The number line has small marks at each tenth and a big mark at each whole number. So, if you wanted to do -6.3, then you would do the same thing you did with -5 1/2(5.5) and count, in this example, three tick marks to the left of the -6 to get where -6.3 is. Same for all of the other ones there.
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.
Answer:
62.8 m^2
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = (3.14) ( 2)^2 *5
V = 62.8 m^2
Answer:
2077.42
Step-by-step explanation:
There are 52 weeks in a year, so there are 26 "biweekly" weeks in a year.
Cory receieves $54013 per year, so he gets 54013 / 26 dollars biweekly.
We can compute that number, getting 2077.42 dollars.
The answer is the second image from left to right (B). Examples of direct and inverse variations are showed in the image below. :)
