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Home » Discover the Hidden Secrets of Atlantic Iowa: A Small Town With Massive Surprises! - Veritas Home Health

Discover the Hidden Secrets of Atlantic Iowa: A Small Town With Massive Surprises! - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A palynologist observes two pollen dispersal patterns repeating every 9 and 12 days. What is the smallest day number when both patterns coincide?

📌 Solution: The smallest day both patterns coincide is the LCM of 9 and 12. Factorize: $9 = 3^2$ and $12 = 2^2 \times 3$. The LCM is $2^2 \times 3^2 = 36$. The patterns coincide on day $\boxed{36}$.

📌 Question: How many lattice points lie on the ellipse $x^2 + 4y^2 = 16$?

📌 Solution: Rewrite the equation as $\frac{x^2}{16} + \frac{y^2}{4} = 1$. Possible integer values for $y$ are $-2, -1, 0, 1, 2$. For each $y$, solve for $x$:

📌 $y = 0$: $x^2 = 16 \Rightarrow x = \pm4$ (2 points).

📌 $y = \pm1$: $x^2 + 4(1) = 16 \Rightarrow x^2 = 12$ (no integer solutions).

📌 $y = \pm2$: $x^2 + 4(4) = 16 \Rightarrow x^2 = 0 \Rightarrow x = 0$ (2 points).

📌 Total lattice points: $2 + 2 = \boxed{4}$.

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