Answer:
where is the Worksheet
Step-by-step explanation:
there is no Worksheet
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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Answer:
I believe the answer is 2. You may want to get a second opinion though because Im not sure
<h3>A regular polygon has equal length sides with equal angles between each side. Any other polygon is an irregular polygon, which by definition has unequal length sides and unequal angles between sides. Circles and shapes that include curves are not polygons - a polygon, by definition, is made up of straight lines.</h3>
hope it helps :-) good morning ☀️.
Solution 1:
In the given statement :
"The settlers traveled west in covered wagons"
The Predicate is <u> traveled west in covered wagons.</u>
So option c. traveled west in covered wagons is the correct choice.
Solution 2:
In the given sentence:
"Soon, telegraph lines provided additional communication to the city."
The simple subject and verb are given by lines provided.
Answer : Option a: lines provided.