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Home » Find the minimum value of this expression for $ x \in \left(0, \frac\pi2\right) $. - go-checkin.com

Find the minimum value of this expression for $ x \in \left(0, \frac\pi2\right) $. - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \boxed{32000\pi}A zoologist in the Amazon recorded that a troop of 18 spider monkeys split into three equal subgroups during foraging. After 2 hours, one subgroup returned to the main group, while 4 monkeys from the largest remaining subgroup were tagged and released back in. If the original drinking pool was replenished every time a subgroup of 6 or more monkeys passed by, how many replenishments occurred due to subgroup sizes over this period?

📌 Subgroup size initially: 18 ÷ 3 = <<18/3=6>>6 monkeys each.

📌 One subgroup returns: now subgroups are two of 6 and one of 12. Largest subgroup has 12 > 6, so replenishment occurs here: 1st replenishment.

📌 After tagging 4 monkeys from the largest subgroup (size 12 → 8), no new replenishment because group size remains 8 ≥ 6, but tagging does not change size.

📌 Only one replenishment occurred at the largest remaining subgroup.

📌 An entrepreneur invested $25,000 in a solar panel startup. The value of the investment grows at a compound annual rate of 12%. After 3 years, she sells 60% of her shares. What is the value of the sold portion?

📌 Value after 3 years: $25,000 × (1 + 0.12)³ = $25,000 × 1.404928 = $35,123.20.

📌 60% of this value: 0.60 × 35,123.20 = $21,073.92.

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