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: 3.3
Step-by-step explanation: maximum was 250 yards and each pool is 75 yards, how many pools did he use? divide the 250 by 75 which you should've gotten 3.33333333333. round to the nearest tenth.
Substitute 2x+1 where y is in the equation:
9x-2(2x+1)=8
Then distribute the -2(2x+1)
9x-4x+2=8
Then combine like terms (the x)
5x+2=8
Then do -2 on both side of the equation sign
5x+2=8
- 2 -2
Then you'd get
5x=6
Then divide 5 on both sides
X= 1.2
Answer:
The maximum height of the ball is 28.2 yards.
Step-by-step explanation:
When we have a quadratic equation in the following format:
The maximum value happens when
The maximum value will be
In this problem, we have that:
So
The maximum height is:
The maximum height of the ball is 28.2 yards.