y=2x so replacr the -y with -2x so 2x+6 is 8x. :)
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
Answer31 i don't know :(
Step-by-step explanation:
Answer:
RS = 16
Step-by-step explanation:
If a line is parallel to a side of a triangle and intersects the other 2 sides , it divides those sides proportionally.
PR is such a line , then
= 
( substitute values )
= 
= 2 ( multiply both sides by RS )
32 = 2 RS ( divide both sides by 2 )
16 = RS
Answer:
4 / 15
Step-by-step explanation:
The total number of ways 2 students can be picked is 15 * 14 = 210 because you have 15 students to begin with and after you pick one, you're left with 14 more to choose from.
The total number of ways a senior and a junior can be picked is 8 * 7 = 56 because there are 8 seniors and 7 juniors.
The probability will then be 56 / 210 = 4 / 15. Hope this helps!
