Given y = ax^2 + (b/x), express volume in terms of x, a, b, and c.

[Gospy]

Given y= ax^2+(b/x)
An open water tank is in the form of a circular cylinder having its base horizontal & axis vertical.
The costs are: In terms of
a for each unit area of base
b for each unit area of curved surface
c for total cost
Given radius is x cm, express volume of tank in terms of x, a, b and c. If x varies, find the cost of base when volume is maximum.


How am I supposed to solve this problem?
Mind helping me? Please.

 

[stapel]

Given y= ax^2+(b/x)

For what does "y" stand? What does this "given" equation represent?

An open water tank is in the form of a circular cylinder having its base horizontal & axis vertical.
The costs are: In terms of
a for each unit area of base
b for each unit area of curved surface
c for total cost
Given radius is x cm, express volume of tank in terms of x, a, b and c.

What is the formula for the area of a circle with radius r? Then what is the expression for the area of the bases of this cylinder (where, in this case, r = x)? What expression then stands for the cost of this area? (Hint: Use what you learned back in pre-algebra for finding total costs, given a base rate and a number of units.)

What is the formula for the surface area of a cylinder with radius r and height h? Then what is the expression for the surface area of the vertical portion of this cylinder (where r = x and h = (whatever unknown variable or constant they gave you for this))? What expression then stands for the cost of this area?

If x varies, find the cost of base when volume is maximum.

How am I supposed to solve this problem?

By using the methods they've taught you in class and in your textbook. By the way, finding max/min points is usually done with calculus, but you're apparently in algebra (that is, before calculus). So what method did your book give for this?

When you reply, please include a clear listing of your efforts so far, starting with the relevant geometrical formulas that you applied. Thank you!

 

[Gospy]

For what does "y" stand? What does this "given" equation represent?


What is the formula for the area of a circle with radius r? Then what is the expression for the area of the bases of this cylinder (where, in this case, r = x)? What expression then stands for the cost of this area? (Hint: Use what you learned back in pre-algebra for finding total costs, given a base rate and a number of units.)

What is the formula for the surface area of a cylinder with radius r and height h? Then what is the expression for the surface area of the vertical portion of this cylinder (where r = x and h = (whatever unknown variable or constant they gave you for this))? What expression then stands for the cost of this area?


By using the methods they've taught you in class and in your textbook. By the way, finding max/min points is usually done with calculus, but you're apparently in algebra (that is, before calculus). So what method did your book give for this?

When you reply, please include a clear listing of your efforts so far, starting with the relevant geometrical formulas that you applied. Thank you!

Hello, first of all, thanks for the response! I got this question on an exam (it's actually pre-calculus, so I know how to differentiate, that's the way to find the maximum since a and b are the constants)

The thing is, the problem may be flawed because I didn't remember it correctly. What could a possible correct version of this question be? I am REALLY sorry for the inconvenience and the waste of time, but I'd appreciate it!

Thank you so much.

 

[Gospy]

For what does "y" stand? What does this "given" equation represent?


What is the formula for the area of a circle with radius r? Then what is the expression for the area of the bases of this cylinder (where, in this case, r = x)? What expression then stands for the cost of this area? (Hint: Use what you learned back in pre-algebra for finding total costs, given a base rate and a number of units.)

What is the formula for the surface area of a cylinder with radius r and height h? Then what is the expression for the surface area of the vertical portion of this cylinder (where r = x and h = (whatever unknown variable or constant they gave you for this))? What expression then stands for the cost of this area?


By using the methods they've taught you in class and in your textbook. By the way, finding max/min points is usually done with calculus, but you're apparently in algebra (that is, before calculus). So what method did your book give for this?

When you reply, please include a clear listing of your efforts so far, starting with the relevant geometrical formulas that you applied. Thank you!

I am so sorry! I should've posted this on calculus, I ended up doing it with differentiation. But I don't think it's ok, because of that y=ax^2+b/x thingy. I don't know if I can move this thread to calculus or not, but this is what I got:

But what the **** is the y=ax^2+b/x there for!!!

What do you think? I really got nothing else on it and I haven't started university yet so no teacher to ask, would you direct me please?

 

[stapel]

I got this question on an exam (it's actually pre-calculus, so I know how to differentiate....)[/tex]
Pre-calculus is algebra. If you're doing differentiation, then you're doing calculus. I can't speak to how your particular institution is naming its courses, but it seems to be quite non-standard. :shock:

The thing is, [my statement of] the problem may be flawed because I didn't remember it correctly. What could a possible correct version of this question be?

The statement seems fine. The question is the purpose and meaning of the "y=" formulation.

I ended up doing it with differentiation. But I don't think it's ok, because of that y=ax^2+b/x thingy.

Until we can see the actual exercise, there is likely no way for us to understand, let alone explain, what the exercise was doing with that formula. Sorry.