This website uses cookies to ensure you have the best experience. Learn more

Sydney Harbour Bridge Investigation Essay

1520 words - 7 pages

Sydney Harbour Bridge – Directed Investigation – Quadratic functions
Aim: To find the multiple unknowns in the Sydney Harbour bridge
The Sydney Harbour Bridge will be used to investigate a diverse number of points in the structure such as the height and length. Quadratics will be used to solve the height of the bridge at different points on the x axis.
A quadratic is an equation constructed from information collected from a graph; this equation can also be used to produce a graph. Quadratics can be used to solve the problem dealt in this investigation as the Sydney Harbour Bridge is identified as a parabola shape. Only basic information is given about the bridge and the ...view middle of the document...

Therefore the highest point of the bridge will be:
Highest Point of the bridge:
Highest point of the bridge – the road on the pylon = x
182.25m – 50m = xm
182.25m – 50m = 132.25m
Therefore if a painter is painting at the highest point of the arch, the painter will be 132.25m above the road.

The quadratic function y=-1/100 x^2+27/10 x can be used to model the arc by implementing the information provided into the vertex form. The equation of the vertex form is y=〖a(x-h)〗^2+k. Completed, it shall look like =〖a(x-135)〗^2+182.25 , where a≠0. ‘a’can be identified by substituting into the formula a point from the bridge, in this example, it shall be (0, 0).

Therefore a=-1/100
Hence the equation of the quadratic is y=-1/100 〖(x-135)〗^2, if expanded, the equation will become:
y=-1/100 (x^2-270x+18225)+182.25
y=-1/100 x^2 27/10 x-182.25+182.25
Therefore y=-1/100 x^2+27/10 x
The expanded formula of the bridge in the vertex form is proven to be exactly the same as the one given, proving that the formula y=-1/100 x^2+27/10 x can be used to find the curve of the arc. The Sydney Harbour Bridge’s road lies 50m above sea level. The central steel arc of the bridge passes through two points on the road and then to the pylons. The points at which the arc meets the road can be solved using the graphing function of a graphics calculator.
The equation y=-1/100 x^2+27/10 x was inserted into the calculator (Figure 1) Values window was altered to see the full graph
Figure 1.

The graph is then drawn onto the calculator (Figure 2)
Figure 2

The x-cal function under the g-solve option was used to make the road. By enteringy=50, the points of the arc are shown. (Figure 3 and 4)

Figure 3 Figure 4

The results indicate that the two points where the arc meets the road are (20, 50) and (250, 50). Using these points, it is possible to determine the length of the road under the arch by using the formula x^2- x^1.
x^2- x^1
= 250-20
= 230m
Therefore the length of the road is 230m long.
Using this information, the amount of steel cable required to construct the supports can be identified. As stated, there are 19 vertical steel cables evenly spaced out which indicates that there are 20 spaces in between the arc and the road. The distance between each point can be calculated by dividing the total length of the road by the number of spaces in between the structure.
Length of road/number of spaces
= 230m/20
Defining that the space in between each steel cable is 11.5m, the distance of each cable can now be identified.

Other Essays Like Sydney Harbour Bridge Investigation

Assess The Contribution Of Christianity In Australia Towards Reconciliation, In The Past 25 Years

1656 words - 7 pages ). It is part of the process of reconciliation which has been happening since the 1990s. This contributes to the reconciliation process by allowing people to reflect on the past through prayer therefore allowing Australia to move forward into our future.The Corroboree 2000 'sorry' Sydney Harbour Bridge Walk on the 28th of May in 2000 is another example of Anglican contribution to the process of Reconciliation. It was a major National Event organized

Australia-simply the best Essay

705 words - 3 pages . A few amazing natural landmarks of Australia are the awe-inspiring Blue Mountains which have many scenic activities to offer, the gorgeous Hunter and Barossa valley where you can taste delicious wine, Kakadu National Park and the captivating GBR which is actually one of the 7 natural wonders of the world where you can snorkel and go on boat tours. Some manmade structures include the eye-catching Opera House, the busy Harbour Bridge, the world

Gold At The End Of The Rainbow

1274 words - 6 pages Sydney, Australia1995, age 18I'm on a bus staring at the ocean as I go over the Harbour Bridge, the sun's reflection on the water is nothing like I have ever seen before. Boats crossing the ocean give me many memories; I look away, and see tall skyscrapers everywhere, buildings towering over me, shadowing me from the sun's bright light. I look up at the beams above and my eyes follow the girders. I can see the Australian flag above me and I know

The Separation Of Capital Ownership And Control

1577 words - 7 pages The argument of whether the separation of capital ownership and control is an efficient form of organization has constantly been a controversial issue. The criticism whether the controllers’ act is in the best interest of the owners’ wills never end as long as hired managers operate management. As the number of public companies has been increasing over the course of this century, meanwhile the American style of contact based corporation has

