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Home » x^2 = 4x - x^2. - Ready Digital AB

x^2 = 4x - x^2. - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 A circle is inscribed in a square with side length 10 cm. What is the area of the region outside the circle but inside the square?

📌 The diameter of the circle is 10 cm, so the radius is 5 cm.

📌 Area of the square is \( 10^2 = 100 \) square cm.

📌 Area of the circle is \( \pi \times 5^2 = 25\pi \) square cm.

📌 Area outside the circle is \( 100 - 25\pi \).

📌 Approximating \( \pi \approx 3.14 \), the area is \( 100 - 78.5 = 21.5 \) square cm.

📌 A loan of $5000 is taken at an annual interest rate of 6% compounded monthly. What is the amount after 2 years?

📌 Monthly interest rate is \( \frac{6}{12} = 0.5\% = 0.005 \).

🔥 Popular Posts

This implies $ n^2 - 1 \equiv 0 \pmod{12} $, or $ (n - 1)(n + 1) \equi...
So $ 12 \mid (n - 1)(n + 1) $.
We test small values of $ n $:
$ n = 1 $: $ 1^2 = 1 \equiv 1 \pmod{12} $ ✅
Thus, the smallest such $ n $ is $ \boxed{1} $.
Solution: Consider four consecutive integers: $ n, n+1, n+2, n+3 $.
The product is $ P = n(n+1)(n+2)(n+3) $.
Among any four consecutive integers, one is divisible by 4.
At least two are even, so the product is divisible by $ 2^3 = 8 $.
Thus, $ P $ is divisible by $ \text{lcm}(8, 3) = 24 $.

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