I have developed the formula to determine the radius of a cylinder with a fixed volume: f (

Agostarawz 2022-07-02 Answered
I have developed the formula to determine the radius of a cylinder with a fixed volume:
f ( x ) = V π 3  
Substituted into the formula for the surface area of a cylinder, I get the following function. This would give me the minimum surface area of a cylinder for a given volume.
S ( V ) = 2 π ( V π 3 ) 2 + 2 π ( 2 V π 3 )
However, my assignment for class asks for a rational function for this problem. How could I take my existing function and make it rational?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Immanuel Glenn
Answered 2022-07-03 Author has 12 answers
I assume the cylinder in question has h = r, so that:
r = V / π 3
The surface area is then:
A = 2 π r 2 + 2 π r h = 4 π r 2 = 4 ( π V ) 2 / 3
This of course is not a rational function in V (and never will be), but is a rational function in r. Perhaps this is what the assignment means?
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-25
True or False. The graph of a rational function may intersect a horizontal asymptote.
asked 2022-06-06
Can anyone help me prove the convexity of this rational function? The man who proved the convexity of function used these facts. But I don't know this fact is correct or not. Here are the facts and function:
1. As N increases, f(N) goes to infinity, That implies that there must be a minima (either at N=0 or somewhere else with a finite N)
2. There cannot be more than one (positive) minima since we're dealing with second order equation.
f ( N ) = + c N 4 + d N 3 + e N 2 + f N + g / + a N 2 + b N
a,b,c,d,e,f,g is constants. and N 1. I guess the second order equation means that between the leading coefficient of the numerator and the denominator is 2.
Are these facts correct? I think fact 1 is no problem, but fact 2 is correct or not.
I am waiting for any answers.
asked 2022-07-07
I'm learning about holes in rational functions in precalculus, and I'm confused as to why they exist, having some knowledge of limits. Say I have a function R ( x ) = ( x 5 ) ( x + 2 ) ( x + 4 ) ( x + 2 ) . If I were to find where the hole lies for this function, I would plug −2 into x 5 x + 4 which would give me a hole at ( 2 , 7 2 ). However, that turns out to be the limit of R ( x ) (using L'Hopital's Rule):
lim x 2 ( x 5 ) ( x + 2 ) ( x + 4 ) ( x + 2 ) = lim x 2 x 2 3 x 10 x 2 + 6 x + 8 = lim x 2 2 x 3 2 x + 6 = 7 2
So why is there a hole in the graph if the limit exists at ( 2 , 7 2 )? Am I misunderstanding the definition of a limit? Thanks.
asked 2022-02-17
Is a rational function or a rational equation or none of these?
1.y=5x32x+1
2.g(x)=7x34x+1x2+3
Help!!!
asked 2022-09-11
Without graphing, what is the transformation that takes place between the graph y = 1 x and the graph of y = 1 x + 5 - 2 ?
asked 2022-06-20
Some rational function is giving me some trouble...
  x 2 9 x + 16 ( x 1 ) ( x 2 + 6 x 7 ) d x
I simplified it like so:
  x 2 9 x + 16 ( x 1 ) 2 ( x + 7 ) d x
If I get it right I can transform it into this:
  A ( x 1 ) + B ( x 1 ) 2 + C ( x + 7 ) d x
And then I get this:
  A x 2 + 6 A x 7 A + B x + C x 2 2 C x + C = x 2 9 x + 16
So I forgot how to get ABC values. Could somebody remind me this?
I am showing all the steps because I am not 100% confident that with have not made any mistakes.
asked 2022-05-23
Let L = C ( X , Y , Z ) be the rational function field over the complex field and σ be automorphism of L over C,
σ ( X ) = Y , σ ( Y ) = Z , σ ( Z ) = X
Moreover let M be the intermediate field of the extension L / C fixed by the group < σ >. I think the degree of filed extension L / M is 3 since the order of group < σ > is 3. But is it true? I know this is true if the extension L / C is finite degree Galois extension. But now the extension L / C is infinite degree extension. So I don't know it is true.
Please give me some advice.