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Home » If the sum of the squares of two consecutive integers is 85, what are the integers? - Aurero

If the sum of the squares of two consecutive integers is 85, what are the integers? - Aurero

📅 March 16, 2026 👤 scraface

Mar 16, 2026

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w(t) = R\sin\left(\frac{\pi}{6}t + \phi\right)
where $ R = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25 $
So the maximum water level is $ \boxed{25} $.
To find the first time it occurs:
\tan\phi = \frac{24}{7} \Rightarrow \phi = \arctan\left(\frac{24}{7}\r...
Maximum occurs when:
\frac{\pi}{6}t + \phi = \frac{\pi}{2} \Rightarrow t = \frac{6}{\pi} \l...
t \approx \frac{6}{\pi} (1.571 - 1.287) = \frac{6}{\pi} (0.284) \appro...
So the maximum water level is $ \boxed{25} $, and it first occurs appr...
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