Empty
  • Empty
5x^2+y^4 = -9 Evaluate y'' at x=2, y=1 --- This question seems to have an answer, but does the answer actually mean anything?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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dan815
  • dan815
it depends do u want it to mean anything
anonymous
  • anonymous
he wants acceleration at that point (2,1) I guess.
pujan20
  • pujan20
@dan815 i agree with fbi2015

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dan815
  • dan815
who says its d^2y/dt^2
anonymous
  • anonymous
well if x is time
Empty
  • Empty
y'' = d^2y/dx^2 here
imqwerty
  • imqwerty
wait a sec i got the answer :)
Empty
  • Empty
There is an "answer" no problem. But that's not what I care about.
anonymous
  • anonymous
true that, you can swabb answer from wolfram all day everyday
ikram002p
  • ikram002p
@dan815 yeah it mean something in complex maybe xD
dan815
  • dan815
|dw:1440371299983:dw|
imqwerty
  • imqwerty
u have to double differentiate the equation with respect to x nd then u'll get an equation in x nd y then u jst put the values nd get the answer LOL
Empty
  • Empty
Stop solving it, I don't care, I only care about this: x=2, y=1 \[5x^2+y^4=-9\] \[5*4+1 \ne -9\]
dan815
  • dan815
i see
Empty
  • Empty
\[y'' = 12.5\] I believe, just so no one else tries to solve it haha
dan815
  • dan815
maybe in complex plane
dan815
  • dan815
like what does it mean to have complex routes
dan815
  • dan815
roots*
Empty
  • Empty
I don't think so, because although there are complex solutions to \(5x^2+y^4=-9\) x=2 and y=1 are still not solutinos
dan815
  • dan815
like can we try a simpler example Y=x^3 y'=3x^2 y''=12x what does y''(0,2) mean? 0,2 is not a solution yo y=x^3 but at the same time it just works because 0 can be put in for x
dan815
  • dan815
maybe something similiar to that is happening here
Empty
  • Empty
Yeah that looks good
dan815
  • dan815
the way the 2nd derivative behaves is just not a function of the y domain so with other functions maybe u can get it to not be functions of some lines and the point 2,1 happens to be on that line
dan815
  • dan815
the way the 2nd derivate behaves in this case*
dan815
  • dan815
the point (2,1) could belong to some other function too, a function along which the 2nd derivative is constant
dan815
  • dan815
you can try to think of a function where the 2nd derivative will be cosntant along some other curves
dan815
  • dan815
|dw:1440372327851:dw|
Empty
  • Empty
Ok I kinda see what you're saying, add a constant value to our original equation and we have a family of curves: \[5x^2+y^4+C = -9\] This will have all the same derivatives as the original case C=0 but now we can also find the curve that satisfies x=2 and y=1. I guess this would be a way to think of it?
dan815
  • dan815
ya that makes sense
dan815
  • dan815
what would the gradient and the gradient field of this function look like for example could be an example
dan815
  • dan815
but i see what u mean this only works out if theres a constant and some variation so that this function exists everywhere over the space
dan815
  • dan815
what would the gradient and the gradient of the gradient* field of this function look like for example could be an example
dan815
  • dan815
im not really satisfied with that lol but ya
dan815
  • dan815
also i was thinking about that complex root stuff with a parabola
dan815
  • dan815
|dw:1440373563511:dw|
dan815
  • dan815
|dw:1440373638686:dw|
Empty
  • Empty
Hmmm I don't really understand what you mean
dan815
  • dan815
its gonna give us a complex answer in uv plane but what does that complex value mean in x,y plane
dan815
  • dan815
like suppose you have a transformation of coordinates and you tried to solve for the complex roots
dan815
  • dan815
like okay for example x^2+y^2=1 is not a well defined function with a simple x domain or y domian it has to have both x,y domain, its a 1:1 function in theta:r so im saying if u take your given function and do some transformation of coordiantes where its 1:1 and then fiding complex roots in that domain what does that complex number mean in x,y domain?
dan815
  • dan815
so technically for example your function 5x^2+y^2=-9 we werent able to thjink about this as having complex routes
dan815
  • dan815
but for some transformation of coordinates u can think about complex roots
dan815
  • dan815
i dunno =.=
Empty
  • Empty
Well wait I think there's a difference here between complex answers and nonsense answers. For example, a set of complex values that work for \(x^2+y^2=1\) would be x=2 and \(y=i \sqrt{3}\) A set of nonsense values that don't work are x=2 and y=2.
dan815
  • dan815
ya i was thinking about that lol, but who says complex root arent just nonsense too
Empty
  • Empty
Me, I say that they aren't
dan815
  • dan815
lol
Empty
  • Empty
lol
dan815
  • dan815
it has a use so they arent nonsense all of a sudden
dan815
  • dan815
what if these will have uses later then
Empty
  • Empty
complex answers are just expanding your domain and range, nonsense answers are just picking values that don't satisfy the equation. So we can pick a pair of complex nonsense answers or a pair of real nonsense answers.
dan815
  • dan815
okay himm hoow about this argument
dan815
  • dan815
is it possible that some non parabolic functions can be defined in sum of an infinite set of parabolic functions
dan815
  • dan815
okay well the way i see it is that
dan815
  • dan815
this complex value came because someone wanted to see the intersection of a parabola with the y=0 line
dan815
  • dan815
but we can pick other lines for other functions
dan815
  • dan815
it will still give specific answers, for each line and which domain you pick, but yet every point can be covered depending on how u change your domain and what line you pick
dan815
  • dan815
im just saying random stuff right now :>
Empty
  • Empty
hmmm so wait give an example cause I'm not seeing these parabolas or something like wanna start a twiddla or cosketch or whatever
Empty
  • Empty
http://cosketch.com/Rooms/hkedsyu

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