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
Answer: C
<u>Explanation:</u>
see 1st attachment
********************************************************
Answer: [-1, 1]
<u>Explanation:</u>
see 2nd attachment
Answer:
m = 8
Step-by-step explanation:
5(m+5)=7m+9 (distribute & evaluate parenthesis)
5(m)+5(5)=7m+9
5m + 25 = 7m + 9 (move all m-terms to one side and constants to the other)
5m - 7m = 9 - 25 (evaluate both sides)
-2m = -16 (divide both sides by -2)
m = (-16) / ( -2) = 8
The answer would be B) -5, 3. The roots can be found where the graph crosses the x-axis, which on this graph is -5 and 3.
Answer:x = 1
Step-by-step explanation:
3x + x/4 = x + 3/4
Subtract x from each side
2x + x/4 = 3/4
Times each side by 4
The 4 beneath the x cancels out
3/4 x 4 = 3
2x + x = 3
3x = 3
Divide each side by 3
x = 1
