moongazer
  • moongazer
If y^3 = at^2 , then (d^2 y)/dt^2 ?
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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moongazer
  • moongazer
I only got to the part: dy/dt = 2at/3y^2
Yttrium
  • Yttrium
Just derive again, so you can solve the d^2y/dt^2. :))
Yttrium
  • Yttrium
it's like solve for y''

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More answers

amriju
  • amriju
let it remain as 3y^2=2at..differntiate again....using multiplication rule....
moongazer
  • moongazer
it says the answer is: -2a/9y^2 but I am getting a different answer
moongazer
  • moongazer
is "a" here constant?
Yttrium
  • Yttrium
Quotient rule, remember?
amriju
  • amriju
yo constnt
Yttrium
  • Yttrium
for easier calculation, you can factor out 2a/3 and just derive (t/y^2)
moongazer
  • moongazer
could you show me the first step for the second derivative? maybe I did something wrong
moongazer
  • moongazer
i'll try again :)
amriju
  • amriju
may be u need to substitute y as (at^2)^2/3
moongazer
  • moongazer
I got: (6ay^4 - 8a^2 t^2 y)/9y^6 I think I am doing something wrong.
moongazer
  • moongazer
i'll try again :)
Yttrium
  • Yttrium
\[y' = \frac{ 2at }{ 3y^2 }\], right? Therefore, \[y' = \frac{ 2a }{ 3 } (\frac{ t }{ y^2 })\] \[y'' = \frac{ 2a }{ 3 } [\frac{ y^2 - 2tyy') }{ y^4 }]\] \[y'' = \frac{ 2a }{ 3 } \frac{ y^2 - 2ty(\frac{ 2a }{ 3 })(\frac{ t }{ y^2 }) }{ y^4 }\] Simplifying this equation we will get. \[y'' = \frac{ 2a }{ 3 } [ \frac{ 3y^4 -4at^2y }{ 3y^6 }]\]
Yttrium
  • Yttrium
can you follow @moongazer ?
moongazer
  • moongazer
That's what I got. I think there is some typo in my answer sheet. Thanks :)
myininaya
  • myininaya
Well you could simplify
Yttrium
  • Yttrium
@moongazer, it isn't the answer in simplest form. Maybe you can continue this and let us verify if we get the same answers.
moongazer
  • moongazer
@myininaya could you simply it further? @Yttrium yes, I understood your solution
myininaya
  • myininaya
Could I? Yes. Can you?
myininaya
  • myininaya
Eye ball the numerator and the denominator. You should see they share a common factor.
Yttrium
  • Yttrium
For our class, the definition of simplest form is that it is factored out completely. Just factor out some stuff and do cancellation.
moongazer
  • moongazer
2a(3y^3 - 4at^2) / 9y^5
moongazer
  • moongazer
that's what I got
myininaya
  • myininaya
You can also choose to write at^2 as y^3
myininaya
  • myininaya
Recall our initial equation: y^3=at^2
myininaya
  • myininaya
I see at^2
myininaya
  • myininaya
Replace it y^3 then combine like terms
Yttrium
  • Yttrium
@moongazer , do you what myininaya told you?
myininaya
  • myininaya
@moongazer I'm leaving for tonight but I think Yttrium is still here to help. Goodnight you guys. I think you guys got it from here for sure. :)
moongazer
  • moongazer
WOW! Thank you very much to both of you. I failed to notice that until you said it. Thanks :) I now got the answer. :)

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