Thread: V as a function of H

1. V as a function of H

V = (3-(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.

2. Originally Posted by gearshifter
V = (3-(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.
$\displaystyle V=(3-r^{\frac{2}{3}})h$

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

Rearranging gives:

$\displaystyle h=\frac{5(2-r)}{2}$

$\displaystyle 2h=10-5r$

$\displaystyle 2h-10=-5r$

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

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

Now substitute the second one into the first one and you're home dry!

3. I got:

(-4h^3+125h)/75

Would anybody know if it is correct?

4. We know that:

$\displaystyle V=(3-r^{\frac{2}{3}})h$

and

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

Therefore:

$\displaystyle V=(3-(2-\frac{2h}{5})^{\frac{2}{3}})h$

hmm, I can't actually see a way of cancelling it down from here, can you post your working?