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Home » So only \(n \equiv 2 \pmod5\) works. - DNSFLEX

So only \(n \equiv 2 \pmod5\) works. - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Thus, the expression is a perfect square:

📌 4x^2 - 20x + 25 = (2x - 5)^2

📌 2x - 5 = 0

📌 2x = 5 \quad \Rightarrow \quad x = \frac{5}{2}

📌 Thus, the value of \(x\) is \(\boxed{\frac{5}{2}}\).**Question:** An electrical engineer is designing a battery system with compartments shaped like squares. If each compartment can hold exactly one 1x1 square cell, what is the smallest number of 1x1 compartments needed to cover a square region of 16 square units completely?

📌 To cover a square region of 16 square units, we need to determine the side length of the square. Since the area of a square is given by the side length squared, we have:

📌 \[ \text{Side length}^2 = 16 \]

📌 \[ \text{Side length} = \sqrt{16} = 4 \]

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To find the ratio of the area of the circle to the area of the octagon...
The formula for the area of a circle is:
A_{\text{circle}} = \pi x^2
Area of the Octagon:
For a regular octagon with side length \( s = x \), the area \( A \) i...
A_{\text{octagon}} = 2(1 + \sqrt{2})s^2 = 2(1 + \sqrt{2})x^2
A_{\text{octagon}} = 2(1 + \sqrt{2})x^2
The ratio of the area of the circle to the area of the octagon is:
\text{Ratio} = \frac{A_{\text{circle}}}{A_{\text{octagon}}} = \frac{\p...
Thus, the ratio of the area of the circle to the area of the octagon i...

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