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:
I can’t answer
Step-by-step explanation:
Pls take a state photo I can’t tell if it is a rectangle or a polygon
If the sides of the pentagon are the same length, it is probably a regular pentagon. If the angles are all the same within the shape, it is definitely a regular pentagon.
Answer:
60 seconds, 7715 feet
Step-by-step explanation:
Plane A and B start out 615 feet apart, and we find this by subtracting the height of plane A from plane B, getting 5000-4385=615. Now we have to find how many more feet of altitude plane A is gaining per second over plane B.
To find this we subtract 45.25 from 55.5 and get 10.25 feet per second. Now to find out how many seconds until they'll be at the same altitude we simply divide 615 by 10.25, getting 60 seconds.
For the second part, to find the altitude at this point, we simply multiply the altitude gain of one of the planes per second by the time of 60 seconds to get how much altitude they gained over that time, and add it to the starting altitude. Doing this with plane B we get 45.25*60=2715, and we add that to 5000 to get the final answer of 7715.
Answer:
d =(m-q)/a
Step-by-step explanation:
