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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Solution:
Given:
![\begin{gathered} P=\text{ \$25,000} \\ r=\text{ 6\%}=\frac{6}{100}=0.06 \\ n=2(compounded\text{ semiannually)} \\ t=2\text{years} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%3D%5Ctext%7B%20%5C%2425%2C000%7D%20%5C%5C%20r%3D%5Ctext%7B%206%5C%25%7D%3D%5Cfrac%7B6%7D%7B100%7D%3D0.06%20%5C%5C%20n%3D2%28compounded%5Ctext%7B%20semiannually%29%7D%20%5C%5C%20t%3D2%5Ctext%7Byears%7D%20%5Cend%7Bgathered%7D)
To get the compound amount, we use the amount formula;
![A=P(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Substituting the values given into the formula,
![\begin{gathered} A=25000(1+\frac{0.06}{2})^{2\times2} \\ A=25000(1+0.03)^4 \\ A=25000(1.03)^4 \\ A=25000\times1.03^4 \\ A=28137.72 \\ \\ \text{Hence,} \\ A=\text{ \$28137.72} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D25000%281%2B%5Cfrac%7B0.06%7D%7B2%7D%29%5E%7B2%5Ctimes2%7D%20%5C%5C%20A%3D25000%281%2B0.03%29%5E4%20%5C%5C%20A%3D25000%281.03%29%5E4%20%5C%5C%20A%3D25000%5Ctimes1.03%5E4%20%5C%5C%20A%3D28137.72%20%5C%5C%20%20%5C%5C%20%5Ctext%7BHence%2C%7D%20%5C%5C%20A%3D%5Ctext%7B%20%5C%2428137.72%7D%20%5Cend%7Bgathered%7D)
Therefore, the compound amount, if she invests for 2 years, is $28137.72
Answer:
200 divided by 15 multiplied by 2
Y = 7^3 + 1 is a constant value, all of the others include an x variable in the form of a linear function.
Answer:
18 inc wide is the qnswer