## moongazer Group Title If y^3 = at^2 , then (d^2 y)/dt^2 ? 11 months ago 11 months ago

1. moongazer Group Title

I only got to the part: dy/dt = 2at/3y^2

2. Yttrium Group Title

Just derive again, so you can solve the d^2y/dt^2. :))

3. Yttrium Group Title

it's like solve for y''

4. amriju Group Title

let it remain as 3y^2=2at..differntiate again....using multiplication rule....

5. moongazer Group Title

it says the answer is: -2a/9y^2 but I am getting a different answer

6. moongazer Group Title

is "a" here constant?

7. Yttrium Group Title

Quotient rule, remember?

8. amriju Group Title

yo constnt

9. Yttrium Group Title

for easier calculation, you can factor out 2a/3 and just derive (t/y^2)

10. moongazer Group Title

could you show me the first step for the second derivative? maybe I did something wrong

11. moongazer Group Title

i'll try again :)

12. amriju Group Title

may be u need to substitute y as (at^2)^2/3

13. moongazer Group Title

I got: (6ay^4 - 8a^2 t^2 y)/9y^6 I think I am doing something wrong.

14. moongazer Group Title

i'll try again :)

15. Yttrium Group Title

$y' = \frac{ 2at }{ 3y^2 }$, 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. $y'' = \frac{ 2a }{ 3 } [ \frac{ 3y^4 -4at^2y }{ 3y^6 }]$

16. Yttrium Group Title

17. moongazer Group Title

That's what I got. I think there is some typo in my answer sheet. Thanks :)

18. myininaya Group Title

Well you could simplify

19. Yttrium Group Title

@moongazer, it isn't the answer in simplest form. Maybe you can continue this and let us verify if we get the same answers.

20. moongazer Group Title

@myininaya could you simply it further? @Yttrium yes, I understood your solution

21. myininaya Group Title

Could I? Yes. Can you?

22. myininaya Group Title

Eye ball the numerator and the denominator. You should see they share a common factor.

23. Yttrium Group Title

For our class, the definition of simplest form is that it is factored out completely. Just factor out some stuff and do cancellation.

24. moongazer Group Title

2a(3y^3 - 4at^2) / 9y^5

25. moongazer Group Title

that's what I got

26. myininaya Group Title

You can also choose to write at^2 as y^3

27. myininaya Group Title

Recall our initial equation: y^3=at^2

28. myininaya Group Title

I see at^2

29. myininaya Group Title

Replace it y^3 then combine like terms

30. Yttrium Group Title

@moongazer , do you what myininaya told you?

31. myininaya Group Title

@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. :)

32. moongazer Group Title

WOW! Thank you very much to both of you. I failed to notice that until you said it. Thanks :) I now got the answer. :)