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An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 4 inches tall and stand 40 inches apart. At some point along the road from the lowest point of the cable, the cable is 0.64 inches above the roadway. Find the distance between that point and the base of the nearest tower.

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I might be mistaken, but it looks like there isn't enough information. Based on the information provided--the diagram looks like this.
1 Attachment
can someone explain me in words plz
There's enough information. Can more than likely assume the towers are of equal height. Then that's enough to derive the coefficients of the parabola. Then you just take the inverse of it, sort of.

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Other answers:

You've got a parabola f(x) = x^2 + ax + b. Where f(40)=f(0)=4, and f(20)=0. Use that to find the coefficients a, b. Now set f(x) = 0.64, and rearrange to find what value of x makes that happen.
a= 4 b=0?
No. f(0) = b = 4.
f(40) = 40^2 + a*40 + b = 40^2 + a*40 + 4 = 4. implies that 1600 + 40 * a = 0. implies that a = -1600 / 40.
the answer I got is -14396
Can you show your derivation? I've shown my derivation above and it's different, and I can't see any error in it...
That can't be true, it is a bridge, that means the towers must be above AND below the road.
It's not realistic though. The arch should also be a catenary, but it's not...
now i got 4
I bet the question designers meant it to be interpreted as the tower height measured from road level. Otherwise the description would be more complicated again and wouldn't add anythign except to make people happy who want it measured as it would be in real life, in some circumstances.
A suspension bridge has the roadway in between the top and bottom of the towers, the roadway won't be at the bottom (then it won't really be a bridge at all...).
Scarydoor, you may be right
Probably am. Questions like this, designed to present basic calculus with some variation, don't want to confuse people with the intricacies of engineering...
Maybe we should account for material expansion due to seasons, as well? We might need to know the latitude as well.
I am just surprised at how badly this problem was described :P. I mean seasonal expansion would have to involve advanced statistics and advanced calculus. But the tower thing is a pretty big error. My worst fear is always that test makers end up doing something like this on a test :(.
is all the given information
a=-40. b=4. Pretty sure my derivation above is right. But feel free to show how you got something different...
so now you want to solve for x: f(x) = x^2 -40x + 4 = 0.64. Use the quadratic formula.
I made a mistake somewhere.
I haven't done this stuff for years. So my brain got all confused about what you can do with polynomials, and what the point is. So actually you want to shift the polynomial so that it's in [-20,20]. Then you get f(x) = 1/100 x^2 to describe the bridge thing.

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