The aim of this coursework is to investigate which shape gives the largest enclosed area for a fixed perimeter of 1000m. In the coursework I will be investigate different shapes with different number of sides to see which encloses the largest area.
Jugdeesh Singh Maths Coursework 2003 Mrs Phull 0 Blue Aim The aim of this coursework is to investigate which shape gives the largest enclosed area for a fixed perimeter of 1000m. In the coursework I will be investigate different shapes with different number of sides to see which encloses the largest area. Three sided shape Triangle The only three sided shapes are triangle. There area depends on the length of each side. For the triangle I will be investigating which triangle with has the largest area by changing the lengths of each side and eventually getting the triangle with the largest area. Prediction: I predict that the triangle with equal sides will have the largest area. This is the equilateral triangle. First I will start by changing the length of the base. To calculate the area of the triangle I will be using the following formula /2 Base x Perpendicular Height E.g. /2 Base x Perpendicular Height (1/2 x 10m) x 15m = 5m x 15m = 75 m2 For some triangles the perpendicular height is not given, therefore we have to work the height out our selves. We will do this by applying Pythagoras' Theorem, which is. The square on the hypotenuse is equal to the sum of the squares on the other two sides. a2 + b2 = c2 E.g. At this point we do not know the perpendicular height so by using Pythagoras' Theorem we can work out the height, but first we must divide the
t shape t toal
T-Total Part 1 The aim of the investigation is to find out the relationship between the t-number and t-total. The t-number is the number in the t-shape, which is at the base of the T. The t-total is the sum of all numbers inside the t-shape. I will start my investigation by looking at t-shapes on a 9 by 9 grid. To solve the problem of finding the relationship between the t-number and t-total I will look at the information algebraically. I will firstly assign a letter to the t-number of the shape, this letter will be T. I will then express the rest of the numbers in the t-shape with the letter assigned to the t-number in the t-shape. Therefore it will give me a standard expression to apply to all the t-shapes. Where the expression is equal to the t-total. Examples ` The expression works for all t-shapes in a 9 by 9 grid. I will now simplify the expression into a simple formula. T + (T-9) + (T-17) + (T-18) + (T-19) = T-total 5T - 63 = T-total I will see if this new formula still works. 5 ? 20 - 63 = T- total 00 - 63 =T - total 37 = 37 5 ? 21 - 63 = T- total 05 - 63 = T - total 42 = 42 Part 2 I will now as part of my investigation use different grid sizes, transformations of the t-shape and investigate the relationship between both. Then I will see how the t-number and the t-total relate to the new factors. The smallest grid size can only be a 3 by 3 grid
Spoleèná dopravní politika.
Ekonomicko-správní fakulta Masarykovy univerzity Letecká doprava v EU Martin Chromec 15. listopadu 2003 SPOLECNÁ DOPRAVNÍ POLITIKA Spolecná dopravní politika patrí mezi ty politiky Evropské unie, které se staly soucástí procesu evropské integrace v dobe založení EHS v roce 1957, a ustanovení o této politice Spolecenství proto mužeme najít už v Rímské smlouve. Bylo k tomu nekolik závažných duvodu: * Ekonomická integrace a její postup rozširuje obchod mezi zememi, což si vyžaduje spolehlivé fungování dopravy. Tento sektor je klícovým odvetvím, což je potvrzováno také tím, že jeho príspevek k rustu hrubého domácího produktu (7-8 %) je vetší než príspevek zemedelství. * Doprava napomáhá volnému pohybu zboží a osob, což je predpoklad jednotného vnitrního trhu. V sektoru dopravy je treba vytvorit takové konkurencní podmínky, aby se dopravní náklady nestaly bariérou obchodu. * Dopravní sektor pohlcuje 40 % verejných investic v zemích Unie a jeho fungování ovlivnuje mnoho dalších sfér a hospodárských cinností. Citelné jsou dopady na regionální rozvoj, na situaci životního prostredí, na utvárení krajiny a plánování velkých aglomerací, na spotrebu energie aj. Postavení dopravního systému v zemích Spolecenství, má-li být vnitrní trh skutecne funkcní, vyžaduje integraci mezi zememi
Take ivy leaves from the North and South side of a hedge to come to the conclusion of what natural factors will effect the ivy leaves and why.
