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Quadratics and other Polynomials

Two electic poles AB and DC are 50m high and 100m long apart. An electrical wire is suspended between B and C and it assumes the shape of a parabola under its own weight. The maximum sag at the middle is 10m.

How high is the wire above point X, given thar XD= 25m

The answer is 42.5

How do you get this answer?

Re: Quadratics and other Polynomials

I would orient my coordinate axes such that the vertex is at the origin. And so we know:

y(0)=0

y(±50)=10

A parabola opening upwards, with its vertex at the origin can be written:

y=ax^2 where 0<a

Now, using the point (50,10), can you determine the parameter a?

Once you do this, then evaluate y(25)+40 to find the height of the wire above the ground at X.

edit: Normally I like to use LaTeX, but it is not working at the moment.

Re: Quadratics and other Polynomials

i don't know how to determine the parameter of a :/

Re: Quadratics and other Polynomials

In the equation $\displaystyle y = ax^2$, let x = 50 and y = 10, then solve for a.

Re: Quadratics and other Polynomials

we can also proceed to solve this question as under:

As very correctly advised by markFL we will translate the coordinate axis such that the vertex of the parabola is at the origin.

Since the parabola is upward concave let assume its equation is

y^2 = ax Now with present coordinate system the coordinates of b and c would be ( -50,10) and ( 50,10) since these points are on the parabola the coordinates must satisfy the equation. Thus we have

10^2= a * 50 Hence a = 2

Now we have the equation of parabola as y^2 = 2x

we are given XD = 25 Then OX = 25 Now we have to find the corresponding y

In equation y^2 = 2x we plug in x = 25 , we will get y^2 = 50 and y = 5sqrt2, Note that this is the height of the rope above x axis, the height of the wire above the ground would be = ( 5sqrt 2 + 90 ) m

now you can take it further