Zachary-+Sydney+Bridge

=**Sydney Harbour Bridge**=



The Sydney Harbour bridge, located in Sydney, Australia. This bridge designed at 1857, 1932 is completed. It is nearby Sydney Opera House is an iconic image of both Sydney and Australia. It carries rail, vehicular, bicycle and pedestrian traffic between the Sydney central business district (CBD) and the North Shore.In 1857, Sydney Engineer Peter · Hande draws the first design drawing, spent 8 years by 1400 workers to build the bridge, the spend amounted to 13,500,000 Australian Dollar (to be approximately equal to 6,900,000 US dollars). This bridge is fixed by about 6,000,000 rivets, the bridge arch span is 503 meters, the roof is away from the sea level 139 meters. According to the Guinness World Records, it is the world's widest long-span bridge. It is also the fifth longest spanning-arch bridge in the world, and it is the tallest steel arch bridge, measuring 134 metres (440 ft) from top to water level. Until 1967 the Harbour Bridge was Sydney's tallest structure.The bridge was opened on Saturday March 19 1932. From 1998, the sydney bridge open to the public to climb up, the process bridge was safe. Groups of climbers are provided with protective clothing appropriate to the prevailing weather conditions and are given an orientation briefing before climbing.


 * = Sydney Harbour Bridge ||
 * ~ Official name ||< Sydney Harbour Bridge ||
 * ~ Carries ||< Trains, Motor vehicles, pedestrians and bicycles ||
 * ~ Crosses ||< Port Jackson ||
 * ~ Locale ||< Sydney, Australia ||
 * ~ Design ||< Through arch bridge ||
 * ~ Total length ||< 1,149 m (3,770 ft) ||
 * ~ Width ||< <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">49 m (161 ft) ||
 * ~ <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Height ||< <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">139 m (456 ft) ||
 * ~ <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Longest span ||< <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">503 m (1,650 ft) ||
 * ~ <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Clearance below ||< <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">49 m (161 ft) at mid-span ||
 * ~ <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Construction begin ||< <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">28 July 1923 ||
 * ~ <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Construction end ||< <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">19 January 1932 ||
 * ~ <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Opened ||< <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">19 March 1932 ||
 * ~ <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Opened ||< <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">19 March 1932 ||

<span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Graph: <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 14px; text-align: left; text-decoration: none;">I will let surface of the water be the //x//-axis. According to my research, the height of the bridge is 139m. So then, the point (0,139) is on my parabola, the vertex. The //y//-axis will be the at the middle of the bridge, and the span is 503 feet, I divided 503 by 2, so is 251.5. so the x-intersept is -251.5 and 251.5. I got all the point to get my equation. Here is the graph I created using Microsoft Excel. <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;"> <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Equation: <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">I used Microsoft Excel to find the equation for my parabola, got //y// = -0.0022x^2+139. This equation is in standard form. So here are the three forms for my equation: <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;"> <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Standard form: y=-0.0022x^2 +139 <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Vertex form: y-139=-0.0022(x)^2 <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">To find the vertex form of my parabola, first I have to find the vertex, which is (0.139). Since (h,k) is the vertex in the y-k=a(x-h)^2, and the a stay the same, -0.0022. so i got my vertex form. <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12px; text-align: left; text-decoration: none;">Factored form: y=-0.0022(x+251.5)(x-251.5) To find the factored form of my parabola, i need to know the x intercept, which are (-251.5,0) and (251.5,0). And the a stay the same.

=<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 16px; text-decoration: none; vertical-align: baseline;">Vertex: = The Vertex of my parabola is (0,139). Is the maximum of my parabola, the highest point. Also in the equation y-139=-0.0022(x)^2 the vertex is (h,t) which is (0,139). The vertex is the highest point of my parabola, or the height. The equation of axis symmetry is x=0. And we know it's open down, because the a in the equation is negative.

Y- intercept:
The y-intercept of my parabola is 139, my parabola cross the y-axis at 139. Or u can find it in the equation(standard form) y=-0.0022x^2+139. the 139 is the y- intercept. The y intercept is the highest point of my bridge.

Discriminant:
The standard of my parabola is y=-0.0022x^2 +139. The discriminant is square root of 0^2 - 4*-0.0022c*139. is 1.2232, my parabola have two solutions, is a irrational number. So the polynomial -0.0022x^2 +139 cannot be factored into linear factors with integer coefficients.

=**X intercept:**=

=
there are 2 **//x//-intercepts**, and that if we tried to use the quadratic formula to find the //x//-intercepts, there would be 2 solutions. I could also tell just by looking at the graph that there are 2 //x//-intercepts,(251.5,0)(-251.5,0). So my parabola cross the X axis twice.======

=Solutions:=

Now let's use the quadratic formula to find some **solutions**. Let's say that an iron rod was being replaced on the bridge, but we don't know exactly where. When the new rod arrives, we measure it to be 50 feet long. Where could this rod go? <span style="font-family: Arial,Helvetica,sans-serif;">Well, since the rod is 50 feet long, let's let //y// = 50 in our standard form equation.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px;">Then we have this equation: 50=-0.0022x^2+139
 * <span style="font-family: Arial,Helvetica,sans-serif;">In order to use the quadratic formula, we need the left side to be 0, so we will subtract 50 from both sides: 0 =-0.0022x^2+ 89.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Now we know our //a//, //b//, and //c// values: -0.0022, 0, and 89
 * <span style="font-family: Arial,Helvetica,sans-serif;">Let's use the quadratic formula to solve for //x//:
 * <span style="font-family: Arial,Helvetica,sans-serif;">-//b// +- (square root of b^2-4ac)over 2//a//
 * <span style="font-family: Arial,Helvetica,sans-serif;">//-b=0 b^2=0 4ac=-0.7832//
 * <span style="font-family: Arial,Helvetica,sans-serif;">//square root of 0.7832, which is almost 0.885//
 * <span style="font-family: Arial,Helvetica,sans-serif;">//0-0.885=-0.885 0+0.885=0.885//
 * <span style="font-family: Arial,Helvetica,sans-serif;">//0.885/-0.0044=-201.136 -0.885/-0.0044=201.136//
 * <span style="font-family: Arial,Helvetica,sans-serif;">The two solutions are about -201.136 and 201.136. So, the cable could go at one of those distances the middle of the bridge. Those are the two points at which the height of the cable will be 50 feet.
 * <span style="font-family: Arial,Helvetica,sans-serif;">The graph above shows our parabola with a line at //y// = 50. The places where this line crosses the parabola are the points (-201.136,50) and (201.136,50).

=Focus and Directrix:= In a standard form : y=-0.0022x^2 +139 Vertex: (-b/2a, (4ac-b²)/4a)= (0, 139)

Focus = (-b/2a, c+((1-b²)/4a) = (0, 25.36)

Directrix : y = c-(b²+1)/2a.= y=366.27

=Resources:=

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