclusion          Adding a ninth guide to the rod would mean that the rod would be longer. The positive effect of adding a ninth guide to a longer rod would be that it would ensure that the line does not become tangled.

The table below shows the given set of data, which is Mark’s fishing rod that h as a 300cm line.

Table

 Guide No. (from tip) Distance from tip (cm) 1 10 2 22 3 34 4 48 5 64 6 81 7 102 8 124

The graph below shows the calculated quadratic function passing through the second set of data points (Mark’s fishing rod) from Table It can be clearly seen that the quadratic function does not fit this new set of data. In order for that model to fit this new data, an enhanced quadratic would need to be recalculated using these new data points i.e. the same approach of matrices will be required. One limitation with this model is that it disregards the length of the fishing rod. A fishing rod with a different length would result in different data points. Different data points, would result in a new curve, which the original model does not fit.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related International Baccalaureate Maths essays

1. ## Extended Essay- Math

~ ï¿½'Ä¸(ï¿½ ï¿½ï¿½(ï¿½ï¿½-;8ï¿½7^ï¿½3/4ï¿½0ï¿½ï¿½ï¿½ï¿½ ;xZ %&'0Bï¿½Oï¿½ Bäï¿½'#ï¿½(c)0ï¿½!Xï¿½/ï¿½ï¿½Gï¿½#--ï¿½ï¿½ï¿½,ï¿½orï¿½ï¿½ S(3/4ï¿½È¤Pï¿½ï¿½ï¿½ï¿½ï¿½ 2(tm)ØFIï¿½ï¿½ï¿½ï¿½"ï¿½ï¿½#ï¿½ï¿½ï¿½EFZÚ0ï¿½Û°"ï¿½ï¿½?ï¿½ï¿½ ï¿½ï¿½Fî­¨ï¿½_6Cx ÎgG"ï¿½ï¿½ï¿½#|mwï¿½ï¿½ucLï¿½ï¿½...ï¿½ï¿½ w0ï¿½ï¿½ ï¿½ï¿½8;ï¿½ï¿½ï¿½ï¿½)ï¿½Fï¿½ï¿½Eï¿½ï¿½ï¿½&ï¿½ ï¿½Xï¿½Ø ï¿½_ï¿½ï¿½wpFï¿½0ï¿½{bMï¿½xï¿½>%ï¿½ï¿½oï¿½oï¿½ï¿½ï¿½a8ï¿½jjï¿½ &Sï¿½,vï¿½bFl.iï¿½ï¿½2ï¿½ ï¿½@ï¿½ i#ï¿½ ï¿½Fï¿½ï¿½ï¿½V ï¿½"ï¿½ï¿½ÅPï¿½ï¿½ï¿½ÈHdL\$ï¿½ï¿½ï¿½ï¿½3ï¿½_ï¿½_ãqï¿½)'ï¿½!1/4ï¿½ï¿½{6~dï¿½?2(c)ï¿½ï¿½ï¿½dï¿½ï¿½3/4ï¿½b1/2(c)ï¿½ï¿½ï¿½Ç1/4_ï¿½ï¿½_ï¿½ï¿½-ï¿½ï¿½Zï¿½ï¿½VAï¿½uÐºh ï¿½ï¿½fEsï¿½2Zmï¿½ï¿½Ck!}ï¿½1/4G\$ ï¿½ï¿½qG~ï¿½ï¿½ï¿½"ï¿½ï¿½dM-`ï¿½wï¿½ï¿½ï¿½.ï¿½ï¿½(c)ï¿½<ï¿½/ uxï¿½}ï¿½ï¿½\$!ï¿½ï¿½È¨ï¿½jPpï¿½ï¿½rï¿½ï¿½-"ï¿½dï¿½ï¿½ï¿½vï¿½ï¿½ï¿½\;1ë·²_~ï¿½"ï¿½ï¿½Ñ¿h!(c)ï¿½ï¿½!ï¿½xï¿½_ï¿½ï¿½qï¿½^!ï¿½"ï¿½_4ï¿½ï¿½;ï¿½ï¿½ï¿½ï¿½"ï¿½[-ï¿½\$ï¿½#-ï¿½xï¿½GÞ³"[email protected]ï¿½Kï¿½ 8wï¿½ ï¿½`ï¿½ [email protected]"ï¿½ ï¿½@.ï¿½ ï¿½ PNï¿½Pï¿½ï¿½ï¿½ nï¿½^p <#ï¿½)ï¿½S`|ï¿½ï¿½;Xï¿½ ' &ï¿½ï¿½D )HRï¿½t!ï¿½rï¿½ï¿½!(ï¿½ï¿½ï¿½1/2ï¿½>(*"* ï¿½Ptï¿½"zï¿½{ï¿½cï¿½9ï¿½ï¿½ï¿½-ï¿½ï¿½0 ï¿½...(tm)a-X-ï¿½ï¿½aï¿½ vï¿½1/2ï¿½ 8Nï¿½sï¿½ï¿½ (r)ï¿½ï¿½ï¿½6ï¿½~?...ï¿½ï¿½Oï¿½ ï¿½(V"Jï¿½ï¿½2Bï¿½By Q1ï¿½tï¿½!T ï¿½uï¿½...ï¿½ï¿½CMï¿½Pkh,ï¿½ Í-Aï¿½ï¿½ï¿½CGï¿½ï¿½Ñï¿½ï¿½ztï¿½=ï¿½~ï¿½^DoaHnï¿½Fcï¿½qï¿½a1ï¿½ï¿½Lï¿½3ï¿½yï¿½(tm)ï¿½|ï¿½bï¿½ï¿½X1ï¿½ï¿½ï¿½ ï¿½ï¿½bc"ï¿½-ï¿½-ï¿½cï¿½4vï¿½ï¿½qï¿½p:ï¿½]8 .

