We'll never know. The shifting mists and misting shifts of time
and consciousness have blocked the lists from our vision, and
we cannot see them.
The smallest amount of material needed is 54 square centimeters
<h3>How to determine the amount of material needed?</h3>
The given parameters are:
Volume = 36 cubic centimeters
Represent length with x, width with y and height with z.
So, we have
x = 3y
The volume is calculated as:
V = xyz
This gives
V = 3y²z
Substitute 36 for V
3y²z = 36
Divide by 3
y²z = 12
Make z the subject
z = 12/y²
The surface area is:
S = 2(xy + xz + yz)
This gives
S = 2(3y² + 3yz + yz)
Evaluate the like terms
S = 2(3y² + 4yz)
Expand
S = 6y² + 8yz
Substitute z = 12/y²
S = 6y² + 8y * 12/y²
This gives
S = 6y² + 96/y
Differentiate
S' = 12y - 96/y²
Set to 0
12y - 96/y² = 0
Multiply through by y²
12y³ - 96 = 0
Add 96 to both sides
12y³ = 96
Divide by 12
y³ = 8
Take the cube root of both sides
y = 2
Recall that:
x = 3y and z = 12/y²
This gives
x = 3 * 2 = 6
z = 12/2² = 3
Recall that:
S = 2(xy + xz + yz)
So, we have:
S = 2(6 * 2 + 3 * 3 + 2 * 3)
Evaluate
S = 54
Hence, the smallest amount of material needed is 54 square centimeters
Read more about surface areas at:
brainly.com/question/76387
#SPJ1
Six billion six hundred fifty-one million two-hundred ninety-seven thousand.
6,651,297,000 rounded to nearest hundred million = 6,700,000,000
So this statement is caused for subtracting. So we have to subtract 6,700.00 from 3,995.00 and the answer would be 2705
Hope this helps :)
