Question

If y^3 = at^2 , then (d^2 y)/dt^2 ?

Answer 1

I only got to the part:

dy/dt = 2at/3y^2

Answer 2

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

Answer 3

it's like solve for y''

Answer 4

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

Answer 5

it says the answer is:

-2a/9y^2

but I am getting a different answer

Answer 6

is "a" here constant?

Answer 7

Quotient rule, remember?

Answer 8

yo constnt

Answer 9

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

Answer 10

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

Answer 11

i'll try again :)

Answer 12

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

Answer 13

I got:

(6ay^4 - 8a^2 t^2 y)/9y^6

I think I am doing something wrong.

Answer 14

i'll try again :)

Answer 15

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

Answer 16

can you follow @moongazer ?

Answer 17

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

Answer 18

Well you could simplify

Answer 19

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

Answer 20

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

Answer 21

Could I? Yes. Can you?

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

that's what I got

Answer 26

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

Answer 27

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

Answer 28

I see at^2

Answer 29

Replace it y^3
then combine like terms

Answer 30

@moongazer , do you what myininaya told you?

Answer 31

@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. :)

Answer 32

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