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HonourableDragon6239

Hi, I tried answering this question but I do not know what to do. Could you please guide me? Thank you.

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Andréa C

Hello, HonourableDragon6239!

There are different ways to solve the problem depending on where you put the origin.

There are two parabolas, an inner and an outer one.

Let's put the origin (0, 0) as the vertex of the inner parabola.

We put (0, 1) because the width is of 1 m at this part. This is the vertex of the outer parabola.

We put (0, -10) because the longest cable measures 10 m.

We put (0, -16) because the bridge deck is 6 m above the highway.

We put (16, -10) because every cable is separated by a distance of 2 m.

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Since the inner parabola has a vertex at the origin, we can use the formula f(x)=ax².

We can find the rule by simply knowing the coordinates of a point on the parabola. 

f(x)=ax² => -10 = a(16)² => a = ...

https://www.alloprof.qc.ca/en/students/vl/mathematics/finding-the-rule-of-a-quadratic-function-m1247

To find the distance between the two arches, you have to use the previous rule, plug in y=-16 and see for which values of x this happens.

I'll leave you to find the width!

Do no hesitate to ask more questions!