The answers in order are
Y= 10/4
Y=5/3
Answer:
4√73
Step-by-step explanation:
x^2= 12^2 + 32^2
x^2= 144+ 1024
x^2=1168
x= 4√73
Step-by-step explanation:
(a) Fₙ₋₁ > 0, so Fₙ₊₁ > Fₙ. Each term is bigger than the one before it, so the function is increasing, meaning the series will diverge to infinity.
(b) Fₙ₊₁ / Fₙ = (Fₙ + Fₙ₋₁) / Fₙ
Divide.
Fₙ₊₁ / Fₙ = 1 + (Fₙ₋₁ / Fₙ)
Rewrite the second fraction using negative exponent.
Fₙ₊₁ / Fₙ = 1 + (Fₙ / Fₙ₋₁)⁻¹
Take the limit of both sides as n approaches infinity.
lim(n→∞) Fₙ₊₁ / Fₙ = 1 + lim(n→∞) (Fₙ / Fₙ₋₁)⁻¹
Substitute with φ.
φ = 1 + φ⁻¹
Solve.
φ² = φ + 1
φ² − φ − 1 = 0
φ = [ -(-1) ± √((-1)² − 4(1)(-1)) ] / 2(1)
φ = (1 ± √5) / 2
Since the ratio can't be negative:
φ = (1 + √5) / 2
Answer: It is 0.7
Step-by-step explanation: Seven tenths is the first digit on the right of the decimal. Hope this helped! If you need anymore help or further explanation I will be glad to help!
