Which of the following figures could have both line symmetry and rotational symmetry?
1 answer:
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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:
We need to find the value of the function at the indicated value.
Indicated values are : f(-7), f(0), f(6), f(7)
To find f(-7), put x = -7 in the given function
To find f(0), put x = 0 in the given function
To find f(6), put x = 6 in the given function
To find f(7), put x = 7 in the given function
Hence, this is the required solution.