Solution: For an equilateral triangle with side length \(s\), the radius \(R\) of the circumscribed circle is given by:
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- r = 4
- Thus, the radius of the base of the cone is \(\boxed{4}\).
- Question: A circle is circumscribed around an equilateral triangle with side length \(6\) units. Find the radius of the circumscribed circle.
- Substituting \(s = 6\), we have:
- R = \frac{6}{\sqrt{3}} = 2\sqrt{3}
- Therefore, the radius of the circumscribed circle is \(\boxed{2\sqrt{3}}\).Question: A computational biologist is analyzing a dataset of genetic sequences and encounters the equation $ x\sqrt{x} - 5x + 6\sqrt{x} = 0 $. Compute the sum of all real, non-negative roots of this equation.
