• 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. 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

Middle To find [X], we could use this formula: So: So, the Cubic Function is: 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:  . 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: 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.

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

This graph also increases more at the upper end to more closely match total braking distances for faster speeds. Speed [km/h] Stopping distance [m] 10 2.5 40 17 90 65 160 180 The linear equation y = x - 27 gives a totally impossible negative stopping distance for the answer for a speed of 10 km/h.

1. 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

2. Stopping Distances

speed is 0 the braking distance would be 0 as well therefore the y intercept will be a repeated root, this will mean that a=0 given the equation y=a(x+a)� y=a(x+ a)� =a(x+0)� =a(x)� y=ax� The points (80, 0.053) are chosen to substitute into the equation: y=ax� 0.053=a(80)� 0.053=a(6400)

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

+ B (9) + C (3) + D Equation 3: 74 = A (125) + B (25) + C (5) + D Equation 4: 149 = A (512) + B (64) + C (8) + D Now, to represent these equations in matrix form: Using the same methods to isolate the unknown variables

1. Population trends. The aim of this investigation is to find out more about different ...

Other countries' graphs would look more like a curve because the population in certain countries is going up very fast whilst in others it is either flat because it is approaching a decline or it is declining already. This particular concept of controlling the population isn't enrolled anywhere else and

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