Math help?

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.

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

*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.

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

Feb 21, 2013, 8:32am, marbleduck wrote: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?

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

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?

I get confus with negatives sometimes.

So I'm still confused as to why y=2x