Answer:
Reflection
Step-by-step explanation:
It is reflecting across the Y axis. It is not a dialation, since it is the same shape, but not a different size. Its not rotation, because it wasnt rotated to get to the new shape. And it is not translation, because it is not exactly the same shape (the shape was mirrored)
The probability would be 2/6 or 1/3
57 = 3 * 19 so he drank 97 * 3 = 291 calories (answer)
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