2. ## A logistic model

This could be solved by recurring to an analysis of the discriminant of the quadratic equation: ?5 2 (?1?10 )(un?1 ) ? 0.6(un?1 ) ? H ? 0 ? un?1 ? ?0.6 ? 0.62 ? 4(?1?10?5 )(?H ) 2(?1? 10?5 )

1. ## Creating a logistic model

1.687056965 14 70720.67479 0.592614358 15 41910.08729 1.687416683 16 70719.78048 0.592648342 17 41911.96064 1.687345496 18 70719.958 0.592641596 19 41911.58878 1.687359626 20 70719.92278 0.592642934 An estimate for the logistic function would be : y = When we round this off, it becomes approximately: y = Although the rounding off errors were relatively large this time, (i.e.

2. ## Fishing Rods Portfolio. Leo has a fishing rod with an overall length of 230 ...

This domain is: . Using this domain, I can determine the distances of the guides from the tip (cm) of the fishing rod. To find the y values for this domain, on Excel, I created a formula that would allow me to plug in the x values and find the y values.

1. ## Fishing Rods

Using the first 3 data points, 3 equations can be formed: The three equations can then be transformed to form a 3 x 3 and a 3 x 1 matrix with the corresponding coefficients: We will call this first matrix - Matrix A We will call the second matrix -

2. ## Math Portfolio: trigonometry investigation (circle trig)

Highlighted means 0 and number with E will be just defined as undefined values. This later was verified by TI-83 plus calculator. Once again, upon the analysis of the above table of values, the values of sin? are found to have a specific range; no smaller than -1 and no bigger than 1 (-1?sin??1).

1. ## SL Math IA: Fishing Rods

The placement of these will depend on the number of guides as well as the length of the rod. Companies design mathematical equations to determine the optimal placement of the guides on a rod. Poor guide placement would likely cause for poor fishing quality, dissatisfied customers and thus a less successful company.

2. ## In this investigation, I will be modeling the revenue (income) that a firm can ...

+ 4 P= -Q + 6 We can test its validity by inserting other points to ensure that these linear demand equations are correct, If we get the same equation we then know that our equations are accurate. Quarter 2 3 4 Values of P & Q Gradient 1. 2. • Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to 