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Home » The diagonal \(d\) of a square with side \(s\) is given by \(d = s\sqrt2\). - Groen Casting

The diagonal \(d\) of a square with side \(s\) is given by \(d = s\sqrt2\). - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 5Question: What is the sum of all the odd divisors of the number of hours in a week?

📌 Solution: The number of hours in a week is $7 \times 24 = 168$. The prime factorization of $168$ is $2^3 \times 3 \times 7$. The odd divisors are the divisors of $3 \times 7 = 21$, which are $1, 3, 7, 21$. Their sum is $1 + 3 + 7 + 21 = 32$.

📌 Question: What is the greatest common divisor of the number of vowels in "atmospheric" and "mitigation"?

📌 Solution: The word "atmospheric" has $4$ vowels (A, O, A, I), and "mitigation" has $3$ vowels (I, I, I). The GCD of $4$ and $3$ is $1$, since they share no common divisors other than $1$.

📌 Question: What is the smallest three-digit number divisible by the number of letters in "climate" and "modeling"?

📌 Solution: The word "climate" has $7$ letters, and "modeling" has $8$ letters. The LCM of $7$ and $8$ is $56$. The smallest three-digit multiple of $56$ is $112$ (since $56 \times 2 = 112$).

📌 \boxed{112}1. A climatologist observes that the average global temperature has increased by 0.2°C every decade since 1950. If the temperature in 1950 was 14.0°C, what will the average global temperature be in 2050 assuming this trend continues?

📌 From 1950 to 2050 is 100 years, or 10 decades.

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