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

Fishing Rods Portfolio. Leo has a fishing rod with an overall length of 230 cm. The diagram shows a fishing rod with eight guides, plus a guide at the tip of the rod.

Extracts from this document...

Introduction

FISHING RODS

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 task, you will develop a mathematical model for the placement of line guides on a fishing rod.

Leo has a fishing rod with an overall length of 230 cm. The diagram shows a fishing rod with eight guides, plus a guide at the tip of the rod.

image00.png

The table below shown below gives the distances for each of the line guides from the tip of his 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


The distance of each guide from the tip of the fishing rod is measured in cm. The
x value, or the independent variable, is the guide number, and the y value, or the dependent variable, is the distance from tip. Only positive numbers can fit this scenario, because a fishing rod cannot have negative lengths. We can even further limit the domain, because the fishing rod only has 8 guides, so x

...read more.

Middle

image19.png

To find [X], we could use this formula:

image03.png

So:

image20.png

So, the Cubic Function is:

image07.png

In order to graph accurately, I decided to only graph the quadratic and cubic functions only with the domain of the original data points. This domain is: image22.pngimage22.png . 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. The table loos like this:

Table 2: Distances of guide numbers from tips calculated from Quadratic and Cubic Functions

Guide number (from tip)

1

2

3

4

5

6

7

8

Distance from tip (cm)

10

23

38

55

74

95

118

143

The graph illustrating the original data points and the model functions looks like this:image23.png

The quadratic and cubic functions that I found were the same in the first quadrant. Because the guide number cannot be negative, I chose to only compare these two in the first quadrant. If we looked at the values in the other quadrants, they would be different.

...read more.

Conclusion

th guide was added, then a total of 10 guides would be on the rod including the guide at the tip of the rod.

Mark’s fishing rod:

Guide number (from tip)

1

2

3

4

5

6

7

8

Distance from tip (cm)

10

22

34

48

64

81

102

124

My quadratic model does not quite fit this data set because there are some differences in the y value. Looking at the graph of the data, it seems that it fits the model but when looking at the equation from the graph, we can see that it is slightly different:

image39.png

The r2 value for this graph is 0.998, while for my quadratic model it is 1. I would need to change the equation that I obtained. To do this I could use the matrix method, but instead use these three data points: (1, 10), (2, 22), (3, 34) Using these points in the matrix method, I could calculate the new quadratic model, and then compare it to the original data points. My equation would also change once I do this. The new values for a, b, c, would be 0, 12, -2 respectively. So the new quadratic model that would fit this data is:         

image40.png

...read more.

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

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Investigating Quadratic functions

    So if a is positive and less than 1, it is moving closer to the x-axis. Then, I made another graph where a (the coefficient) is a negative number to investigate how it affects the graph. Now, we could see a drastic change compared to the 2 previous graphs.

  2. Fishing Rods

    inverse of Matrix A and multiply it with Matrix B to get Matrix C, using the graphics calculator. Matrix C will contain the a,b,c and d values of the quadratic equation in a 4x1 Matrix. x = the quadratic equation in a 3 Matrix Therefore the respective values of the

  1. Stopping distances portfolio. In this task, we may develop individual functions that model the ...

    This graph can be used to tell how significant the braking distance is as it clearly shows the difference between the stopping distance and the thinking distance. Additional data - Model fit Speed (km/h) Overall stopping distance (m) 10 2.5 40 17 90 65 160 180 If two of the

  2. A logistic model

    The interval of calculation is 1 year. Year Population Year Population 1 1.0?104 11 7.07?104 2 2.9?104 12 4.19?104 3 6.32?104 13 7.07?104 4 5.56?104 14 4.19?104 5 6.49?104 15 7.07?104 6 5.28?104 16 4.19?104 7 6.73?104 17 7.07?104 8 4.87?104 18 4.19?104 9 6.96?104 19 7.07?104 10 4.42?104 20 4.19?104 Estimated magnitude of population of fish

  1. fishing rods portfolio (SL maths)This portfolio deals with Leo's fishing rod which has an ...

    First I will find the pattern in the sequence. To find the pattern, I will list the numbers, and find the differences for each pair of numbers. That is, I will subtract the numbers in pairs (the first from the second, the second from the third, and so on), like

  2. Fishing Rods Internal Assessment

    To find this median, I went three up from the start guide and landed on guide # 4. I tried going up by a sequence of four, which would have result in guide # 5 as the median, but after I went up 4 more, it landed on guide number #9, which does not exist.

  1. SL Math IA: Fishing Rods

    Since the length of the rod is finite (230cm) then the number of guides is known to be finite. Domain = , where n is the finite value that represents the maximum number of guides that would fit on the rod. Dependent Variable: Let y represent the distance of each guide from the tip of the rod in centimetres.

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

    = = -0.33 In this case, for every 1% increase in price the quantity demanded will fall by only -0.33% meaning that the quantity demanded is not very sensitive to price changes therefore it is inelastic. Calculating Elasticity for Quarter 2.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work