2
$\begingroup$

I need to find $y$ in the following formula. I used an online algebraic calculator, but the answer wasn't correct (it omitted the index):

$0.25=1-(\sqrt[r]{|y-v|}×s)$

EDIT

The online calculator gave the following:

$y=v+\dfrac{0.5625}{s^2}$

This doesn't produce correct results, even for r = 2.

1 Answers 1

4

Rearrange to get $(\textstyle\sqrt[r]{|y-v|}\times s)=1-0.25=0.75.$ Divide by $s$ to get $\textstyle\sqrt[r]{|y-v|}=\dfrac{0.75}{s}=\dfrac{3}{4s}.$ Take the $r$th power to get $|y-v|=\left(\dfrac{3}{4s}\right)^r.$ Now, if $y-v$ is non-negative, we have $|y-v|=y-v$, hence $y=v+\left(\dfrac{3}{4s}\right)^r,$ and if $y-v$ is negative, we have $|y-v|=v-y$, hence $y=v-\left(\dfrac{3}{4s}\right)^r.$ Thus, $y=v\pm \left(\dfrac{3}{4s}\right)^r$ and whether the $\pm$ is a $+$ or $-$ depends on the sign of $y-v$. Also, note that this equation doesn't make sense for $s=0$.

  • 0
    All sorted! Thanks again @Zev2012-06-27