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 answer is 2 x 10^4 or 2 to the power of 4 (4th power) where;
2 x 10 x 10 x 10 x 10
2 x 10 =20
20 x 10= 200
200 x 10 = 2000
2000 x 10 = 20 000
Expressing a number to a single digit integer times a power of 10 is also writing a number in scientific form,where the number is multiplied by 10 to nth "power". Scientific notation is also called standard index form whereby, too large or too big numbers.
In writing the scientific notation of a number it follows this form: m x 10^n ( m is multiplied to 10 to the power of n) where, m, the coefficient, is the real number and n is the exponent integer.<span><span /></span>
Answer:
W = 450 + 16.83V
Step-by-step explanation:
For 40 hours Carissa
earning = $450
earning for 1 hour of over time = $16.83
multiplying both side by V
earning for v hour of over time = $16.83*V = $16.83V
weekly wage(W) = earning for 40 hours + earning for V hour of over time
W = 450 + 16.83V
Thus equation will be as given below for weekly earning
Answer:
HCF = 1
Step-by-step explanation:
Smallest 2 digit composite number = 10
Smallest 3 digit prime number = 101
Factors of 10 = 1 , 2 , 5
Factors of 101 = 1 , 101
HCF = 1
