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Home » \fracs^3{6\sqrt2} = 100 - Simpleprint

\fracs^3{6\sqrt2} = 100 - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 A plant biologist modifies a rice strain to increase yield by 28% and reduce maturation time by 15%. If the original variety yields 6.5 tons per hectare in 120 days, what is the new yield per day in kilograms?

📌 New yield: 6.5 × 1.28 = <<6.5*1.28=8.32>>8.32 tons/ha = 8,320 kg/ha.

📌 New time: 120 × (1 - 0.15) = 120 × 0.85 = <<120*0.85=102>>102 days.

📌 Yield per day: 8320 / 102 ≈ <<8320/102=81. Charleston=81.58>>81.58 kg/day.

📌 #### 81.58

📌 A pharmacologist designs a drug cocktail where Drug A has a half-life of 4 hours and Drug B has a half-life of 9 hours. A patient receives both simultaneously at 8:00 AM with initial doses of 200 mg and 300 mg respectively. How much of Drug A remains at 5:00 PM the same day?

📌 Time elapsed: 5:00 PM - 8:00 AM = 9 hours.

📌 Number of half-lives for Drug A: 9 / 4 = <<9/4=2.25>>2.25.

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Solution: We are given the recurrence
b_1 = 1, \quad b_{n+1} = f(b_n), \quad \text{where } f(u) = u - \frac{...
We aim to find $ \lim_{n \to \infty} b_n $.
First, observe that $ f(u) < u $ for all $ u > 0 $, since $ \frac{u^4}...
Taking limits on both sides of the recurrence:
\lim_{n \to \infty} b_{n+1} = \lim_{n \to \infty} f(b_n) = f(L).
But since $ \lim_{n \to \infty} b_{n+1} = \lim_{n \to \infty} b_n = L...
L = f(L) = L - \frac{L^4}{4} \Rightarrow \frac{L^4}{4} = 0 \Rightarrow...
Thus, the sequence converges to $ \boxed{0} $.
To confirm convergence, note that $ f(u) $ is continuous and decreasin...

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