Answer:
x = y = 26 cm; z = 13 cm
Step-by-step explanation:
We can calculate the dimensions of the square base as
∛(2·8788) = 26 cm
the height of the box will be half of 26/2 which is 13 cm.
x = y = 26 cm; z = 13 cm
then the minimum area for the given volume can be calculated using what we call Lagrange multipliers, this makes it easier
area = xy +2(xz +yz)
But we were given the volume as 8788
Now we will make the partial derivatives of L to be in respect to the cordinates x, y, z, as well as λ to be equal to zero, then
L = xy +2(xz +yz) +λ(xyz -8788)
For x: we have
y+2z +λyz=0
For y we have
y: x +2z +λxz=0
For z we have 2x+2y +λxy=0............eqn(*)
For we have xyz -8788=0
If we simplify the partial derivative equation of y and x above then we have
λ = (y +2z)/(yz).
= 1/z +2/y............eqn(1)
λ = (x +2z)/(xz)
= 1/z +2/x.............eqn(2)
Set eqn(1 and 2) to equate we have
1/z +2/y = 1/z +2/x
x = y
From eqn(*) we can get z
λ = (2x +2y)/(xy) = 2/y +2/x
If we simplify we have
1/z +2y = 2/x +2/y
Then z = x/2
26/2 =13
Therefore,
x = y = 2z = ∛(2·8788)
X= 26
y = 26 cm
z = 13 cm
B. -5/2 is the correct answer
Answer:
0.995
Step-by-step explanation:
Total for
a = 368
b = 320
c = 269
d = 149
All accurate orders = 965
Not accurate order = 141
Total = 1106
We are required to find probability that all three orders are from A
= 368 + 367 + 366
= 1101
1101/1106 = 0.995
Answer:
-37
Step-by-step explanation:
1) to find the equation of the given line (its slop-interception form is y=mx+i, where m - slop, i - interception):
a) y=2x+i, where m=2;
b) it is possible to calculate the value of 'i' after the substitution the point (5;-3) into the equation y=2x+i:
-3=2*5+i; ⇒ i= -13;
c) the equation of the given line is y=2x-13.
2) to calculate the value of 'R':
if to substitute the point (-12;R) into the equation y=2x-13, then
R=2*(-12)-13; ⇒ R= -37.