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.
The accurate definition is that the circle that's closest to the 2 dimensional figure where all the set of point in the plane should be equal distance.
<h3>How to illustrate a circle?</h3>
A circle simply means the set of all the points that are the same distance from a given point.
In this case, the contradiction is that the definition should be applied to three dimensional space so that it will be a sphere.
The accurate definition is that the circle that's closest to the 2 dimensional figure where all the set of point in the plane should be equal distance. A example is a point or line.
Learn more about circle on:
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ANSWER
w=48,l=60
EXPLANATION
Let the width of the field be, w , then,
the length of the field will be:
The area of a rectangle is
This implies that:
Expand
This implies that,
The dimensions are positive, the width is 48 and the length is 12+48=60
Answer:
Gregs age is 13
Step-by-step explanation:
13 + 13 = 26
which is equivalent to 13 × 2 = 26
