need help on this fraction equation $2/5=2/3-r/5$

I'm trying to find r. Can anyone give me a step by step?

I'm trying to find r. Can anyone give me a step by step?

Frederick Kramer
2022-07-01
Answered

need help on this fraction equation $2/5=2/3-r/5$

I'm trying to find r. Can anyone give me a step by step?

I'm trying to find r. Can anyone give me a step by step?

You can still ask an expert for help

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Absolute values in logarithms in a solution of differential equation

How have the moduli signs disappeared in the following step:

$\frac{1}{k}(\mathrm{ln}|g+kv|-\mathrm{ln}|g+ku|)=-t$

Therefore

$\mathrm{ln}\left(\frac{g+kv}{g+ku}\right)=-kt$

$g$, $k$ and $u$ are positive constants. $t$ is time, $v$ is velocity.

Context: the above calculations are from solving the equation $dv/dt=-g-kv$ given that $v=u$ when $t=0$, and that $u$, $g$ and $k$ are positive constants.

How have the moduli signs disappeared in the following step:

$\frac{1}{k}(\mathrm{ln}|g+kv|-\mathrm{ln}|g+ku|)=-t$

Therefore

$\mathrm{ln}\left(\frac{g+kv}{g+ku}\right)=-kt$

$g$, $k$ and $u$ are positive constants. $t$ is time, $v$ is velocity.

Context: the above calculations are from solving the equation $dv/dt=-g-kv$ given that $v=u$ when $t=0$, and that $u$, $g$ and $k$ are positive constants.