Answer:
Remember, the power set of any set S is the set of all subsets of S, including the empty set and S itself.
Then the power set of is
Let r = radius, h = height and l = slant height
Lateral area = rlpi
But l = sqrt(r^2 + h^2)
Lateral area = r sqrt( r^2 + h^2) pi = 20 pi..................(1)
Total area = r sqrt( r^2 + h^2) pi + r^2 pi = 36pi......(2)
Subtract (1) from (2)
r^2 pi = 16 pi
r^2 = 16
r = 4 cm
Put this value in (1) to find h
4sqrt(4^2 + h^2) pi = 20 pi
sqrt(16 + h^2) = 5
Square both sides
16 + h^2 = 25
h^2 = 9
h = 3 cm
Now that we know h and r we can find the volume
V = 1/3 pi r^2 h
= 1/3 pi (4^2)(3)
<span>= 16 pi cm^3 .........( = 50.27 cm^3)
I hope my answer has come to your help. God bless and have a nice day ahead!
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Answer:
A
Step-by-step explanation:
f(x)=x^2-4x+3
x coordinate: -b/2a
-(-4)/2(1)=4/2=2
and to find the y coordinate just plug in the value of -b/2a for x and solve for y
Answer:
12.8
Step-by-step explanation:
8 x 1.6 = 12.8
That should be the answer
Answer:
d³y/dx³ = (-2xy² − 3x³ − 4xy²) / (8y⁵)
Step-by-step explanation:
d²y/dx² = (-2y² − x²) / (4y³)
Take the derivative (use quotient rule and chain rule):
d³y/dx³ = [ (4y³) (-4y dy/dx − 2x) − (-2y² − x²) (12y² dy/dx) ] / (4y³)²
d³y/dx³ = [ (-16y⁴ dy/dx − 8xy³ − (-24y⁴ dy/dx − 12x²y² dy/dx) ] / (16y⁶)
d³y/dx³ = (-16y⁴ dy/dx − 8xy³ + 24y⁴ dy/dx + 12x²y² dy/dx) / (16y⁶)
d³y/dx³ = ((8y⁴ + 12x²y²) dy/dx − 8xy³) / (16y⁶)
d³y/dx³ = ((2y² + 3x²) dy/dx − 2xy) / (4y⁴)
Substitute:
d³y/dx³ = ((2y² + 3x²) (-x / (2y)) − 2xy) / (4y⁴)
d³y/dx³ = ((2y² + 3x²) (-x) − 4xy²) / (8y⁵)
d³y/dx³ = (-2xy² − 3x³ − 4xy²) / (8y⁵)