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Home » Increasing each side by \(50\%\) gives a new side length: - Midis

Increasing each side by \(50\%\) gives a new side length: - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Let \(a\) be the distance from the wall. Then \(a^2 + 12^2 = 15^2\).

📌 So, \(a^2 + 144 = 225\) â \(a^2 = 81\) â \(a = 9\).

📌 Evaluate the integral \(\int_0^1 (3x^2 + 2x) \, dx\).

📌 Integrate term by term: \(\int 3x^2 dx = x^3\), \(\int 2x dx = x^2\), so \(\int_0^1 (3x^2 + 2x) dx = [x^3 + x^2]_0^1 = (1 + 1) - (0 + 0) = 2\).

📌 A function \(f(x) = rac{x^2 - 4}{x - 2}\) is defined for \(x

📌 e 2\). Simplify and find \(\lim_{x o 2} f(x)\).

📌 Factor numerator: \(x^2 - 4 = (x - 2)(x + 2)\), so \(f(x) = rac{(x - 2)(x + 2)}{x - 2} = x + 2\) for \(x

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Problem 2:
A regular hexagon is inscribed in a circle with a radius of 12 cm. Wha...
A regular hexagon inscribed in a circle has each of its vertices lying...
Radius of circle = 12 cm
Number of sides of hexagon = 6
Therefore, each side length of the hexagon is:
s = 12 \text{ cm}
The perimeter \(P\) of a regular hexagon is:
P = 6 \times s = 6 \times 12 = 72 \text{ cm}
So, the perimeter of the hexagon is:

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