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Home » $ \sum t_i t_j = 7 $ - Aurero

$ \sum t_i t_j = 7 $ - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 R = \frac{17 \cdot 25 \cdot 28}{4 \cdot 210} = \frac{11900}{840} = \frac{1190}{84} = \frac{595}{42} = \frac{85}{6}

📌 \boxed{\frac{85}{6}}

📌 $$Question: If the area of a circle is $ 25\pi $, what is the radius?

📌 Solution: The area of a circle is given by $ A = \pi r^2 $. Setting $ \pi r^2 = 25\pi $, divide both sides by $ \pi $ to get $ r^2 = 25 $. Taking the square root yields $ r = 5 $. \boxed{5}

📌 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}

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