Question

an open-topped box can be made from a rectangular sheet of aluminum, with dimensions 40 cm by 25 cm, by cutting equal-sized squares from the four corners and folding up the sides.

Declare your variables and write a function to calculate the volume of a box that can be formed.

I figured out this part because the function would be f(x)=x(25-2x)(40-2x)

x being the height
25-2x being the width
40-2x being length

Then it asks what cut lengths to the nearest hundredth are acceptable if the volume of the box must be between 1512 and 2176cm^3.

So you would the write 1512<x(40-2x)(25-2x)<2176

how to you solve the inequality to get the x
PLEASE HELP THNX I HAVE A TEST TMR

Answer 1

use
http://www.webmath.com/_answer.php
to get
4 x^3 - 130 x^2 + 1000 x
or just FOIL the last two and multiply by x
Then
4 x^3 - 130 x^2 + 1000 x -1512 = 0
and
4 x^3 - 130 x^2 + 1000 x - 2176 = 0

Answer 2

but how do they both equal zer

Answer 3

then:

http://www.solvemymath.com/online_math_calculator/algebra_combinatorics/polynomial_calculator/polynomial_roots.php

I get 21.85, 2 and 8.65
and
22.4 4 and 6.06

well x between 2 and 4 works

21 and 22 are too big

you might try between 8.65 and 6.06

Answer 4

ok, I tried x = 3 and it works
now for x = 7 which is between those last roots
7(40-14)(25-14) = 7*26*11= 2002
so that region also works

Answer 5

Oh well
4 x^3 - 130 x^2 + 1000 x = 1512
is the same as
4 x^3 - 130 x^2 + 1000 x - 1512 = 0

Answer 6

but its an inequality

Answer 7

oh wait never mind damon sorry

Answer 8

but why are you testing numbers between 2 and 4

Answer 9

on never mind sorry lol

Answer 10

but is it two graphs
s or one

Answer 11

It is two functions and there are three regions where they cross the x axis
Any x between the curves on the x axis should work.
However the third region on the right has too big an x so the width will come out negative
however when I tested in the middle of the first two regions it worked.