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
Answer:
The investment will generate $ 60 in interest, with which the new balance will be $ 1060.
Step-by-step explanation:
To determine how much interest would $ 1,000 earn in one year at a rate of 6%, compounded annually, and what would be the new balance, the following calculations must be performed:
1000 x (1 + 0.06 / 1) ^ 1x1 = X
1000 x 1.06 ^ 1 = X
1000 x 1.06 = X
1060 = X
Therefore, the investment will generate $ 60 in interest, with which the new balance will be $ 1060.
Answer:
Step-by-step explanation:
two-dimension
Answer:
She is 17 miles from the airport.
Step-by-step explanation:
Formula
Taxi base + Taxi per mile cost(miles) = Uber base + Uber per mile cost(miles)
2.60 + 2.70m = 1.75 + 2.75m
subtract 2.70m from both sides of equation
2.60 = 1.75 + .05m
subtract 1.75 from both sides of equation
0.85 = .05m
divide .05 to both sides of equation
m = 17 miles