What is a counterexample of the following conjecture? Conjecture: Any number that is divisible by 9 is also divisible by 6 ?
1 answer:
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Answer:
x = 33.8°
Step-by-step explanation:
The resulting diagram we have is a right triangle. To find x, apply trigonometric function.
Reference angle = x
Opposite = 116
Adjacent = 173
Apply TOA:
Tan x = Opp/Adj
x = 33.8° (nearest tenth)
Answer:
π/10
Step-by-step explanation:
When we rotate the region about the y-axis, we get something that looks like a volcano, or a bundt cake. Instead of slicing this into flat washers, we'll slice it in concentric rings, or "shells".
Each shell has a radius x, a thickness dx, and a height y. The volume of an individual shell is:
dV = 2π r h t
dV = 2π x y dx
Since y = x² − x³:
dV = 2π x (x² − x³) dx
dV = 2π (x³ − x⁴) dx
The total volume is the sum of all the shells from x=0 to x=1.
V = ∫ dV
V = ∫₀¹ 2π (x³ − x⁴) dx
V = 2π (¼ x⁴ − ⅕ x⁵) |₀¹
V = 2π (¼ − ⅕)
V = π/10