B3: WHAT AFFECTS THE LEAVE SIZE OF IVY? AIM: To take ivy leaves from the North and South side of a hedge to come to the conclusion of what natural factors will effect the ivy leaves and why. THEORY: The main factors that will affect the ivy leaves are how much sunlight the ivy gets, which I will be concentrating on in my investigation. Industrial factors would affect the ivy but the hedge we are taking them from this would not have any noticeable affects. PREDICTION: I predict that the ivy leaves that have more sunlight will be of a smaller size because if they get more sunlight they don't need as much energy that is taken from the sun. Meaning that they have a smaller leave surface area. Some people might think that if they get more sunlight they will be larger because it is easier to get energy from the sun and that it can grow bigger with the energy it gets from the sunlight. I also think that the ivy leaves that are in the shade most of or all the day will be larger because they do not get as much energy from the sun as the ones on the other side so it they do ever get sun light they will have to be bigger so they can take in as much energy as possible. Other factors which might affect my results is the kind of tree the ivy has grown up because of how much nutrients and minerals it is getting from the ground. I will prevent this from interfering by taking it from
Maths GCSE Courswork
Introduction A farmer has exactly 1000 metres of fencing and wants to fence off a plot of level land. She is not concerned about the shape of the plot, but it must have a perimeter of 1000m. So it could be or anything with a perimeter (or circumference) of 1000m. She wishes to fence off the plot of land which contains the maximum area. Investigate the shape, or shapes, that could be used to fence in the maximum area using exactly 1000 metres of fencing each time. Triangles I will start the investigation with triangles. The triangle is one of the basic shapes as it has only three sides to it. I will calculate the maximum areas for two types of triangles: > Equilateral Triangle > Isosceles Triangles An equilateral triangle is a triangle with all three of its sides the same length. An isosceles triangle is a triangle which has two of its sides the same length and the other is different. It is usually the base of an isosceles triangle which has a different length to the other two sides. Here are some of the formulae I will need to find the maximum areas of each triangle: > Area: base x height / 2 > Pythagoras Theorem: a2 + b2 = c2 > Heron's Formula: Equilateral Triangle This shape has a perimeter of 1000m: Perimeter = 333.33 + 333.33 + 333.33 = 1000m I will need to use the formula base x height/ 2 to calculate the area of triangle but in this case and every
Is there a connection between the size (surface area) of a leaf and the between the trunk to the road?
Surface Area of leaves Research question: Is there a connection between the size (surface area) of a leaf and the between the trunk to the road? Aim: To find a connection between the size(surface area) of the leaf and the distance between the trunk and the road. Hypothesis: Yes, I believe that the surface area of the leaves will increase the further away from the road they are. I believe that there are many reasons all due to different pollutions, caused by the cars driving on the road. I'm sure that it affects the leaves in other ways such as premature leaf drop, delayed maturity, plant growth, reproduction....but also the size will get affected. Cars are responsible for a tremendous amount of air pollution and wasted energy that affect humans and our environment. Acid rain, which is caused by air pollution, poisons our water as well as plants. The smoke and fumes from burning fossil fuels rise into the atmosphere and combine with the moisture in the air to form acids rain. The main chemicals here are sulphur dioxide and nitrogen oxides. The tree's roots absorb water from the ground, as a life source and when the acid rain, rains around that tree its life source is poisoned. The acid rain also harm the leaves as fog, acid fog, which the leaves will bath in, and that will make their protective waxy coating can, wear away. Which could lead to water loss, which makes the
Symmetry in Nature
Khan Salinder Snowflake . A snowflake is an example of rotational symmetry. When you rotate it 60 degrees you will find that the snowflake will still look the same as it did before it was rotated. Or you can say that it has six lines of symmetry. It can be folded in half in six different ways and both halves look the same. Snowflakes can have either hexagonal or triangular symmetry although the hexagonal snowflake is most common. Beehive A beehive has translational symmetry meaning that it has a repeating pattern of hexagons. Individual cells of a honeycomb have rotational symmetry they can be rotated one sixth of a turn and still look like the same as before the rotation. A honey comb is built slanted so that honey doesn't fall over. The hexagonal shape of a cell gives strong construction and also uses less building material. Seashell A seashell has reflectional or bilateral symmetry. A seashell only has one line of symmetry. It can be split in half so that one side is like a mirror reflection of the other side. The lines on a seashell are arranged in such a way that you see perfect symmetry. Animal Most animals are symmetrical in at least one way. For animals, symmetry is related to fitness. Symmetrical horses can run faster than non-symmetrical horses. There are two types of animals; radiata and bilateria. Radiata has radial symmetry. Bilateria
The Tetrahedron.
