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
Answer:
the answer is 6 and below
To find the area of the shape which is the shaded area I assume: we must find the sum of the area of the rectangle AECD and triangle BEC
Total Area =area of rectangle AECD + triangle BEC
= 9 * 15 + (1/2) * 6 * 15 = 136 + 45 = 181 square milimeters
Hope that helped!
The <em><u>correct answer</u></em> is:
x=6/7.
Explanation:
First we find the general form by solving for x:
a-bx = cx+d
Subtract a from each side:
a-bx-a = cx+d-a
-bx = cx+d-a
Subtract cx from each side:
-bx-cx = cx+d-a
-bx-cx = d-a
We can divide both sides by -1:
(-bx-cx)/-1 = (d-a)/-1
bx+cx = -d+a
bx+cx = a-d
Factor out an x on the left:
x(b+c) = a-d
Divide both sides by (b+c):
(x(b+c))/(b+c) = (a-d)/(b+c)
x = (a-d)/(b+c)
In this equation, a = 5, b = 6, c = 8 and d = 17:
x = (5-17)/(6+8) = -12/14
This simplifies to -6/7.
