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Let \(r = \sqrtx^2 + y^2 = c \sin^2\phi\) - AMAZONAWS
Let \(r = \sqrtx^2 + y^2 = c \sin^2\phi\) - AMAZONAWS
📅 March 6, 2026
👤 scraface
Mar 06, 2026
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📌 Solution: First, choose 4 distinct layers from 7, which is $ \binom{7}{4} = 35 $. Then, select 2 of these 4 layers to apply the "pump water" operation, which can be done in $ \binom{4}{2} = 6 $ ways. The remaining 2 layers are analyzed without the operation, and the sequence of 4 layers is ordered, giving $ 4! = 24 $ permutations. However, since the operation affects only the selection (not the order of non-pump layers), the total is:
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📌 Thus, all vectors \(egin{bmatrix} a \ - rac{4a + 5}{3} \end{bmatrix}\) satisfy the condition.
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