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Home » 幅を \( w \) とします。すると、長さは \( 2w \) です。 - Portal da AcÃºstica

幅を \( w \) とします。すると、長さは \( 2w \) です。 - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 If the sum of the first \(n\) natural numbers is given by \(\frac{n(n+1)}{2}\), find \(n\) when the sum is 210.

📌 Set up the equation: \(\frac{n(n+1)}{2} = 210\).

📌 Multiply by 2: \(n(n+1) = 420\).

📌 Solve \(n^2 + n - 420 = 0\) using the quadratic formula:

📌 \(n = \frac{-1 \pm \sqrt{1 + 1680}}{2} = \frac{-1 \pm 41}{2}\).

📌 The positive solution is \(n = 20\).

📌 A triangle has sides of lengths 7, 24, and 25. Verify if it is a right triangle using the Pythagorean theorem.

📌 Check \(7^2 + 24^2 = 25^2\).

🔥 Popular Posts

\(\boxed{\frac{\pi}{6}}\)
Question:** A virologist models a viral capsid as a sphere with radius...
The volume \(V_s\) of the sphere is given by:
\[ V_s = \frac{4}{3}\pi r^3 \]
where \(r = 3\) nm:
\[ V_s = \frac{4}{3}\pi (3)^3 = \frac{4}{3}\pi \times 27 = 36\pi \]
The volume \(V_c\) of the cylinder is given by:
\[ V_c = \pi r^2 h \]
where \(r = 2\) nm and \(h = 6\) nm:
\[ V_c = \pi (2)^2 \times 6 = \pi \times 4 \times 6 = 24\pi \]

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