The Versatility And Flexibility Of OLED's

1014 words - 5 pages In April 1, 2002, organic light emitting diodes gain rise in the scientific community with their published, more practical form at Ames Laboratory. “Scientists at the U.S. Department of Energy's Ames Laboratory, in collaboration with scientists at the University of Michigan, Ann Arbor, have developed and demonstrated a novel, fluorescence-based chemical sensor that is more compact, versatile and less expensive than existing technology of its

Comparing The Moral Virtues Of Antony And Julian The Apostate

1103 words - 5 pages Roman emperor Julian the Apostate and Christian leader Antony both exhibited many qualities of character during their existence. Both of them led very distinctive lives although shared several ethical values. Book 25 of “The Later Roman Empire” and the book “Early Christian Lives” show concrete evidence of this. In the following essay, I will argue how both leaders’ lives were devoted to their religious beliefs and their mutual cardinal virtues

Living In A Cashless Society

1637 words - 7 pages Money in a traditional sense no longer exists. Money is becoming much of a concept than a physical material, and most ordinary bitter have not see the reality of the switch. People today are using credit and debit cards on a regular basis and in everyday situations such as meal purchased at fast food, highway tolls, clothing, groceries, gas stations, etc. all of these means of systems could be regarded as a cashless society or world. The question

The French And Indian War: The "Real" First World War

1955 words - 8 pages The Seven Years War, or more commonly referred to as “The French and Indian War”, has been called the true First World War. In this book The French and Indian War: Deciding the Fate of North America, the author and historian Walter R. Borneman paints a detailed and elaborate picture that justifies the claim of it being the first true war of global proportions. If ever there truly was a climax to the never ending feud of the European powers

Is The Use Of Animals In Medical Research A Necessary Measure?

1513 words - 7 pages Throughout history, animals have been used in experiments to test product safety and obtain medical knowledge that benefits both humans and animals alike. Every year there are numerous medical breakthroughs, such as medications and surgical instruments, which are tested on animals to insure their safety before they are deemed acceptable for human use. Even though the results of the experiments saved millions of human lives, they are also

Education And The Evolving Job Market

2363 words - 10 pages The lives of students today are changing. They are preparing for lives and jobs that have never before existed. If teachers hope to have a significant and worthwhile impact on these quickly changing lives, they must change the way they think, prepare, and instruct our future generations. Children cannot afford to have teachers who remain stagnant in their methods and ideals. Students crave instructors that are willing to allow them to tap

Young And Relentless

1737 words - 7 pages There are numerous influences that can be responsible of teenager’s behaviors and attitude as they develop. One factor that is important to these behaviors is parental figures being over involved or uninvolved in their children’s lives. Many of these effects include illegal substance abuse, rising sexual activity, underage alcohol consumption, and tobacco use. Studies show parental participation plays a key role in the characteristics developed

Related Papers

The Construction Of The Syndey Harbour Bridge

343 words - 2 pages CONSTRUCTION and planning of the BRIDGE.Work on the bridgeConstruction on the bridge began at both ends and at the same time. It was gradually built inwards across the harbour, where it meet in the middle about 5 years later. While the light and heavy workshops work were being built at North Sydney, work had already begun on the approach spans (five at each end of the bridge) and all supported on pairs of concrete piers.The man who prepared the

Late Ferry Comentary Essay

961 words - 4 pages Late Ferry, a quatrain poem written by Robert Gray, concerns the poet, observing the long sight of a ferry leaving the bay, going towards the city as it wades under the Harbour Bridge in Sydney, fading away into the night. The poet has made the ferry the main idea of the poet, vividly describing the different effects of lighting on and around the ferry. In this poem, Robert Gray has portrayed the image of the light effect on the ferry in each

The New Land Essay

623 words - 3 pages of the world! Well, it sure seemed the same, at first. The minutest of differences seemed to make eating there all the more enjoyable, such as the small packets of Vegemite next to the ketchup and mustard. We quickly finished and briskly walked five or six blocks until we found the Sydney Harbour Bridge. We could not simply look at it, so we climbed it! The sight of cars zooming underneath us was breathtaking! After 12 hours of wonder, we ate

Research In Motion Essay

1429 words - 6 pages North Sydney, New South Wales, Australia in February 2009. Just across the Harbour Bridge, ten minutes from the Sydney CBD, the new RIM offices were formally unveiled by Mr. Thomas A. MacDonald, Consul General of Canada, at a ceremony attended by dignitaries from the New South Wales Government and North Sydney Council, as well as RIM’s partners and customers. The new office features training facilities, a research and development centre, a