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A slab (dark brown) of mass \(m_1 = \SI{40}{\kilo\gram}\) rests on a frictionless floor (orange), and a block (light brown) of mass \(m_2 = \SI{10}{\kilo\gram}\) rests ...

In the above figure, \(P_{1}\) and \(P_{2}\) are massless pulleys, \(P_{1}\) is fixed and \(P_{2}\) can move. Masses \(A,B\) and \(C\) are ...

\[\large f(a+b)=f(a)+f(b)+4ab\]

The functional equation above is true for all real numbers \(a\) and \(b\). Find the value of ...

Let us say that the domain of the function \[f(x)=\sqrt{\log_{\large{\sin x+\cos x}} {(2\sin x})}\] where \(0 \leq x \leq \pi\) is of the ...

If \(\tan \theta =\dfrac 34\) for \(0 \le \theta \le \dfrac \pi 2 \), then \(\cos \dfrac \theta 2 = \dfrac x {\sqrt{y}} \), where \(x\) and \(y\) are positive integers with ...

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