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Given clues:
- Arjun is immediately left of Chetan: ...A, C...
- Dinesh is at extreme right: position 5 = D
- Bimal is between Chetan and Dinesh: ...C, B, D or ...C...B...D
- Eshan is immediately left of Arjun: ...E, A...
From 4 and 1: E, A, C (consecutive)
From 3: after C comes B before D: C, B, D
Combined: E, A, C, B, D β Eshan, Arjun, Chetan, Bimal, Dinesh β
A projectile is launched from the ground with initial velocity $\vec{u} = u_0\hat{i} + v_0\hat{j}$. Gravity acts in the $-y$ direction. The maximum displacement in the $x$-direction is:
Time of flight $= \dfrac{2v_0}{g}$ (time for vertical displacement to return to zero).
Horizontal range $= u_0 \times \dfrac{2v_0}{g} = \mathbf{\dfrac{2u_0 v_0}{g}}$
When the text states 'all organizations can have the same technology and financial resources,' but people create the real difference, it means:
While organizations can access similar technology, capital, and materials, the workforce is the competitive advantage that's hardest to replicate. People create innovation and creativity - they're the distinctive resource that competitors cannot easily copy.
The statement 'If we are to maintain some semblance of that life
If the determinant $\begin{vmatrix}x-4&2x&2x\\2x&x-4&2x\\2x&2x&x-4\end{vmatrix} = (A+Bx)(x-A)^2$, find the ordered pair $(A,B)$.
Apply $R_1\to R_1+R_2+R_3$: each element in row 1 becomes $5x-4$.
Factor out $(5x-4)$: $\Delta = (5x-4)\begin{vmatrix}1&1&1\\2x&x-4&2x\\2x&2x&x-4\end{vmatrix}$
Apply $C_2-C_1, C_3-C_1$: $= (5x-4)\begin{vmatrix}1&0&0\\2x&-x-4&0\\2x&0&-x-4\end{vmatrix} = (5x-4)(x+4)^2$
Comparing with $(A+Bx)(x-A)^2$: $A=-4$, $B=5$. So $(A,B)=\mathbf{(-4,5)}$.
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