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Home » Thus, the radius of the inscribed circle is \(\boxed{3 \text cm}\). - 500apps

Thus, the radius of the inscribed circle is \(\boxed{3 \text cm}\). - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 But if the eigenvalues (intensities) are reported per volcano, and we care about the full assignment, then $3^4 = 81$ is correct.

📌 But profile usually means the distribution, not assignments.

📌 In volcanology, eruption profile often refers to the spectrum of activity, not labeled assignments.

📌 But the question says combinations of eruption profiles, and distinct — and given the clickbait style, likely they want the number of possible **distinct intensity distributions**, i.e., partitions of 4 into at most 3 parts, order irrelevant.

📌 For example: (4,0,0), (3,1,0), (2,2,0), (2,1,1), (1,1,2)—but unique up to permutation.

📌 So number of non-negative integer solutions to $x+y+z=4$, unordered: this is equivalent to number of integer partitions of 4 with at most 3 parts.

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Approximate \( \sqrt{444} \approx 21.07 \).
Solutions: \( n = \frac{-2 + 21.07}{2} \approx 9.535 \) (valid, as \(...
Round to nearest integer: \( n = 10 \).
An isosceles triangle has an area of \(48 \, \text{cm}^2\). If the bas...
Let the base of the original isosceles triangle be \(b\). The area of...
\frac{1}{2} \times b \times h = 48
where \(h\) is the height from the vertex to the base. Using the Pytha...
h = \sqrt{10^2 - \left(\frac{b}{2}\right)^2} = \sqrt{100 - \frac{b^2}{...
Substituting into the area equation:
\frac{1}{2} \times b \times \sqrt{100 - \frac{b^2}{4}} = 48

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