15 Jun '10 22:39>
Originally posted by clandarkfirethats wat i said...
In theory, 42 would work. I was looking for 41 though...
Originally posted by clandarkfireThe cable follows a function F(x) = cosh(x) (I have no desire to explain why)
One more:
A flexible cable was hung across a chasm between two points that were exactly 1 km apart and at the same elevation. During the cool night the cable length was calculated to contract by .2 meters. The cable dip was actually measured to decrease by .2 meters. What is the length of the cable after cooling?
Originally posted by clandarkfirehttp://calculuslab.deltacollege.edu/ODE/7-A-1/7-A-1-h.html
That's a good start! Anyone want to help out the master? My first thought was that it was a parabolic curve which would make it a lot easier. It's actually a catenary, but the length can still be found with the help of a little calculus. 🙂
Originally posted by mtthwYeah, I don't remember if DiffEq was 2nd or 3rd year of my engineering degree, but I've forgotten most of it by now anyway.
Deriving the formula is the interesting part! Calculus of variations, with a constraint (minimise the potential energy subject to the length being fixed).
It is, admittedly, not basic maths. I think it was in my final year of an undergraduate maths degree where I first had to solve that particular problem.
Originally posted by mtthwSo what set of degrees did you end up with?
Deriving the formula is the interesting part! Calculus of variations, with a constraint (minimise the potential energy subject to the length being fixed).
It is, admittedly, not basic maths. I think it was in my final year of an undergraduate maths degree where I first had to solve that particular problem.
Originally posted by iamatigerIf the cable is taught, the dip can't rise by 0.2 meters after cooling.
I'm puzzled about the lines:
[b]>>The lenght of the cable then is L = INTEGRAL(SQRT(1+F'(x)^2))dx from x=0 to x= 1000m.
>>L = INTEGRAL(SQRT(1+sinh(x)^2))dx = INTEGRAL(cosh(x))dx = sinh(1000)
The cable length is not given in the question, and nor is the dip, so it is possible the cable is:
a) Taught, with a length of 1000
b) Loose, with a longer ...[text shortened]... nd a maximum of +infinity, the equation given has a constant value though - what am I missing?[/b]
Originally posted by forkedknightThis is (in, for example, set theory) incorrect.
There are only two magnitudes of infinity. Countably infinite, and uncountably infinite.
Originally posted by clandarkfireThere are always problems with integer sequences, namely that there is never a unique answer.
1). 1,2,5,14: find the next term and a formula for the nth term.
Originally posted by FabianFnasFor the first point, yes, this is correct (if you take your ordering to be cardinality, as |N|<|R|, look up Cantor's Diagonal Argument).
You, Swlabr, seem to know some about transfinite numbers...
Let N be the number of natural numbers.
Let R be the number of real numbers.
Is it correct to say that R > N ?
Is there any X such as N < X < R ?