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:
d
Step-by-step explanation:
becuase it is
Just multiply 17 x 6=102
Then write 0.102
Answer:
HL
SAS
SSS
Step-by-step explanation:
Since these are right triangles, and you have the two hypotenuses are congruent to each other and two legs that are also congruent to each other, then HL can be applied.
For HA to work we must have been given something else about one of those angle (besides the 90 degree one).
Since you have two corresponding sides that are congruent, then the 90 degree angles in both are congruent, and then the sides right after that 90 degree angle are also congruent to each other, so SAS can be applied.
We can't use AAS. We only know something about one angle per each triangle due to the markers.
LA? Needed another angle besides the 90 degree one.
All three corresponding sides are congruent. The markers tell us this. So we can apply SSS.
The difference between properties of equality and properties of inequality that you need to take into account when you are solving equalities and inequalities is the effect that some operations have on the sign.
1) The multiplicative property of equality permits you to multiplicate both members (sides) on an equality times a factor and the equality will remain. But in an inequality, while the factor is positive the inequality will remain but when the factor is negative, the sign of the inequality will change.
2) The same is true about the division property:
3) When you use othe functions like absoulte value and square root you will also need to be attentive of the effect of the function on the sign of the equality,.
