Write a mathmatical proof show (3x)(5y)7z is equivalant to 105xyz.

Mathematics

1 answer:

Anika [276]3 years ago

8 0

(3x)(5y)7z

(3x)(5y)=15xy

(15xy)(7z)=105xyz

plz rate as brainliest answer

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Rearrange the ODE as

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So we can write the ODE as

$\dfrac{\mathrm du}{\mathrm dx}+2xu=x^3$

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$e^{x^2}\dfrac{\mathrm du}{\mathrm dx}+2xe^{x^2}u=x^3e^{x^2}$
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Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx$
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Substitute $t=x^2$ , so that $\mathrm dt=2x\,\mathrm dx$ . Then

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Integrate the right hand side by parts using

$f=t\implies\mathrm df=\mathrm dt$
$\mathrm dg=e^t\,\mathrm dt\implies g=e^t$
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You should end up with

$e^{x^2}u=\dfrac12e^{x^2}(x^2-1)+C$
$u=\dfrac{x^2-1}2+Ce^{-x^2}$
$\tan y=\dfrac{x^2-1}2+Ce^{-x^2}$

and provided that we restrict $|y|$ , we can write

$y=\tan^{-1}\left(\dfrac{x^2-1}2+Ce^{-x^2}\right)$