THE TETRAHEDRON Figure 1 Let each side of the tetrahedron (in blue) = s. The tetrahedron has 6 sides, 4 faces and 4 vertices. Here the base is marked out in gray: the triangle ABC. From The Equilateral Triangle we know that: Area ABC = (\/¯3 / 4)s². Now we need to get the height of the tetra = ED. E |\ | \ | \ ----\ D A figure 2 From The Equilateral Triangle we know that: DA = (1 / \/¯3)s. Now that we have DA, we can find ED, the height of the tetrahedron. We will call that h. h² = ED = EA² - DA² = s² - (1/3)s² = (2/3)s² h = ED = (\/¯2 / \/¯3)s So V(tetra) = 1/3 * area ABC * height(tetra) = 1/3 * (\/¯3 / 4)s² * (\/¯2 / \/¯3)s, V(tetra) = (\/¯2 / 12) s³ = (1 / 6\/¯2 )s³ = 0.11785113s³ What is the surface area of the tetrahedron? It is just the sum of the areas of its 4 faces. We know from above that the area of a face is (\/¯3 / 4)s². So the total surface area of the tetrahedron = \/¯3 s². We have found the volume of the tetra in relation to it's side. Since all 4 vertices of the tetra will fit inside a sphere, what is the relationship of the side of the tetrahedron to the radius of the enclosing sphere? Also, where is the centroid (the center of mass) of the tetrahedron? It's easier to see the radius of the enclosing sphere if we place the tetrahedron inside a
The fencing problem 5-6 pages
The Fencing Problem - Mathematics A farmer has exactly 1000 meters of fencing, with it she wishes to fence off a plot of level land. She is not concerned about the shape of the plot, but it must have a perimeter of 1000m. She wishes to fence off a plot of land, which contains the maximum area. Part One Using rectangles; I will investigate how she may obtain a maximum plot of land, using rectangles with a perimeter of 1000m. I will do this by using calculations to find the area of each different possible perimeter situation. For the first part of the investigation, I will calculate some possible areas for the plot of land, making sure the perimeter is exactly 1000m. For my first examination, I will try quadrilaterals. Side 1: 100m Side 2: 400m Side 1: 200m Side 2: 300m Side 1: 250m Side 2: 250m Side 1: 450m Side2: 50m Side 1: 350m Side2: 150m Side 1 Side 2 Area 00 m 400 m 40000 m2 250 m 250 m 62500 m2 300 m 200 m 60000 m2 350 m 50 m 52500 m2 450 m 50 m 22500 m2 The graph and the table indicate that when the width and the height of the regular quadrilateral have the least difference, the Area seems to be at its greatest. The statement is proven by the square. A square has all the sides the same, so the difference is the smallest possible value since it is zero. The area of the square is the
A Settlement Enquiry
Contents page Page 2- Aim Hypothesis Introduction Method Page 3- Area of Study Page 4- Results Analysis Page 5- Results Analysis Page 6- Results Analysis Page 7- Results Analysis Page 8- Results Analysis Page 9- Results Analysis Page 10- Results Analysis Page 11- Conclusion Evaluation A Settlement Enquiry Aim- To investigate the perceived effects of the building and operation of Terminal 5 on the quality of life and standard of living of different people. This means we are going to find out how the building of Terminal 5 will affect all types of peoples life in the surrounding areas. Hypothesis- Terminal 5 will benefit all different groups of local people equally. This is a geographical theory of what the affects of Terminal 5 will be. This theory is saying that Terminal 5 will affect all people living in the surrounding area the same. The objective of my study is to figure out if the hypothesis is right or wrong, I am going to do this by going to Staines and Ashford and Shepperton surveying all the different types of people (Male, female, adult, child, pensioner, disabled, working class, Family) I am going to ask different questions to find out how terminal 5 affects each group of people and compare the results. I'm also going to find other geographical theories to see if they agree with the hypothesis. Method I collected my data by
