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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A point P on the line segment GK may be parametrically represented as
t is a real parameter which controls where on the segment P is. t=0 means P=G, t=1 means P=K. We're interested in the t that gives a 3:2 ratio for PG:PK. That's closer to K so t>1/2. t=3/(3+2) = 3/5.
Answer: (26/5, 8)
Answer:
3/8
Step-by-step explanation:
Step 1: Find common denominators
1/2 = 4/8
2/4 = 4/8
Step 2: Evaluate
4/8 + 4/8 - 5/8
8/8 - 5/8
3/8
Alternatively, you can just plug this into a calc to evaluate and get your answer.
Answer & Step-by-step explanation:
Answer after you have shown organized work to get to the solution. 4. If you have ... content that you may have trouble with- search under 6th and 7th grade math. If you are ... Olivia has $143 in the bank. She withdraws. $40. Then she deposits $92. Write an addition expression to represent the situation. Then find the sum. 8
Answer:
Step-by-step explanation:
<u>Put input value instead of the x into equation and calculate the output:</u>
<u>x = -4, then find the value of y:</u>
- y = -5(-4) - 7 = 20 - 7 = 13
The output is 13 when the input is -4
