Mathematics
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OpenStudy (anonymous):
@study100 Help me on these two questions please
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OpenStudy (anonymous):
I'll try ;u;
OpenStudy (anonymous):
OpenStudy (anonymous):
I did what we did in the previous ones right and took "y" out of the equation and took the integral based on x
OpenStudy (anonymous):
\[\large \large \frac{ dy }{ \sqrt{y} } = \frac{ dx }{ \sqrt{x}}\]
OpenStudy (anonymous):
and just intergrate both sides : DDD
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OpenStudy (anonymous):
\[\frac{ 2 }{\sqrt{\frac{1}{x}}}+ C\]
OpenStudy (anonymous):
\[\large 2y^{1/2} = 2 x ^{1/2} + C\]
OpenStudy (anonymous):
the other side is \[\frac{ y^2}{2} +C\]
OpenStudy (anonymous):
lol im wrong then
OpenStudy (anonymous):
f(x) =\[2\sqrt{x}\]
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OpenStudy (anonymous):
well integrate we have
\[\large 2 y ^{-1/2 +1}\] = \[2 x ^ {-1/2 + 1} + C???\]
OpenStudy (anonymous):
simplify I got
\[\sqrt{y} = \sqrt{x} +C\]
OpenStudy (anonymous):
nice i simplified and got the same thing
OpenStudy (anonymous):
one more question and thats it
OpenStudy (anonymous):
Ok! xD I almost have to eat dinner too!
\[\large \frac{ dy }{ y } = 3x dx\]
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OpenStudy (anonymous):
\[\large \ln (y) =\frac{ 3x^{2} }{ 2 } + C\]
OpenStudy (anonymous):
ok
OpenStudy (anonymous):
should I exponentiate it? o.o like e^lny to get y alone?
OpenStudy (anonymous):
\[\large e^{lny} = e^{3x^{2}/2+C}\]
OpenStudy (anonymous):
got it
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OpenStudy (anonymous):
\[y = Ce^{3x^{2}/2}\]
OpenStudy (anonymous):
the answer is |dw:1406778535745:dw|