SOLUTION: If 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. I did: V(h)=V(r(h)) r(h)? r

Algebra ->  Expressions -> SOLUTION: If 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. I did: V(h)=V(r(h)) r(h)? r      Log On


   

Question 1052763: If
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.
I did: V(h)=V(r(h))
r(h)? r=(-2h+10)/5
then for V(r(h))=(3-((-2h=10/5)^2/3))h
How can I simply this? Thank you
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
You stated THESE two equations: system%28V=%283-%28r%5E2%2F3%29%29%28h%29%2Ch%2F%282-r%29=5%2F2%29


Solve the second equation for r in terms of h.
2h=5%282-r%29
2h=10-5r
-5r=2h-10
r=-2h%2F5%2B2
r=2-2h%2F5
easier soon if as r=2%281-h%2F5%29
r=2%285-h%29%2F5
r=%282%2F5%29%285-h%29-----might be easiest to use


Substitute for r in the first equation , formula for V.
V=%283-%28%282%2F5%29%285-h%29%29%5E2%2F3%29h
and start simplifying...
V=%283-%284%2F25%29%2825-10h%2Bh%5E2%29%2F3%29h
and continue.
V=%283-%284-%2840%2F25%29h%2B%284%2F25%29h%29%2F3%29h, not quite done yet...

...the solving steps shown above might not be the most efficient or neat, but the finished answer in most general form seems to be (work done on paper separately),
V%28h%29=3h-%284%2F3%29h%2B%288%2F15%29h%5E2-%284%2F75%29h%5E3
or finally,
highlight%28V%28h%29=%285%2F3%29h%2B%288%2F15%29h%5E2-%284%2F75%29h%5E3%29.