Answer: ZB = 48 degree
Explanation:
Complementary angle means 2 angel add together and create a right angle (90 degree).
Thus, ZA + ZB = 90 degree
But ZA = 42 degree
=> 42 degree + ZB = 90 degree
=> ZB = (90 - 42)degree
=> ZB = 48 degree
Answer:
x = 5, y = 20
Step-by-step explanation:
Since AB and CD are parallel, then
∠ AOC and ∠ OCD are Alternate angles and congruent, thus
12x + 8 = 68 ( subtract 8 from both sides )
12x = 60 ( divide both sides by 12 )
x = 5
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∠ OCD and 5y + 12 are adjacent angles and supplementary, thus
5y + 12 + 68 = 180 , that is
5y + 80 = 180 ( subtract 80 from both sides )
5y = 100 ( divide both sides by 5 )
y = 20
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
128w^2x^2-36y^2z^2
or if you need it factored
4(32w^2x^2-9y^2z^2)
Answer:
Start at the Origin, and then go up 5, Right 1.
Step-by-step explanation:
