In a sample of people on the school board 2 out of 5 were in favor of a new high school being built if 3,500 people vote in the
2 answers:
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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.
Step-by-step explanation:
2(x-3)=5(x-3)+10
=> 2x - 6 = 5x - 15 + 10
=> -6 + 15 -10 = 5x - 2x
=> 5x -2x = 15 - 6 - 10
=> 3x = 15 - 16
=> 3x = -1