Answer:
What u said dosent make sense lol
Answer:3x
Step-by-step explanation:
If 2x+y=2y−x, then the value of y in terms of x can be
3x
I think it is equivalent to 16
hope that helps! :)
since we know those two triangles are similar then we can use proportions.
![\cfrac{AE}{AB}=\cfrac{AD}{AC}\implies \cfrac{14-8}{2x}=\cfrac{14}{2x+4}\implies \cfrac{6}{2x}=\cfrac{14}{2x+4}\implies \cfrac{3}{x}=\cfrac{14}{2x+4} \\\\\\ 6x+12=14x\implies 12=8x\implies \cfrac{12}{8}=x\implies \cfrac{3}{2}=x \\\\[-0.35em] ~\dotfill\\\\ AB=2x+4\implies AB=2\left( \frac{3}{2} \right)+4\implies AB=3+4\implies AB=7](https://tex.z-dn.net/?f=%5Ccfrac%7BAE%7D%7BAB%7D%3D%5Ccfrac%7BAD%7D%7BAC%7D%5Cimplies%20%5Ccfrac%7B14-8%7D%7B2x%7D%3D%5Ccfrac%7B14%7D%7B2x%2B4%7D%5Cimplies%20%5Ccfrac%7B6%7D%7B2x%7D%3D%5Ccfrac%7B14%7D%7B2x%2B4%7D%5Cimplies%20%5Ccfrac%7B3%7D%7Bx%7D%3D%5Ccfrac%7B14%7D%7B2x%2B4%7D%20%5C%5C%5C%5C%5C%5C%206x%2B12%3D14x%5Cimplies%2012%3D8x%5Cimplies%20%5Ccfrac%7B12%7D%7B8%7D%3Dx%5Cimplies%20%5Ccfrac%7B3%7D%7B2%7D%3Dx%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20AB%3D2x%2B4%5Cimplies%20AB%3D2%5Cleft%28%20%5Cfrac%7B3%7D%7B2%7D%20%5Cright%29%2B4%5Cimplies%20AB%3D3%2B4%5Cimplies%20AB%3D7)
The first thing we are going to do for this case is define variables.
We have then:
y = the cost of the box
x = one side of the square base
z = height of the box
The volume of the building is 14,000 cubic feet:
x ^ 2 * z = 14000
We cleared z:
z = (14000 / x ^ 2)
On the other hand, the cost will be:
floor = 4 (x ^ 2)
roof = 3 (x ^ 2)
for the walls:
1 side = 16 (x * (14000 / x ^ 2)) = 16 (14000 / x)
4 sides = 64 (14000 / x) = 896000 / x
The total cost is:
y = floor + roof + walls
y = 4 (x ^ 2) + 3 (x ^ 2) + 896000 / x
y = 7 (x ^ 2) + 896000 / x
We derive the function:
y '= 14x - 896000 / x ^ 2
We match zero:
0 = 14x - 896000 / x ^ 2
We clear x:
14x = 896000 / x ^ 2
x ^ 3 = 896000/14
x = (896000/14) ^ (1/3)
x = 40
min cost (y) occurs when x = 40 ft
Then,
y = 7 * (40 ^ 2) + 896000/40
y = 33600 $
Then the height
z = 14000/40 ^ 2 = 8.75 ft
The price is:
floor = 4 * (40 ^ 2) = 6400
roof = 3 * (40 ^ 2) = 4800
walls = 16 * 4 * (40 * 8.75) = 22400
Total cost = $ 33600 (as calculated previously)
Answer:
The dimensions for minimum cost are:
40 * 40 * 8.75
