Question

2w^2-4w-128

Answer 1

First of all, you know the formula to the volume of a rectangular box, correct?

V = height x length x width
V = hlw

Secondly, you know that the volume is equal to 128 cubed inches, correct?

128 = hlw

Because you know there is a square cross section, you can assume that length and width are equal, and therefore can replace one with the other. In this case, let's replace length with width

128 = hww
128 = hw^2

To help us in the following steps, we would like to isolate one of the variables. In this case, it would be easier to isolate h than w, which is squared and would take a lot of work to solve. So let's use h.

128 / w^2 = h
h = 128 / w^2

Alright, let's focus on the other formula now. They're asking you to use the least amount of material to construct the box. That means surface area, right? You know the formula for that, too.

S = 2lw + 2lh + 2wh

Once again, because you know it has a square cross section, let's replace lenght with width.

S = 2ww + 2wh + 2wh
S = 2w^2 + 4wh

Now go back to the first formula, and plug it in for the h value.

h = 128 / w^2
S = 2w^2 + 4w(128/w^2)
S = 2w^2 + 512/w

That will be your formula. In order to find the least amount, we will need to find its derivitive.

S = 2w^2 + 512/w
S' = 4w - 512/w^2

If you'd like, you can put the two monomials over the same denominator.

S' = (4w^3 - 512)/w^2

Now set it equal to zero.

0 = (4w^3 - 512)/w^2
0 = 4w^3 - 512
512 = 4w^3
128 = w^3

Find the cubed root of 128 on a calculator. It's about 5.040 inches.

w = 5.040

Now you know your width, and your width and length are the same, so the length is also 5.040 inches.

l = w
l = 5.040

Now that you have your width and your length, let's find the height with our original formula.

128 = hlw
128 = h(5.040)(5.040)
128 = 25.402h
h = 5.040

There. Now you have all three figures. A closed retangular box with a square cross section and a capacity of 128 cubed inches can be constructed with the least amount of material when made in a 5.040 x 5.040 x 5.040 inches box.
Source(s):
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Answer 2

righ but i need an answer like (x+2)(x-3) for example but i need it from 2w^2-4w-128

Answer 3

oh ok hold on

Answer 4

did i typed it in that large comment box

Answer 5

?

Answer 6

what did you get

Answer 7

sorry ill still help but i didnt get this far im in 3rd grade homeschool and my my mother making me learn more in higher grades but i know 12th grade calculus

Answer 8

wow youre smart

Answer 9

its okay ill ask my teacher tomorrow

Answer 10

but if you have time tomorrow ill learn the whole lesson tomorrow if you want.

Answer 11

its okay you domt have to

Answer 12

thank you though

Answer 13

ok ill fan you man see you

Answer 14

You can look at this: http://www.mesacc.edu/~scotz47781/mat120/notes/factoring/trinomials/a_is_not_1/trinomials_a_is_not_1.html

Answer 15

You need to think of two numbers that add up to -4 and that multiply two -256.

Answer 16

If it's impossible, then you have to use the quadratic formula. a=2, b=-4, and c=-128

Answer 17

In this problem, you can't really get something like (___)(___). You can factor out the 2 though and keep it like this: \[2w^2-4w-128=2(w^2-2w-64)\] You can't factor x^2-2w-64.