DAmon you equaled them to zero that is not rightt
An open-topped box can be made from a rectangular sheet of aluminum,
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
I set them equal to 1512
and then to 2176
THEN
I subtracted 1512 from the first both sides
AND
I subtracted 2176 from the second both sides
PLEASE calm down and think
ya but they are inequalities
1512<x(40-2x)(25-2x)<2176
it does not equal 1512 it is bigger than it hence this (<)
so wouldnt it be
4x^3 - 130x^2 + 1000x - 1512 > 0 instead of equalling
I did the two equations at the limits and said look between them
go back to where Steve is helping you as well and look at the graphs. Watch out though, the third region makes the box higher than half the width so will not work.
If you are still stuck, look at the graphs Steve linked you to carefully and see three areas between the curves on the x axis. Those are values of x where your original function is between the limits. The last area on the right is not feasible because the width would be negative if the box were that high.
To solve the inequality for x, we can first simplify the equation:
1512 < x(40-2x)(25-2x) < 2176
We can then divide the entire inequality by x to get rid of x from the equation:
1512/x < (40-2x)(25-2x) < 2176/x
Next, we can expand the expression on both sides of the inequality:
1512/x < (1000 - 90x + 4x^2) < 2176/x
Now, we can multiply both sides of the inequality by x to eliminate the division:
1512 < x(1000 - 90x + 4x^2) < 2176
Expanding the equation further:
1512 < 1000x - 90x^2 + 4x^3 < 2176
Rearranging the terms:
4x^3 - 90x^2 + 1000x - 1512 < 0
Now, to solve this inequality, we need to find the values of x that satisfy it. One way to do this is by graphing the function and finding the x-values where it is negative.
Alternatively, we can use a numerical method such as the Newton-Raphson method or the bisection method to approximate the values of x that make the inequality true.
Since you mentioned that you have a test soon, it would be best to consult your teacher or textbook for specific methods and techniques that are taught in your class to solve polynomial inequalities like this.
Remember to always double-check your work and solutions, especially when dealing with inequalities. Good luck on your test!