Answer:
See Explanation
Step-by-step explanation:
Required
Determine any equation where n = 6
Add n to both sides
<em></em><em> ----- This is 1 equation</em>
Multiply both sides by n
<em></em><em> ----- This is another</em>
<em></em>
Add 5n to both sides
<em></em><em> ---- This is another</em>
Subtract 10 from both sides
<em></em><em> --- This is another</em>
<em>You can have as many equations as possible</em>
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.
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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.
