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
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I can't see. This is kinda blurry
Answer:
B = 90
C = 44
D = 46
Step-by-step explanation:
a right angle means that it is 90 degrees, and the combination of all angles must be 180 degrees. This means that angles D and C must equal 90. If you add together the equations assuming the answer is 90, you can solve for x.
(5x - 29) + (2x + 14) = 90
7x - 29 + 14 = 90
7x - 15 = 90
7x = 105
(7x = 105) ÷ 7
x = 15
When you get the value for x you can then plug it into the individual equations to find the degree of the angle
5(15) - 29
75 - 29 = 46
Angle D = 46
2(15) + 14
30 + 14 = 44
Angle C = 44
To check your answer you can add all of the angles together and if they equal 180 then your answer is correct
44 + 46 + 90
90 + 90 = 180
The answer is 7/15
hope it helps
