Answer:
18
Step-by-step explanation:
Answer:
the dimensions of the box that minimizes the cost are 5 in x 40 in x 40 in
Step-by-step explanation:
since the box has a volume V
V= x*y*z = b=8000 in³
since y=z (square face)
V= x*y² = b=8000 in³
and the cost function is
cost = cost of the square faces * area of square faces + cost of top and bottom * top and bottom areas + cost of the rectangular sides * area of the rectangular sides
C = a* 2*y² + a* 2*x*y + 15*a* 2*x*y = 2*a* y² + 32*a*x*y
to find the optimum we can use Lagrange multipliers , then we have 3 simultaneous equations:
x*y*z = b
Cx - λ*Vx = 0 → 32*a*y - λ*y² = 0 → y*( 32*a-λ*y) = 0 → y=32*a/λ
Cy - λ*Vy = 0 → (4*a*y + 32*a*x) - λ*2*x*y = 0
4*a*32/λ + 32*a*x - λ*2*x*32*a/λ = 0
128*a² /λ + 32*a*x - 64*a*x = 0
32*a*x = 128*a² /λ
x = 4*a/λ
x*y² = b
4*a/λ * (32*a/λ)² = b
(a/λ)³ *4096 = 8000 m³
(a/λ) = ∛ ( 8000 m³/4096 ) = 5/4 in
then
x = 4*a/λ = 4*5/4 in = 5 in
y=32*a/λ = 32*5/4 in = 40 in
then the box has dimensions 5 in x 40 in x 40 in
Answer:
Step-by-step explanation:
Given that there is a group of 17 people in a party. There takes place a number of hand shakes between them.
To show that there is always two people who shake hands with the same total number of people.
If possible let each person did a different number of handshake.
We know that since there are 17 people, there cannot be more than 16 hand shakes for any one in the group.
Hence if different hand shakes must be 0,1,2...16
Consider the last person having 16 hand shakes. He has shaken hand with each other person in the group thus making it clear that no one could have done 0 hand shakes. Since we get a contradiction, our assumption was wrong. That is, there is always two people who shake hands with the same total number of people.
Answer:
60
Step-by-step explanation:
So they are showing you a chart in which the column y is determined by the column x, so you divide y/x in any of the rows so that you get the relation.
100/4=25 (which is the same for every row)
It works pretty much the same for the graph, but the relation is different.
Now instead of a chart you have to figure out the values of x and y by looking at the points that make up the line. For example we have a point that is in the coordinate (2, 60), and that represents that the x value is 2 and its correspondent y is 60. And to find the relation we do it as in the first step but now with 2 and 60.
60/2=30 (which is the same for every point)
Finally we just calculate the value of y both in the graph and the chart when x=12
So for the chart: 12*25= 300
And for the graph: 12*30= 360
The difference between those two is 60.
