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Home » Vertical component: \( v_y = 20 \sin(30^\circ) = 10 \) m/s - AMAZONAWS

Vertical component: \( v_y = 20 \sin(30^\circ) = 10 \) m/s - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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🔥 Popular Posts

Equality occurs when $ \frac{x}{y} = \frac{y}{z} = \frac{z}{x} $, whic...
\frac{(1/3)^2}{1/3} + \frac{(1/3)^2}{1/3} + \frac{(1/3)^2}{1/3} = 3 \c...
Therefore, the minimum value is $ \boxed{1} $.
Question: Compute the sum of the roots of the equation
u\sqrt{u} - 6u + 7\sqrt{u} - 12 = 0,
given that all roots are real and non-negative.
Solution: Let $ \sqrt{u} = t $, so $ u = t^2 $. Substituting into the...
t^2 \cdot t - 6t^2 + 7t - 12 = 0 \Rightarrow t^3 - 6t^2 + 7t - 12 = 0
We are now to find the sum of the roots of the cubic equation
t^3 - 6t^2 + 7t - 12 = 0

📝 Recent Posts

Thus $ \sin 3x \sin x = -1 $ is achievable (e.g., $ x = rac{3\pi}{2}...
Wait â we want to **minimize** $ f(x) = 1 - \sin 3x \sin x $, so we...
So we seek $ \max(\sin 3x \sin x) $. Use identity:
\sin 3x = 3\sin x - 4\sin^3 x
Let $ u = \sin x \in [-1, 1] $. Then:
\sin 3x \sin x = (3u - 4u^3)u = 3u^2 - 4u^4
Define $ g(u) = 3u^2 - 4u^4 $, $ u \in [-1, 1] $.
g'(u) = 6u - 16u^3 = 2u(3 - 8u^2)
Set $ g'(u) = 0 $: $ u = 0 $ or $ 3 - 8u^2 = 0 \Rightarrow u^2 = rac{...
Evaluate $ g(u) $:

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