Answer:
The box should have base 16ft by 16ft and height 8ft Therefore,dimensions are 16 ft by 16 ft by 8 ft
Step-by-step explanation:
We were given the volume of the tank as, 2048 cubic feet.
Form minimum weight, the surface area must be minimum.
Let the height be h and the lengths be x
the volume will be: V=x²h then substitute the value of volume, we have
2048=hx²
hence
h=2048/x²
Since the amount of material used is directly proportional to the surface area, then the material needs to be minimized by minimizing the surface area.
The surface area of the box described is
A=x²+4xh
Then substitute h into the Area equation we have
A= x² + 4x(2048/x²)
A= x² + 8192/x
We want to minimize
A
dA/dx = -8192/x² + 2 x= 0 for max or min
when dA/dx=0
dA/dx= 2x-8192/x²=0
2x=8192/x²
Hence
2x³=8192
x³=4096
x=₃√(4096)
X=16ft
Then h=2048/x²
h=2048/16²
h=8ft
The box should have base 16ft by 16ft and height 8ft
Hence the dimensions are 16 ft by 16 ft by 8 ft
Answer: (-8, -80)
<u>Step-by-step explanation:</u>
y = 10x
y = -3x - 104
Substitute "y" with "10x" into the second equation, then solve for x:
10x = -3x - 104
13x = -104 <em>added 3x to both sides</em>
x = -8 <em>divided both sides by 13</em>
Next, substitute -8 for x into the first equation to solve for y:
y = 10(-8)
= -80
Answer:
Step-by-step explanation:
A.B = A × B
Dimension of the resultant matrix is (3 × 3)
There are 33 numbers between 1 and 100 divisible by 3, therefore the probability is 33% or 1/3
Answer:
2000
Step-by-step explanation:
let the sum=x
3/5 of x=1200
x=1200×5/3=2000
