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Home » \( R(0) = c = 2 \). - DNSFLEX

\( R(0) = c = 2 \). - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 P(X=k) = C(10,k) (0.8)^k (0.2)^(10−k)

📌 P(X=8) = C(10,8) (0.8)^8 (0.2)^2 = 45 × 0.16777216 × 0.04 ≈ 0.30199

📌 P(X=9) = C(10,9) (0.8)^9 (0.2)^1 = 10 × 0.134217728 × 0.2 ≈ 0.268435

📌 P(X=10) = C(10,10) (0.8)^10 = 1 × 0.1073741824 ≈ 0.10737

📌 Sum ≈ 0.30199 + 0.268435 + 0.10737 = <<0.30199+0.268435+0.10737=0.677795>>0.6778 (rounded to 4 decimal places)

📌 #### 0.6778

📌 An ornithologist observes that a flock of birds increases its daily migration distance by 12% each day during a 5-day journey. If they fly 40 km on the first day, what is the total distance flown over the 5 days?

📌 This is a geometric sequence with first term a = 40, ratio r = 1.12, n = 5 terms.

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Also, $\sec x \csc x = \frac{1}{\sin x \cos x}$, so:
2\sec x \csc x = \frac{2}{\sin x \cos x}
And $2\sin x \cos x$ remains.
Let $u = \sin x \cos x$. Since $x \in (0, \frac{\pi}{2})$, $u > 0$, an...
Now rewrite the entire expression in terms of $u$:
\frac{1}{u^2} + \frac{2}{u} + 1 + 2u
Define the function:
f(u) = \frac{1}{u^2} + \frac{2}{u} + 1 + 2u, \quad 0 < u \leq \frac{1}...
We now find the maximum of $f(u)$ on this interval. Note that as $u \t...
But wait: as $u \to 0^+$, $\frac{1}{u^2} \to \infty$, so $f(u) \to \in...

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