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Home » Total: $ 6 \cdot 1 \cdot 2^3 = 48 $ - High Altitude Science

Total: $ 6 \cdot 1 \cdot 2^3 = 48 $ - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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🔥 Popular Posts

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Question: A historian is analyzing three randomly selected scientific...
Solution: The total number of ways to choose 3 papers from 12 is:
\binom{12}{3} = 220
To choose exactly 2 papers by Newton and 1 by Leibniz:
\binom{5}{2} \cdot \binom{7}{1} = 10 \cdot 7 = 70
\frac{70}{220} = \frac{7}{22}
\boxed{\frac{7}{22}}
Question: A geotechnical engineer is testing soil samples from 10 diff...
Solution: The total number of ways to choose 3 sites from 10 is:

📝 Recent Posts

f(x) = \sin^2 x + \cos^2(2x)
We use trigonometric identities to simplify and analyze the expression...
\sin^2 x = rac{1 - \cos 2x}{2}, \quad \cos^2(2x) = rac{1 + \cos 4x}{...
f(x) = rac{1 - \cos 2x}{2} + rac{1 + \cos 4x}{2} = rac{1}{2} - rac...
f(x) = 1 + rac{1}{2}(\cos 4x - \cos 2x)
Now, use the identity for $ \cos 4x - \cos 2x $:
\cos A - \cos B = -2 \sin\left(rac{A+B}{2}
ight)\sin\left(rac{A-B}{2}
Let $ A = 4x $, $ B = 2x $:
\cos 4x - \cos 2x = -2 \sin(3x)\sin(x)

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