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📰 Solution: For vectors to be orthogonal, their dot product must be zero: $\mathbf{m} \cdot \mathbf{n} = x(1) + 2(-1) = x - 2 = 0$. Solving gives $x = 2$. The final answer is $\boxed{2}$. 📰 Question: A science policy analyst evaluates the spread of a technology using roots of $z^4 + z^2 + 1 = 0$. The maximum imaginary part of a root can be expressed as $\sin\theta$. Find $\theta$ in radians. 📰 Solution: Let $w = z^2$, so $w^2 + w + 1 = 0$. Solving gives $w = \frac{-1 \pm \sqrt{-3}}{2} = e^{\pm 2\pi i/3}$. Thus, $z^2 = e^{\pm 2\pi i/3}$, so $z = e^{\pm \pi i/3 + \pi i k/2}$ for $k = 0, 1$. The roots have angles $\pi/3, 5\pi/3, 7\pi/3, 11\pi/3$, but 📰 Painttool Sai Download 9698762 📰 Coral Cover Declined From 45 To 32 Over 10 Years What Is The Average Annual Percent Decrease Assuming Exponential Decay 4932968 📰 Julia Hart Exposed The Mind Blowing Journey Behind Her Unstoppable Rise 4786994 📰 See How To Unzoom Like A Tech Guru In Just Secondsupdate Your Skills Now 4773651 📰 Foliage Plants 5329591 📰 Climate For The Northeast 4022201 📰 Long Island Community Hospital 1313691 📰 No Frizzes No Fusssimplicity Login Works Like Youve Never Seen Before 9836630 📰 Digimon Story The Hidden Truth No Fan Should Missstart Now 9783776 📰 You Wont Believe How Many Awesome Winnie The Pooh Movies Are Hidden In This Epic Collection 9996632 📰 From Frustrated Users To Happy Clients How A Ux Designer Mastered The Art 6041161 📰 Online Games Running Games 7669736 📰 Capability Statement Examples 3823810 📰 Explosive Breakthrough At 1122 Forge Players Are Losing Their Minds Over This Update 4559111 📰 Gta Vice City Free Download Pc 3743638