Pre-calculus help!!?

This may be hard to understand without the pic, but here goes.





The figure shows an open box with a square base and a partition down the middle. The box is to have a volume of 400 cubic inches. Express the amount of material needed to construct the box ,A, as a function of the length of a side of its square base, x.





The box looks like a shoe box with a partition down the center. The length and width are x, and the height is y.





Help, thanks.

Pre-calculus help!!?
The area of base is x^2


The height is 400/x^2


The 4 sides and the partition each have area = 400/x


So total area = x^2 + 5*400/x= x^2 + 2000/x
Reply:okay, basically you want a function of the material needed to make the box (in area) in terms of the length of base (in this case, x)





Volume, V= 400





The volume can also be expressed in terms of width x length x height. So;





V= x.x.y or V= yx²





Therefore, yx² = 400


y = 400/x² -------------------------- (eq. 1)





Now, consider the surface area of the box (the amount of material)





Surface area, A = 4 sides of box + the base + the partition


Therefore,


A = (4)xy + x² + xy





giving





A = 5xy + x² ----------------------------------------... (eq. 2)





now simply replace y in (eq. 2) with (eq.1) above and you'll get;





A = 2000/x + x²





Done! you have just described the surface area in terms of the box's base length, x. :D all the best bro.



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