Yes, it will always be a rational number. I'll expound on this by defining what a rational number is. It is any number that can be expressed as a fraction. Otherwise, it is called an irrational number with a non-terminating decimal expansion. So, although 1/3 has a non-terminating decimal expansion because it is equal to 0.33333333...., it is still a rational number because it can be expressed into a fraction.
Answer:
123
Step-by-step explanation:
Answer:
f(x) = 2π (11 + sin x) √(1 + cos²x)
Step-by-step explanation:
Surface area of a curve rotated about y = a is:
S = ∫ 2π (y − a) ds,
where ds = √(1 + (dy/dx)²) dx.
y = 6 + sin x, and a = -5. dy/dx = cos x. Plugging in:
S = ∫₀²ᵖⁱ 2π (6 + sin x − -5) √(1 + cos²x) dx
S = ∫₀²ᵖⁱ 2π (11 + sin x) √(1 + cos²x) dx
Therefore, f(x) = 2π (11 + sin x) √(1 + cos²x).
Answer:
19
Step-by-step explanation:
