December 22nd, 2008, 02:19 PM
Suppose that you know the area underneath a curve. Let the height of the curve be 'x' and the length of the curve be 'y'. How many possible solutions are there such that x divided by y is always a whole number, and the curve so formed has an area exactly equal to the one you have been given?
December 22nd, 2008, 06:52 PM
What do you mean by THE height of a curve ? Why is height restricted ?Originally Posted by Liongold
Is there some reason that you are reversing the traditinal roles of "x" and "y" ? -- there is nothing wrong about that, but it is a bit unusual.
Finally, does this have anything to do with a homework or test problem ?
Your question is not clear, but I am pretty sure that if one could state it precisely the answer would be c, the cardinality of the continuum.
This doesn't have anything to do with a homework question; it's just a question I've been thinking aobut.
For this curve, let us assume that it resembles the crest of a wave. By height, I meant then the maximum height it reaches, and the length of this curve is not the total length of the curve, but instead the length it has from a Euclidean viewpoint.
It resembles something like this:
_ is the maximum height (x)
/ \
/ \
/ \
/ \
/ \
------------- is the length (y)
As for why I chose to reverse the traditional roles, that was because I am more comfortable with them.
EDIT: It dpesn't seem to have come out quite right...
i'm not sure exactly what the question is.
perhaps you could form a few equations and go from there
the length of a curve is given by the integral of (sqrt(1+(dy/dx)^2)) dx = *y*
the peak of your wave would be given by dy/dx = 0 which occurs at point *x*
it is confusing that you changed the general convention. so my equations are formed from general convention
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