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:
easy so first 190-15=175 175 lbs. is the light heavyweight class weight limit
Step-by-step explanation:
Answer:
<em>slope= -3</em>
Step-by-step explanation:
firstly calculating the values of x and y for slopes.
-3/2x - 1/2y = 8
(-3x-y)= 8×2
-(3x+y) = 16
3x+y = -16
if x= -2
-6 + y = -16
y=-10
.: (x₁,y₁)=(-2,-10)
if x= -5
-15 + y = -16
y = -1
.: (x₂,y₂)=(-5,-1)
Using slope formula,
slope= (y₂-y₁)/(x₂-x₁)
slope = [-1-(-10)] / [-5-(-2)]
slope= [-1+10]/[-5+2]
slope= 9/(-3)
slope= -3
Answer:A
Step-by-step explanation:
