I need this problem solved step by step with formula if anybody could solve it :::::find the length of three metals (hold the bridge)if the length is 80 inch and the width is 200 inch?

Please clarify your question as there is not enough information given.

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Originally Posted by Curlyben

Please clarify your question as there is not enough information given.

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Sorry had trouble logging in. It's actually a picture . It's a parabolic bridge and from where it starts to where it ends is 200 inches. It's height is 80 inches.and there are 3 metals holding the bridge. The center metal is 10 inches and the other two are unknown. So there I hope I made it clearly.

It seems you have a parabola with three known points as in the attached figure, and your job is to determine the equation of the pabola and then determine the length of two support columns ("metals" as you called them) that are located at some specified points - right? Suggestion: set your coordinate system so that the (0,0) is at the midpoint of the bridge, and the use the known data to find the coefficients for the equation:

y-a = b(x-c)^2

Unknowns a, b and c can be solved using known coordinates (0,-10), (100, -80) and (-100,-80). Once you have those coefficients you can determine the value 'y' for the two points in question.

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Originally Posted by ebaines

It seems you have a parabola with three known points as in the attached figure, and your job is to determine the equation of the pabola and then determine the length of two support columns ("metals" as you called them) that are located at some specified points - right? Suggestion: set your coordinate system so that the (0,0) is at the midpoint of the bridge, and the use the known data to find the coefficients for the equation:

y-a = b(x-c)^2


Unknowns a, b and c can be solved using known coordinates (0,-10), (100, -80) and (-100,-80). Once you have those coefficients you can determine the value 'y' for the two points in question.

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I appreciate your answer and I thank you for your time but I think you misunderstood my answer. The picture was right except you forgot the two metal beside the center metal. I have to find the length of the two metals by the center not the ones supporting the bridge. So there, and could you please give me a direct answer with the work.

And again thanks!

To determine the length of the two supports (why do you call them "metals?") from the bridge deck to the parabola you need to know what position they are located at along the x-axis in the diagram. In the figure I didn't know where to show them so I placed them at about +/- 75 for illustrative purposes. Without knowing the position of the supports it's impossible to provide an answer.

Also, we do not simply give answers to homework problems - I've given you a very good start on how to solve it, so if you still aren't sure how to proceed please show us what you have attempted and we can help you along.

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Originally Posted by ebaines

To determine the length of the two supports (why do you call them "metals?") from the bridge deck to the parabola you need to know what position they are located at along the x-axis in the diagram. In the figure I didn't know where to show them so I placed them at about +/- 75 for illustrative purposes. Without knowing the position of the supports it's impossible to provide an answer.

Also, we do not simply give answers to homework problems - I've given you a very good start on how to solve it, so if you still aren't sure how to proceed please show us what you have attempted and we can help you along.

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Once again thank you

Okay I understand you can't give me the answer and I've been working on it. The formula above y-a=b(x-c^2) as you assumed earlier how do you apply them in the formula.

As I pointed out in my first reply you have three data points that you can use to solve for a, b and c. From (0,-10) you have:



From (100,-80) and (-100,-80) you have:



and



Note that these two equations have the same left hand side, so therefore - what does that tell you about the value of c? Once you have that it's easy. By the way - the reason why I suggested setting the coordinate system at the mid-point of the bridge is because it makes determining the values of a, b, and c easier than it would be otherwise.

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Originally Posted by ebaines

As I pointed out in my first reply you have three data points that you can use to solve for a, b and c. From (0,-10) you have:





From (100,-80) and (-100,-80) you have:



and



Note that these two equations have the same left hand side, so therefore - what does that tell you about the value of c? Once you have that it's easy. By the way - the reason why I suggested setting the coordinate system at the mid-point of the bridge is because it makes determining the values of a, b, and c easier than it would be otherwise.

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How would you add the formulas to get the final answer?

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Originally Posted by Aseal

How would you add the formulas to get the final answer?

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I don't understand your question - there is no "adding of formulas."

Have you been able to determine values for a, b and c? What did you get?

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Originally Posted by ebaines

I don't understand your question - there is no "adding of formulas."

Have you been able to determine values for a, b and c? What did you get?

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Fine how do I get final answer. For A(0,10) B(50,unknown) and C (100,80), Is there a possible way to find ABC together.

Go back and review post #8. I've given you three equations in three unknowns: a, b, and c. Do you know how to solve 3 simulteneous equations?

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Originally Posted by ebaines

Go back and review post #8. I've given you three equations in three unknowns: a, b, and c. Do you know how to solve 3 simulteneous equations?

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I ended up with 3 equations but I have to find the final answer for each equation so I can add them all.

I'm not following you. If you have the equation for the parabola you can simply plug in the x-value for the position of the supports whose length you're trying to find.

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Originally Posted by ebaines

I'm not following you. If you have the equation for the parabola you can simply plug in the x-value for the position of the supports whose length you're trying to find.

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Ohh, so that's what you do I finally got the answer to the equation. THANK YOU FOR ALL YOUR HELP. This wasn't a homework question I had a test today and I was stumped on that one question. AND AGAIN THANK YOU!

You're welcome - glad it worked out!