need some calculus help please

[7window]

a box has a rectangular base whose length is twice its width. the box has a volume of 16m cubed. a.) assuming that the box is closed, express the surface area of the box as a function of the width of its base w.



merry xmas and happy new year

 

[joesmoke]

oops read it too quickly

 

[Cogman]

this is not calculus.

b = 2 * w
v = b * w * h
v = 16 m^3
surface area = 2 * (b * w + w * h + h * b)

Given the problem, those should be the formulas you need to solve the problem. I'm not going to do it all for you (though, giving the equations just about does all the hard work).

 

[joesmoke]

its been a long time since i was in ANY math class so this is almost certainly wrong

6W + 32

 

[DrPizza]

A calculus problem would ask you to find the dimensions of the box, under those restraints, that minimize the surface area. Your problem isn't calculus. More like algebra.

Cogman's help should be enough, rather than one of us giving you the answer.

 

[Mr. Pedantic]

This is not calculus. This is rearranging and substituting.

 

[7window]

Thank you all!! I will pass it on to my son in pre-calc.

 

[DrPizza]

its been a long time since i was in ANY math class so this is almost certainly wrong

6W + 32

It certainly is. :awe:

 

[Hacp]

f(w)

 

[borisvodofsky]

its been a long time since i was in ANY math class so this is almost certainly wrong

6W + 32

HAHAHAHA, it happens

this is not calculus.

b = 2 * w
v = b * w * h
v = 16 m^3
surface area = 2 * (b * w + w * h + h * b)

Given the problem, those should be the formulas you need to solve the problem. I'm not going to do it all for you (though, giving the equations just about does all the hard work).

Hang on OP,, do you NEED a CALCULUS answer? as in an integral from 0 to n yadda yadda?

Maybe that's you're question?

 

[borisvodofsky]

f(w)

such that? also you dids nots specifys the uniberses.

 

[Gibson486]

While it's algebra, you can do this with calculus, but it is more trouble than it is worth.

 

[7window]

what would the height be in terms of W? Thanks again!!

 

[Cogman]

what would the height be in terms of W? Thanks again!!

Solve for it yourself. It is literally a 2 step process from the formulas I gave you.

http://www.algebrahelp.com/lessons/simplifying/substitution/
http://www.helpalgebra.com/onlinebook/substitutionmethod.htm
http://www.onlinemathlearning.com/algebra-lesson-substitution.html
http://www.mathsisfun.com/algebra/substitution.html

 

[7window]

I got 8 over w squared. Is this correct. If not I will try again. Thanks Cogman.

 

[Mr. Pedantic]

You know, for problems like this, you can check if you're correct by just putting in a few numbers for the length, width, and height, right? You don't actually need us to tell you whether it's right or not. And it's pretty simple to get the answer from the equations Cogman gave you.

 

[7window]

when we plug it in to a graphing calculator it is not the graph we are looking for or its not a function. thanks

 

[zinfamous]

This is why I always keep a few Asians around.

 

[Gibson486]

Is this calc 3 (multi variable calc?)

 

[7window]

Is this calc 3 (multi variable calc?)

honors pre calc

 

[Gibson486]

honors pre calc

I see....

you can do this in one equation using intergrals, but you are not at that stage yet.

For precalc, the whole point is probably to see if you under stand the meaning of functions.

A(w) = 2x + 2y +2z

x = length = 2w

z = width = w

y = height, which you need to solve in terms of w...I see that you did that part already.

Now when you combine that all together, you just care about the width since that is all you need to know to calculate the surface area.

 

[DrPizza]

yes, 7window, the height is 8/w²

Now, you have all three dimensions in terms of w. Each surface of the box is a rectangle, and there are two surfaces of each particular surface area. Apply the area of a rectangle formula 3 times, and double it.


It does turn out to be a function. Constraints on w are that it is greater than zero. And, taking the derivative of the function (next year in calculus) and setting it equal to zero gives the cubed root of 6 as the value of w which minimizes the surface area. If you graph the function for SA, the lowest point on the curve with have an x-value of cubed root of 6.*
(no guarantees though; I don't have any paper next to me to write this out & double check my work.)

 

[joesmoke]

It certainly is. :awe:

oops... ya, remembering the difference between 2x and x^2 always helps. ill be in the accounting department if anybody needs me! :awe:

 

[7window]

Thanks to everyone that helped especially the combo response off dr pizza ,gibson486 and cogo. Drpizza, Gibson thnks for the last response. Helped us see the light at the end of tunnel. On to the 5 sub question.

 

[DrPizza]

Sub questions? Ahhh, when it asks you to graph it and find the minimum value, I double checked the previous post & it's correct (although the graphing calculator will only give you a decimal value.)