Answer:
a) h = 123/x^2
b) S = x^2 +492/x
c) x ≈ 6.27
d) S'' = 6; area is a minimum (Y)
e) Amin ≈ 117.78 m²
Step-by-step explanation:
a) The volume is given by ...
V = Bh
where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:
123 = x^2·h
h = 123/x^2
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b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.

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c) The derivative of the area with respect to x is ...

When this is zero, area is at an extreme.
![0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583](https://tex.z-dn.net/?f=0%3D2x%20-%5Cdfrac%7B492%7D%7Bx%5E2%7D%5C%5C%5C%5C0%3Dx%5E3-246%5C%5C%5C%5Cx%3D%5Csqrt%5B3%5D%7B246%7D%5Capprox%206.26583)
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d) The second derivative is ...

This is positive, so the value of x found represents a minimum of the area function.
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e) The minimum area is ...

The minimum area of metal used is about 117.78 m².
Well, all you have to do to solve this is multiply 850 times 10, which is 8,500, so that means there are 8 thousands.
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Answer:
K 20
Step-by-step explanation:
f(x) = 7x2 - 4x
f (2) = 7 (2)^2 - 4(2)
= 28 - 8
= 20
Since they replaced the x inside f(x) with 2, just do that the same to the right side, change all x into 2
If you divide 180 by 12 you will get 15 and if you divide 180 by 15 you will get 12 then subtract both products and i t will give you the answer 3