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Home » Horizontal range formula: \( R = \fracv^2 \sin(2\theta)g \) - Get link 4share

Horizontal range formula: \( R = \fracv^2 \sin(2\theta)g \) - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \frac{\pi r}{\frac{a + b + h}{2}} = \frac{2\pi r}{a + b + h}

📌 Final answer: $ \boxed{\frac{2\pi r}{a + b + h}} $Question: A robot builder has two gears with 12 and 18 teeth. What is the least common multiple of their teeth counts to realign them?

📌 Solution: To find the least common multiple (LCM) of 12 and 18, factorize both: $12 = 2^2 \cdot 3$ and $18 = 2 \cdot 3^2$. The LCM takes the highest powers of all primes: $2^2 \cdot 3^2 = 4 \cdot 9 = 36$. Thus, the LCM is $\boxed{36}$.

📌 Question: A glaciologist measures ice cores every 5 meters and every 7 meters. What is the minimum depth where both measurements align?

📌 Solution: The minimum depth where both measurements coincide is the LCM of 5 and 7. Since 5 and 7 are prime, LCM(5, 7) = $5 \cdot 7 = 35$. The answer is $\boxed{35}$.

📌 Question: A science journalist recorded 10, 14, and 16 articles published in three months. What is the average number of articles per month?

📌 Solution: The arithmetic mean is calculated by summing the values and dividing by the count: $\frac{10 + 14 + 16}{3} = \frac{40}{3} \approx 13.\overline{3}$. The exact average is $\boxed{\dfrac{40}{3}}$.

📌 Question: The average of $4y - 3$, $2y + 5$, and $y + 7$ is 10. Find $y$.

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