Graph the lines by finding the points of intersection with the axes (intercepts): y=2.5x+5

1 answer:

8 0

The y intercept is 5, since slope is y=mx+b. The x intercept is at -2. If you have more problems like this there is an amazing calculator that graphs equations like this for you. www.symbolab.com. Hope this helps!

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Why 3/7 is iqual to 9

valina [46]

Answer:

i don't think it is equal to 9

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4 years ago

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Find Integrating Fector: <br> ylogy dx + ( x-logy )dy=0

12345 [234]

Rewrite the ODE as

$y\log y\,\mathrm dx+(x-\log y)\,\mathrm dy=0\iff y\log y\dfrac{\mathrm dx}{\mathrm dy}+x=\log y$
$\dfrac{\mathrm dx}{\mathrm dy}=\dfrac1{y\log y}x=\dfrac1y$

so that it is now linear in $x$ . An integrating factor would

$\mu(y)=\exp\left(\displaystyle\int\frac{\mathrm dy}{y\log y}\right)=e^{\log(\log y)}=\log y$

Multiply both sides by $\mu(y)$ to get

$\log y\dfrac{\mathrm dx}{\mathrm dy}=\dfrac1yx=\dfrac{\log y}y$
$\dfrac{\mathrm d}{\mathrm dy}[x\log y]=\dfrac{\log y}y$
$x\log y=\displaystyle\int\frac{\log y}y\,\mathrm dy$
$x\log y=\dfrac12\log^2y+C$
$x=\dfrac12\log y+\dfrac C{\log y}$