anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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TuringTest
  • TuringTest
no chance that's supposed to be dy/dx=(3x^2+4x)/y is it ?
myininaya
  • myininaya
it is
myininaya
  • myininaya
he didn't like my answer maybe you can try turing

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TuringTest
  • TuringTest
Ah, I see... You should trust myininaya spikey
anonymous
  • anonymous
lol i didnt understand it :(
myininaya
  • myininaya
but no he might understand you better
anonymous
  • anonymous
dy/dx=(3x^2+4x)/y yes thats correct
myininaya
  • myininaya
this is what i did turing if you want to look
anonymous
  • anonymous
yep thats the other one :) do you wanna work off here or of the other one.
TuringTest
  • TuringTest
ok... 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
  • TuringTest
you don't know how to integrate that* correct?
anonymous
  • anonymous
hmm im not sure. if you mean using anti derivaties than sort of
anonymous
  • anonymous
\[\int\limits_{?}^{?}\] but i havent used this yet
TuringTest
  • TuringTest
yes exactly antiderivatives
myininaya
  • myininaya
\[\int\limits_{}^{}x^n dx=\frac{x^{n+1}}{n+1}+C, n \neq -1\]
myininaya
  • myininaya
or you could say the antiderivative of x^n = that
anonymous
  • anonymous
ahh yes that sort of makes sense.
anonymous
  • anonymous
i understand that c is a constant.
TuringTest
  • TuringTest
check that the derivative of that gives x^n
myininaya
  • myininaya
right
anonymous
  • anonymous
the derivative of ydy=(3x^2+4x)dx?
TuringTest
  • TuringTest
antiderivative of that
myininaya
  • myininaya
no we want to integrate both sides or we can use the term antiderivative
myininaya
  • myininaya
like turing said
anonymous
  • anonymous
ahh okay.
TuringTest
  • TuringTest
so what is the antiderivative of ydy according to the formula myin posted?
anonymous
  • anonymous
x^3
anonymous
  • anonymous
for 3x^2
anonymous
  • anonymous
i dont know for 4x
TuringTest
  • TuringTest
yes but that is not ydy... like I said, I can't use latex, myin will have to show you
myininaya
  • myininaya
\[\int\limits_{}^{}y dy =\int\limits_{}^{}y^1 dy=\frac{y^{1+1}}{1+1}+c_1\]
myininaya
  • myininaya
see n was 1 here
anonymous
  • anonymous
okay im struggling alot right now because i havent had enough practice with this.
myininaya
  • myininaya
its cool
myininaya
  • myininaya
struggling happens but the main is don't give up
anonymous
  • anonymous
okay so the rule is for 3x^2 x^n+1
anonymous
  • anonymous
what formula for the 4x?
anonymous
  • anonymous
the anti derivative of dx is x?
TuringTest
  • TuringTest
4x=4x^(1) so we can use the same formula integral of (x^n)dx=x^(n+1)/(n+1)
myininaya
  • myininaya
\[\int\limits_{}^{}3x^2 dx=3 \int\limits_{}^{}x^2 dx=3 \cdot \frac{x^{2+1}}{2+1}+c_2\]
myininaya
  • myininaya
\[\int\limits_{}^{}4x dx=4 \int\limits_{}^{}x dx=4\int\limits_{}^{}x^1 dx=4 \cdot \frac{x^{1+1}}{1+1}+c_3\]
myininaya
  • myininaya
see i'm using that same formula every time
anonymous
  • anonymous
oh okay so i have to do it for each.
myininaya
  • myininaya
right
myininaya
  • myininaya
\[\int\limits_{}^{}(f(x)+g(x))dx=\int\limits_{}^{}f(x) dx+\int\limits_{}^{}g(x)dx\]
myininaya
  • myininaya
so 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
  • anonymous
so for the formula ydy you used the formula.
anonymous
  • anonymous
okay i understand how u got that equation.
myininaya
  • myininaya
or 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
anonymous
  • anonymous
yes
myininaya
  • myininaya
ok great! lets make this prettier
myininaya
  • myininaya
\[\frac{y^2}{2}=x^3+2 x^2+C\]
myininaya
  • myininaya
is that okay?
anonymous
  • anonymous
yes my simplification came out the same
myininaya
  • myininaya
ok we can also multiply two on both sides
myininaya
  • myininaya
\[y^2=2x^3+4x^2+C\]
myininaya
  • myininaya
2C is still constant so I left it as C
anonymous
  • anonymous
yes
myininaya
  • myininaya
you can write 2C if you feel more comfortable with that
anonymous
  • anonymous
and now square both sides?
myininaya
  • myininaya
square root of both sides
myininaya
  • myininaya
we don't need to keep the negative value since your directions say y>0
anonymous
  • anonymous
where do we have a negative value?
myininaya
  • myininaya
take square root of both sides you get plus or minus
anonymous
  • anonymous
thats right!
myininaya
  • myininaya
we only need the plus since y>0
myininaya
  • myininaya
so what I'm saying is that we have \[y=\sqrt{2x^3+4x^2+C}\]
anonymous
  • anonymous
yes.
myininaya
  • myininaya
you were given a point on this curve
myininaya
  • myininaya
\[ (1,\sqrt{10} )\]
myininaya
  • myininaya
x=1 and y=sqrt(10)
anonymous
  • anonymous
yes i plug it in for x and y?
myininaya
  • myininaya
so we can use this to find C
myininaya
  • myininaya
\[\sqrt{10}=\sqrt{2 (1)^3+4(1)^2+C}\] => \[10=2(1)^3+4(1)^2+C\]
myininaya
  • myininaya
\[10=2+4+C\]
myininaya
  • myininaya
=>C=4
myininaya
  • myininaya
so we have \[y=\sqrt{2x^3+4x^2+4} \]
myininaya
  • myininaya
you wanted to know y when x=0, right?
anonymous
  • anonymous
yes
myininaya
  • myininaya
so how do you think we do that?
myininaya
  • myininaya
i brb i think it will be pretty easy for turing to help without latex on this last part that you have to do
anonymous
  • anonymous
okay turing i get now :D
anonymous
  • anonymous
but i need help finishing
myininaya
  • myininaya
ok i'm back
myininaya
  • myininaya
i had to get my glasses
myininaya
  • myininaya
so i can be fully nerd
anonymous
  • anonymous
lol
myininaya
  • myininaya
so we have \[y=\sqrt{2x^3+4x^2+4}\]
anonymous
  • anonymous
yes
myininaya
  • myininaya
it says what is y if x=0
myininaya
  • myininaya
\[y=\sqrt{2(0)^3+4(0)^2+4}\]
myininaya
  • myininaya
i replaced x with 0 so I can see what y is when x is 0
myininaya
  • myininaya
\[y=\sqrt{0+0+4}=\sqrt{4}=2\]
myininaya
  • myininaya
This says when x is 0, y is 2
anonymous
  • anonymous
got it! :D thank you!!!! sorry i didnt really try hard enough before you were a great help!
myininaya
  • myininaya
It 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
  • myininaya
Or you know like I way you prefer.
anonymous
  • anonymous
lol yeah :D thanks again.
myininaya
  • myininaya
np

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