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Home » „Unlock Your Ultimate FFXIV Inventory: Top Online Store Secrets Revealed! - AMAZONAWS

„Unlock Your Ultimate FFXIV Inventory: Top Online Store Secrets Revealed! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Find the sum of the first 20 terms of the arithmetic sequence where the first term is 5 and the common difference is 3.

📌 The formula for the sum \( S_n \) of the first \( n \) terms is \( S_n = \frac{n}{2} (2a + (n-1)d) \).

📌 \( S_{20} = \frac{20}{2} (2 \times 5 + 19 \times 3) = 10 (10 + 57) = 10 \times 67 = 670 \).

📌 A sphere has a surface area of 314 square centimeters. Find its radius. Use the formula \( A = 4\pi r^2 \).

📌 Given \( A = 314 \), solve for \( r \):

📌 \( 4\pi r^2 = 314 \),

📌 \( r^2 = \frac{314}{4\pi} = \frac{314}{12.5664} \approx 25 \),

📌 \( r = \sqrt{25} = 5 \) cm.

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Now the full expression:
+ \sin 2x + rac{4}{\sin^2 2x}
Let \(t = \sin 2x\), \(0 < t \leq 1\) (since \(x \in (0, \pi/2)\Righta...
Define \(f(t) = 1 + t + rac{4}{t^2}\), \(0 < t \leq 1\)
Derivative: \(f'(t) = 1 - rac{8}{t^3}\)
Set to zero: \(1 = rac{8}{t^3} \Rightarrow t^3 = 8 \Rightarrow t = 2\...
Then \(f(1) = 1 + 1 + 4 = 6\)
As \(t o 0^+\), \(f(t) o \infty\), but wait â is \(t\) bounded bel...
But in domain \(0 < x < \pi/2\), \(\sin 2x = 0\) is not attained, but...
But question says "find the maximum", implying it exists. Contradictio...

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