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Consider all ordered triples of positive real numbers \( (a, b, c) \) such that \[ a^2 + b^2 + c^2 = \frac{5}{2} (ab + bc + ca ) .\] To 3 decimal places, what ...

Find the number of solutions of the system of equations:

\(x+y+z=3\)

\(x^3 +y^3 +z^3 =15\)

\( x^5 +y^5 +z^5 =83\).

In this set, we explore the energy budget of tree circulatory systems. Using fluid mechanics, mass balance, scaling, and dimensional ...

In a triangle \(ABC\) \(\angle A =84^\circ,\) \(\angle C=78^\circ.\) Points \(D\) and \(E\) are taken on the sides \(AB\) and \(BC,\) so that ...

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