Was there something else I needed to do first?
#how do I start this? I tried brute forcing y' and that wasn't going well.
woven rain
stable krakenBOT
Was there something else I needed to do first?
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warm olive
Was there something else I needed to do first?
You can do this in cartesian coordinates, in which case:
dl = √(1 + (dy/dx)^2)dx
Or you can do it by parametrizing the astroid. Then:
dl = √((dx/dt)^2 + (dy/dt)^2)dt
I recommend the second approach, as the first one leads to an integral that's solvable exactly, but quite long.
In any case, find the length of a quarter of the astroid in the first quadrant, then multiply the result by 4.
bitter marlin
parametrise, indeed
woven rain
You can do this in cartesian coordinates, in which case:
dl = √(1 + (dy/dx)^2)dx...
I see, I didn't even think to make it Cartesian.
I don't think I have been taught what parametrizing is, so might just avoid that for now
warm olive
Well, as you want. The first approach might take a while, though.
little marsh
You can do this in cartesian coordinates, in which case:
dl = √(1 + (dy/dx)^2)dx...
how can you be sure that the arc length in each quadrant is the same in any case?
woven rain
Yeah I'm still a tad confused
woven rain
+close