Supplementary means they add up to 180
angle 1 = x
angle 2 = x + 166
so x + x + 166 = 180
2x = 14
x = 7
so angle 1 = 7 angle 2 = x + 166 = 173
<span>The answer is 2431.01. At the end of the first year, 5 percent of 2000 is taken and added on to the 2000 you started with. At the end of the second, another 5 percent of that higher number is taken and added on, and so on and so forth until you end up receiving 2431.01 in total after 4 years.</span>
Answer:
8 years.
Step-by-step explanation:
Mara is 6.
6+8=14
Alberto is 20.
20+8=28
14*2=28.
In 8 years, Alberto will be twice Mara's age.
Step-by-step explanation:
f(x) = 1 / (5 + x)
Divide top and bottom by 5.
f(x) = ⅕ / (1 + ⅕x)
f(x) = ⅕ / (1 − (-⅕x))
Write as a geometric series.
f(x) = ∑ₙ₌₀°° ⅕ (-⅕x)ⁿ
f(x) = ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ xⁿ
f(x) = ∑ₙ₌₀°° (-1)ⁿ (⅕)ⁿ⁺¹ xⁿ
Use ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-1)ⁿ⁺¹ (⅕)ⁿ⁺² xⁿ⁺¹] / [(-1)ⁿ (⅕)ⁿ⁺¹ xⁿ]│< 1
lim(n→∞)│-1 (⅕) x│< 1
│x/5│< 1
│x│< 5
-5 < x < 5
If x = -5, ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ (-5)ⁿ = ∑ₙ₌₀°° ⅕ (1)ⁿ, which diverges.
If x = 5, ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ (5)ⁿ = ∑ₙ₌₀°° ⅕ (-1)ⁿ, which diverges.
The interval of convergence is therefore (-5, 5).
