Answer:
D. a^2 - 6a - 16
Step-by-step explanation:
The product is found using the distributive property.
(a -8)(a +2) = a(a +2) -8(a +2)
= a^2 +2a -8a -16
= a^2 -6a -16 . . . . . matches choice D
Answer: 34
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Work Shown:
S = sum of the first 8 numbers
S/8 = 40 is the mean of those first 8 numbers
S = 8*40
S = 320 so the first 8 numbers add to this value
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R = sum of the 12 remaining values
R/12 = 30
R = 12*30
R = 360 is what the other 12 values add to
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R+S = 360+320 = 680 is what all twenty values add to. Divide this by 20 to get the overall average
(R+S)/20 = 680/20 = 34
The volume of the cylinder is:
V = pi * r ^ 2 * h = 64
The surface area is:
A = 2 * pi * r ^ 2 + 2 * pi * r * h
We write the area as a function of r:
A (r) = 2 * pi * r ^ 2 + 2 * pi * r * (64 / (pi * r ^ 2))
Rewriting:
A (r) = 2 * pi * r ^ 2 + 2 * (64 / r)
A (r) = 2 * pi * r ^ 2 + 128 / r
Deriving:
A '(r) = 4 * pi * r - 128 / r ^ 2
We equal zero and clear r:
0 = 4 * pi * r - 128 / r ^ 2
128 / r ^ 2 = 4 * pi * r
r ^ 3 = 128 / (4 * pi)
r = (128 / (4 * pi)) ^ (1/3)
r = 2.17 cm
The height is:
h = 64 / (pi * r ^ 2)
h = 64 / (pi * (2.17) ^ 2)
h = 4.33 cm
Answer:
The dimensions giving the minimum surface area are:
r = 2.17 cm
h = 4.33 cm