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how many calories in a mango - RTA

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 Question: A marine biologist models the depth of a tide pool as $ d(t) = 10 + 4\sin\left(\frac{\pi t}{12}\right) $. What is the maximum depth?

📌 Solution: The maximum value of $ \sin $ is 1, so the maximum depth occurs when $ \sin\left(\frac{\pi t}{12}\right) = 1 $. Substituting, $ d_{\text{max}} = 10 + 4(1) = 14 $. \boxed{14}

📌 Question: If $ f(x) = 2x + 3 $ and $ g(x) = x^2 - 1 $, compute $ f(g(2)) $.

📌 Solution: First, evaluate $ g(2) = 2^2 - 1 = 4 - 1 = 3 $. Then substitute into $ f(x) $: $ f(3) = 2(3) + 3 = 6 + 3 = 9 $. \boxed{9}

📌 Question: The lines $ 3x + 2y = 6 $ and $ x - y = 1 $ intersect at point $ (a, b) $. Find $ a $.

📌 Solution: Solve the system: From $ x - y = 1 $, express $ x = y + 1 $. Substitute into the first equation: $ 3(y + 1) + 2y = 6 \Rightarrow 3y + 3 + 2y = 6 \Rightarrow 5y = 3 \Rightarrow y = \frac{3}{5} $. Then $ x = \frac{3}{5} + 1 = \frac{8}{5} $. \boxed{\dfrac{8}{5}}

📌 Question: A bioinformatician analyzes a DNA sequence where the number of mutations follows $ m(n) = n^2 - 4n + 7 $. What is $ m(3) $?

📌 Solution: Substitute $ n = 3 $: $ m(3) = 3^2 - 4(3) + 7 = 9 - 12 + 7 = 4 $. \boxed{4}1. A train travels 150 miles in 3 hours at a constant speed. If it continues at the same speed, how many miles will it cover in 5 hours?

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