When dividing 1/8 by 2
we have to first take the reciprocal of 2
reciprocal is when the numerator and denominator are exchanged
2 when written as a fraction is
we need to find the reciprocal of
which is
then
when 'of' function is used it means to multiply the 2 fractions
when multiplying fractions multiply the numerators by numerators and multiply denominators by denominators
is
answer is
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:
20,000
Step-by-step explanation:
Add it up or multiply
2 to the second power times 7 to the seventh power
let us represent the question with a diagram for better understanding.
Using Pythagoras theorem
![\begin{gathered} c^2=12^2+9^2 \\ c^2=144+81 \\ c=\sqrt[\square]{225} \\ c=15\text{ km} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%5E2%3D12%5E2%2B9%5E2%20%5C%5C%20c%5E2%3D144%2B81%20%5C%5C%20c%3D%5Csqrt%5B%5Csquare%5D%7B225%7D%20%5C%5C%20c%3D15%5Ctext%7B%20km%7D%20%5Cend%7Bgathered%7D)
The distance between the parents and grandparent house = 15 km
