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.Com
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(39623)   (Show Source): You can put this solution on YOUR website!
You stated THESE two equations:


Solve the second equation for r in terms of h.





easier soon if as

-----might be easiest to use


Substitute for r in the first equation , formula for V.

and start simplifying...

and continue.
, 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),

or finally,
.

RELATED QUESTIONS

Volume of a Cone: The volume V of a right circular cone is V = 1/3 r^2 h. If the... (answered by stanbon)
2) The volume of a cylinder (think about the volume of a can) is given by V = πr2h... (answered by stanbon)
The surface area S and volume V for a can with a top and a bottom are given... (answered by Alan3354)
V=1/3 π r^2 h; If V=50π when r=5, find... (answered by macston)
The volume of a cylinder is given by {{{V= (3.14)r^2*h}}} where r is the radius of the... (answered by Earlsdon)
solve for r and simplify V=[(pi)(r^2)(h)]/(3) V= pi r^2 h _________ (answered by ewatrrr)
I really need some help with this question. Can anyone explain it to me? Thanks! (answered by fractalier)
A right circular cylinder of radius r and height h has volume given by V=πr^2h and... (answered by ankor@dixie-net.com)
2) The volume of a cylinder (think about the volume of a can) is given by V = πr2h... (answered by Earlsdon)