Answer:
Protraction and retraction are the movements of the mandibule. <em>Protraction is when the lower mandibule is pushed forward and retraction is when the lower jaw is pulled backward. </em>You can see in the image I added the example of these movements.
I hope you find this information useful and interesting! Good luck!
Alright, lets get started.
Height of the bin = 4 ft
Length of the bin = 9 ft
Width of the bin = 11 ft
Volume of the bin = 
Volume V 
Volume V
cubic feet
6 books fiils 1 cubic feet
or
1 cubic feet is filled by = 6 books
So, 396 cubic feet is filles by 
So, 396 cubic feet is filles by 
books
It means 2376 books will fit in the storage bin. : Answer
Hope it will help :)
Lateral surface area is the sum of all sides of a 3D object EXCEPT it's top and bottom bases.
Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width: w = 12 - 2x
length: l = 18 - 2x
height: h = x
Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x
Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6
Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160
Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224
And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
If you're only dealing with integers, then the answer is:
[-8 , -3)
If you're dealing with real numbers, then the answer is:
[-8, -3)∪(-3, -2)
