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Post by MarbleDuck on Feb 21, 2013 0:40:32 GMT
So I have a problem that I'm not sure how to go about solving. The goal is to find the largest cubic box that can fit through a parabolic arch that is 58 ft high, and 28 ft wide. I've figured that the equation of the parabola (with its vertex at the origin) is y=-58/196x^2 but I don't know how to go about figuring out the largest square that can fit within it I'd really appreciate any help. Attachments:
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Post by Jeff on Feb 21, 2013 2:36:33 GMT
I'd help you out if i could MD, but the only thing that pops in my head when I see parabolas is "finding the area under a curve..."...thanks a lot Calc 1 >_>
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whirligig
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Post by whirligig on Feb 21, 2013 2:45:07 GMT
*makes a sudden, unexpected appearance*
I'm pretty sure the diagram you drew of the box's position is correct. First, put the origin at the base of the arch, not at the vertex. This makes the equation y = 58-58/196*x^2. Label one corner of the box at its upper right. Call this point (x,y). We know that y = 2x from the shape of the box (the height is twice half of the bottom side length), and y = 58-58/196*x^2 from the arch (the corner touches the arch). Combine these equations to get 58/196*x^2+2x-58 = 0. Solve for x, which I trust you know how to do at this point. The positive solution, x = 14/29*(√890 - 7), is half the side length of the box.
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Post by MarbleDuck on Feb 21, 2013 13:32:55 GMT
ahhhhhh okay. I was sorta getting the idea of what I had to do before, but this helped me a lot
Appreciate the help, whirli and Jeff
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Post by Jeff on Feb 21, 2013 20:06:05 GMT
ahhhhhh okay. I was sorta getting the idea of what I had to do before, but this helped me a lot Appreciate the help, whirli and Jeff What did I do besides complaining about all I can think about with parabolas is finding the area between them and the X axis?
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Post by MarbleDuck on Feb 22, 2013 16:06:06 GMT
Hey whirli
x = 14/29*(sqrt(890) - 7) or x = 14/29*(sqrt(890-7))
I'm terrible at these quadratic things. I always get lost among the numbers :/
...and I'm quadratic formulaing it, but I keep getting imaginary answers
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whirligig
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Post by whirligig on Feb 23, 2013 21:00:30 GMT
The 7 is outside the square root, obviously. Otherwise it wouldn't be simplified.
If you're getting non-real answers ... my guess would be that you aren't accounting for c being negative?
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Post by MarbleDuck on Feb 25, 2013 16:35:10 GMT
I get confus with negatives sometimes.
So I'm still confused as to why y=2x
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