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Home » Solutions are \(x = 3\) or \(x = 1\). - ClickBalance

Solutions are \(x = 3\) or \(x = 1\). - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 \frac{V_{\text{cone}}}{V_{\text{cylinder}}} = \frac{\frac{1}{3} \pi r^3}{\pi r^3} = \frac{1}{3}

📌 Thus, the final answer is \(\boxed{\frac{1}{3}}\).

📌 A regular tetrahedron has a side length of $s$. Determine the ratio of the volume of the tetrahedron to the volume of the sphere circumscribed around it.

📌 The volume of a regular tetrahedron with side length $s$ is given by:

📌 V_{\text{tetrahedron}} = \frac{\sqrt{2}}{12} s^3

📌 The radius of the circumscribed sphere (circumradius) of a regular tetrahedron is:

📌 R = \frac{s \sqrt{6}}{4}

📌 The volume of the sphere is:

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Let the numbers be \( x \) and \( 20 - x \).
Then \( x(20 - x) = 96 \).
\( 20x - x^2 = 96 \) → \( x^2 - 20x + 96 = 0 \).
Factoring: \( (x - 12)(x - 8) = 0 \) → \( x = 12 \) or \( x = 8 \).
The larger number is 12.
A circle has a circumference of \( 10\pi \) units. What is the area of...
Circumference \( = 2\pi r = 10\pi \) → \( r = 5 \).
The diagonal of the inscribed square equals the diameter: \( 2r = 10 \...
Let side of square be \( s \). Then \( s\sqrt{2} = 10 \) → \( s = \fra...
Area = \( s^2 = (5\sqrt{2})^2 = 50 \).

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