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Mg=Tcos\phi[br]T(AD)=(L/2)sin\thetaMg
TLsin(\theta+\phi)=(L/2)sin\thetaMg \Rightarrow sin(\theta+\phi)=\frac{sin\thetacos\phi}{2}[br]\Rightarrow sin\theta cos\phi+cos\theta sin\phi=\frac{sin\theta cos\phi}{2}[br]\Rightarrow cos\theta sin\phi=-\frac{sin\theta cos\phi}{2}
pq=\frac{x}{a},\ p+q=\frac{y}{a},\ p-q=\sqrt((p+q)^2-4pq)=\sqrt((\frac{y}{a})^2-\frac{4x}a})=\frac{1}{a}\sqrt(y^2-4ax)
Mg=Tcos\phi[br]T(AD)=(L/2)sin\thetaMg
TLsin(\theta+\phi)=(L/2)sin\thetaMg \Rightarrow sin(\theta+\phi)=\frac{sin\thetacos\phi}{2}[br]\Rightarrow sin\theta cos\phi+cos\theta sin\phi=\frac{sin\theta cos\phi}{2}[br]\Rightarrow cos\theta sin\phi=-\frac{sin\theta cos\phi}{2}
\cos \phi=\frac{CE}{\alpha L} \mathrm{\ and\z } \cos \theta=\frac{BE}{L} \Rightarrow \cos \theta=\frac{\alpha}{2}\cos \phi
\Rightarrow \theta=\cos^{-1} \sqrt \Left(\frac{\alpha^2-1}{3}\Right)
I=\int_0^{\lnK}=\Sigma_{r=1}^K[(r-1)(\lnr-\ln(r-1)]
=K \ln K-(\ln2+\ln3+\ln4+...+\lnK)=K \ln K-\ln(K!)
STEP I - Q11
Spoiler
\Rightarrow (5y+6)(y+2) \feq 0
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