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anonymous
 4 years ago
given y>0 and dy/dx=3x^2+4x/y. if the point (1,sqrt{10}) is on the graph relating x and y, then what is y when x=0?
anonymous
 4 years ago
given y>0 and dy/dx=3x^2+4x/y. if the point (1,sqrt{10}) is on the graph relating x and y, then what is y when x=0?

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1no chance that's supposed to be dy/dx=(3x^2+4x)/y is it ?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3he didn't like my answer maybe you can try turing

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1Ah, I see... You should trust myininaya spikey

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lol i didnt understand it :(

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3but no he might understand you better

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3http://openstudy.com/study#/updates/4f1ccb76e4b04992dd23dbf3

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dy/dx=(3x^2+4x)/y yes thats correct

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3this is what i did turing if you want to look

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yep thats the other one :) do you wanna work off here or of the other one.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1ok... this is a very basic separation of variables problem, in which we can treat dy/dx like a regular fraction... dy/dx=(3x^2+4x)/y ydy=3x^2+4xdx now integrate both sides... but according to the other post you don't seem to know how integrate yet :/

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1you don't know how to integrate that* correct?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hmm im not sure. if you mean using anti derivaties than sort of

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{?}^{?}\] but i havent used this yet

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1yes exactly antiderivatives

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[\int\limits_{}^{}x^n dx=\frac{x^{n+1}}{n+1}+C, n \neq 1\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3or you could say the antiderivative of x^n = that

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ahh yes that sort of makes sense.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i understand that c is a constant.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1check that the derivative of that gives x^n

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the derivative of ydy=(3x^2+4x)dx?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1antiderivative of that

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3no we want to integrate both sides or we can use the term antiderivative

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1so what is the antiderivative of ydy according to the formula myin posted?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1yes but that is not ydy... like I said, I can't use latex, myin will have to show you

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[\int\limits_{}^{}y dy =\int\limits_{}^{}y^1 dy=\frac{y^{1+1}}{1+1}+c_1\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay im struggling alot right now because i havent had enough practice with this.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3struggling happens but the main is don't give up

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay so the rule is for 3x^2 x^n+1

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0what formula for the 4x?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the anti derivative of dx is x?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.14x=4x^(1) so we can use the same formula integral of (x^n)dx=x^(n+1)/(n+1)

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[\int\limits_{}^{}3x^2 dx=3 \int\limits_{}^{}x^2 dx=3 \cdot \frac{x^{2+1}}{2+1}+c_2\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[\int\limits_{}^{}4x dx=4 \int\limits_{}^{}x dx=4\int\limits_{}^{}x^1 dx=4 \cdot \frac{x^{1+1}}{1+1}+c_3\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3see i'm using that same formula every time

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh okay so i have to do it for each.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[\int\limits_{}^{}(f(x)+g(x))dx=\int\limits_{}^{}f(x) dx+\int\limits_{}^{}g(x)dx\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3so we have \[\frac{y^2}{2}+c_1=3 \cdot \frac{x^{2+1}}{2+1}+c_2+4 \cdot \frac{x^{1+1}}{1+1}+c_3\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so for the formula ydy you used the formula.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay i understand how u got that equation.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3or you could write instead \[\frac{y^2}{2}=3 \cdot \frac{x^{2+1}}{2+1}+4 \cdot \frac{x^{1+1}}{1+1}+C\] since the sum of some constants is still a constant

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3ok great! lets make this prettier

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[\frac{y^2}{2}=x^3+2 x^2+C\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes my simplification came out the same

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3ok we can also multiply two on both sides

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.32C is still constant so I left it as C

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3you can write 2C if you feel more comfortable with that

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and now square both sides?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3square root of both sides

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3we don't need to keep the negative value since your directions say y>0

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0where do we have a negative value?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3take square root of both sides you get plus or minus

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3we only need the plus since y>0

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3so what I'm saying is that we have \[y=\sqrt{2x^3+4x^2+C}\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3you were given a point on this curve

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes i plug it in for x and y?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3so we can use this to find C

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[\sqrt{10}=\sqrt{2 (1)^3+4(1)^2+C}\] => \[10=2(1)^3+4(1)^2+C\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3so we have \[y=\sqrt{2x^3+4x^2+4} \]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3you wanted to know y when x=0, right?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3so how do you think we do that?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3i brb i think it will be pretty easy for turing to help without latex on this last part that you have to do

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay turing i get now :D

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but i need help finishing

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3i had to get my glasses

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3so i can be fully nerd

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3so we have \[y=\sqrt{2x^3+4x^2+4}\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3it says what is y if x=0

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[y=\sqrt{2(0)^3+4(0)^2+4}\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3i replaced x with 0 so I can see what y is when x is 0

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[y=\sqrt{0+0+4}=\sqrt{4}=2\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3This says when x is 0, y is 2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0got it! :D thank you!!!! sorry i didnt really try hard enough before you were a great help!

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3It is okay. I didn't think any offense to anything you did. Sometimes you may get someone who can explain it better. I know that I'm probably not the best explaining some things.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3Or you know like I way you prefer.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lol yeah :D thanks again.
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