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Essays in Core & Pure Mathematics category
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Design and construction of circuits to solve problems.
... far to much money and time so we can simplify this so we can use the least amount of gates possible to keep the cost down but not the time so if I create the Boolean equation for when the ...
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Design, make and test a Sundial.
... must tilt at the angle of the latitude at the location. Although a sundial seems like a simple device for measuring time, it is not. One cannot simply look at the shadow and find the time. Firstly the sundial will show ...
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Determine an appropriate parabolic model that fits the data I collected of whirlybird wing length vs. time, doing so by using first principles.
... in a parabolic shape well, and these are the first point and the last point. I decided to remove these from my final data. The result is shown below. Length (cm) Time (s) 14 1.29 12 1.7 10 2.27 8 2.33 6 2.1 4 1.65 2 0.99 Function: Y= a(X-b)2+c I will be referring to the letters in this ...
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Estimate a consumption function for the UK economy explaining the economic theory and statistical techniques you have used.
... on the basis of some econometric tests. Keynes, John Maynard introduced consumption function in 1936. In The General Theory of Employment Interest and Money, Keynes pointed out that " We should therefore define what shall call the propensity to consume as ...
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Estimate a consumption function for the UK economy explaining the economic theory and statistical techniques you have used.
... From this he derived the simplest of consumption functions: Where consumption, C, is equal to autonomous consumption, c0, plus disposable income, Y, multiplied by the marginal propensity to consume, c1. The marginal propensity to consume is 'the proportion of a rise ...
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Estimate a consumption function for the UK economy explaining the statistical techniques you have used.
... are responsible for each type of expenditure and therefore they must have different determinants. (William E.Griffiths, R, Carer Hill, George G. Judge, (1993) Learning and Practicing Econometrics, 1993 by John Wiley & Sons, Inc, page 261) Consumption is the most ...
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Examining, analysing and comparing three different ways in which to find the roots to an equation.
... linear interpolation. However, I will be using the decimal search method. With decimal search, you first draw the graph of the curve that is to be investigated, and look for where the curve passes through the x axis, as these ...
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Experimentally calculating the wavelength of an He-Ne laser by means of diffraction gratings
... second order fringes, and so on. When light is passed through two slits, the central bright beam of light is created through constructive interference of the light through the two slits. In the case of constructive interference: dsin? = m?, where ...
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Explore and review the basic physics of how different things relate to one another.
... errors: random and systematic. These errors can have different impacts on the analysis of the results depending on the regression curve that best fits the data collected. This part of the lab will look at these impacts. The last part of ...
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Find methods of solving equations, which can't be solved algebraically.
... the roots for the function x3-3x2+1. The roots, which are to be, identified lie within the intervals [0,1], [-1,0] and [2,3] as shown on the below graph. The root can now be found using the above method as shown below in ...
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Finding one root of an equation by a change of sign method, to 4 figures.
... and bn are. The diagram below shows how the bisection method works. The blue and green lines represent the original lower and upper bounds. The purple lines represent the average value of the lower and upper bounds. These get closer to ...
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Fixed-Point Iteration
... iteration: f(3.3125) = 1.25(3.3125) -2 = 2.140625 Fourth iteration: f(2.140625) = 1.25(2.140625) -2 = 0.67578125 - Copied axes located on page C. Iterations of f(x) = 1.25x - 2 from the right side: First "guess": 10 F(10) = 1.25(10) -2 = 10.5 Second iteration: F(10.5) ...
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GCSE Math Coursework: Triminoes
... until I feel I have used enough numbers. 4. On each set of data I will record the largest number used, the sum of all the cards added together, and the number of cards used. 5. I will then make a results ...
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Graph Original of Equation y=3x^5-3x+1
... to calculate the value of the function at root 3. Below is a zoomed-in view of root 3. This reading says 'Overflow'. This means that it can not be calculated using this method. As seen and stated ...
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Growing Squares
... be: Un = (n - 1) 2 + n2 (n - 1)(n - 1) + n2 n2 - n - n - n + 1 + n Un = 2n2 - 2n + 1 This is correct. Growing Hexagons I will now repeat my investigation, and change ...
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Henna Night
... red and gold coloured embroidery in the middle. She looked like a model posing. At a Henna function it is traditional for the bride to wear the colour yellow or golden. The drole of the drum was getting louder and ...
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In maths equations can be solved using various methods. A very common and efficient method in solving equations is algebraically. But not all equations can be solved algebraically; these equations must be solved using numeric methods.
... crosses the x-axis and changes its sign from negative ( - ) to positive ( + ), and at the interval [a , b] f(x) curve crosses the x-axis changing its sign from positive ( + ) to negative ( ...
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In the photo by Ernest Withers the first thing that jumps out at you is a sign that says no white people allowed in the zoo.
... or there weren't many people in the park that day at all. When wondering that I couldn't help but to think maybe there weren't many people in the park because they didn't want to be where they weren't wanted on ...
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In this coursework I am going to investigate the relationship between the orbital period and the distance of the planet from the sun. Assume that this relationship is a power law of the form: T = KR^n
... in the formula * Log R as the as the base of the exponent n Log T = log K + n log R is the same as Y = c + mx I've calculated the log of R and T in ...
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In this coursework, I am going to solve equations by using the Numerical Methods. Numerical methods are used to solve equation that cannot be solved algebraically
... point at which the curve crosses x-axis is the root. Once an interval where f(x) changes sign then the root must be in the interval. Decimal search: The reason why I choose decimal search is because that is the easiest to ...
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In this investigation I aim to investigate three methods of finding the roots to equations and then compare them. I aim to be able to use fully and understand all three techniques.
... values of x against values of f(x). This will produce a line that will be continuous (will not be using any discontinuous equations in this project). If the function has roots (not all functions have roots e.g. f(x)=x2+5) then you ...
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In this piece of coursework, I will use three different methods (Change of Sign, Newton-Raphson, and the Rearrangement Method) to find the roots of a series of different equations. The number of roots found differs from method to method.
... change of sign at this point. A change of sign is required for this method to work, as it is the basis from which a root is found. The graph of the function is displayed on page 5. An attempt to solve ...
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Information Technology Development Cycle Diary
... second row of the invoice table would be blank. ...
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Investigate the number of winning lines in the game of connect 4.
... connect. For example 2, 3 or 5. Connect 4 Firstly I will do a box with the width constant as 5 and I will change the height. Hx5 Box Any Number=N Connects=C Height= H Width =W Hx5 ...
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Investigate the relationships between the lengths of the 3 sides of the right angled triangles and the perimeters and areas of these triangles.
... and in geometric sequence. 4 , 12 , 24 , 40 8 , 12 , 16 4 , 4 5 , 13 , 25 , 41 8 , 12 , 16 4 , 4 Length of shortest side: Term no 1 2 3 4 5 Sequence 3 5 7 9 11 Sequence 2n 1 4 6 8 10 Sequence 1 1 1 1 1 2n + 1 ...