1. velocity

if:

V= (6-(r^2)/(3))*h and (h/(2-r)) = 5/2

write v as a function of h. Simplify the function so that you can express it as a polynomial in h.

I think you have to find what r^2 is...and then plug it in or something? although that doesnt seem to be working for me, however it may be because im doing that wrong as well.....can anyone help?

2. Originally Posted by samtheman17
if:

V= (6-(r^2)/(3))*h and (h/(2-r)) = 5/2

write v as a function of h. Simplify the function so that you can express it as a polynomial in h.

I think you have to find what r^2 is...and then plug it in or something? although that doesnt seem to be working for me, however it may be because im doing that wrong as well.....can anyone help?
$\frac{h}{2 - r} = \frac{5}{2}$

$\frac{2 - r}{h} = \frac{2}{5}$

$2 - r = \frac{2}{5h}$

$r = 2 - \frac{2}{5h}$

$r = \frac{10h - 2}{5h}$.

So

$V = \left(6 - \frac{r^2}{3}\right)h$

$= \left[6 - \frac{\left(\frac{10h - 2}{5h}\right)^2}{3}\right]h$

$= \left[6 - \frac{\frac{(10h - 2)^2}{25h^2}}{3}\right]h$

$= \left[6 - \frac{(10h - 2)^2}{75h^2}\right]h$

$= 6h - \frac{(10h - 2)^2}{75h}$

$= \frac{450h^2 - (10h - 2)^2}{75h}$

$= \frac{450h^2 - 100h^2 + 40h - 4}{75h}$

$= \frac{350h^2 + 40h - 4}{75h}$.