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Find the largest possible integer value of \(x\) such that the expression below is also an integer:

\[\sqrt{x^2+9x}.\]

Two identical, massive rods are hinged at one end and connected together by a massless ideal spring.

If the system is in static equilibrium, what is the angle \(\theta\) (in ...

Reals \(x\) and \(y\) are such that \(x^2+2x+16y^2 \leq 8\). Find \(M+m\), where \(M\) and \(m\) are the maximum and the minimum of the expression ...

Take a point \(P\) on the graph of \(y=2x^2,\) and draw a line going through \(P\) parallel to the \(y\)-axis. Then call the red area \(A:\) the ...

\[ \Large f(x) = x \log_{\log_{|x^2 - 3 | - 2 } (x^2 - 3|x| + 2) } \left( \dfrac{x^3 - |3x+2|}{x^3 - |3x-2|}\right) \]

If the solution to ...

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