Question

the towers supporting the cable of a suspension bring are 1200 meters apart and 170 meters above the bridge it support.suppose the cable hangs, following the sharp of a parabola,with it's lowest point 20 meters above the bridge.how high is the cable 120 meters away from the tower?​

Answer 1

Answer:

The towers supporting the cable of suspension bridge are 1200m apart and 170m above the bridge it supports.

Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.

How high is the cable 120m away from a tower? Sketch the graph.

:

lets have the bridged centered at the origin

Three points are needed on the parabola

x = 0, y = 20

x = -600, y = 170

x = +600, y = 170

using the form ax^2 + bx + c = y, we know that c=20

x=-600, y = 170 and x =+600, y = 170; write two equations

-600^2a - 600b + 20 = 170

+600^2a + 600 + 20 = 170

use elimination

360000a - 600b + 20 = 170

360000a + 600b + 20 = 170

------------------------------addition eliminates b

720000a + 40 = 340

720000a = 300

a = 300/720000

a = .0004167

Now we can write the equation

y = .0004167x^2 + 20

Graphically

+graph%28+300%2C+200%2C+-700%2C+700%2C+-100%2C+200%2C+.0004167x%5E2%2B20%2C+170%2C+116%29+

:

"How high is the cable 120m away from a tower? "

600 - 120 = 480

Solve for x=480

y = .0004167(480^2) + 20

y = 96 + 20

y = 116 m high (blue line)

Answer 2

Given:

the towers supporting the cable of a suspension bring are 1200 meters apart and 170 meters above the bridge it supports. suppose the cable hangs, following the shape of a parabola, with its lowest point 20 meters above the bridge

To Find:

how high is the cable 120 meters away from the tower?​

Solution:

First, let us draw a diagram to visualise the above situation we will draw a graph with parabola as mentioned and take the lowest point to be in y-axis near to (0,0)

Now we will form an equation of parabola which will be

$y=ax^2+20$

to find the value of we will put the point (600,170) into the equation to get the value of a so that we can fully on the equation

Now put the point and find the value of 'a'

$170=a*600^2+20\\a=\frac{150}{360000}\\=\frac{1}{2400}$

now we have an equation as

$y=\frac{x^2}{2400}+20$

To find the height of the cable which is 120m away from the tower we will find the value of y when x=480

so putting the value

$y=\frac{480^2}{2400}+20\\=96+20\\=116$

so y=116

Hence, the cable will be 116m high when it is 120m away from the tower.