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Home » Let \(y = \sin 2\theta\), where \(y \in (0, 1]\). Define: - DNSFLEX

Let \(y = \sin 2\theta\), where \(y \in (0, 1]\). Define: - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Solution: The sequence is arithmetic with first term $a_1 = 2$ and common difference $d = 3$. The $n$-th term is:

📌 a_n = 2 + (n - 1) \times 3 = 3n - 1

📌 For the 20th term, $a_{20} = 3(20) - 1 = 59$. However, the question asks for the count of terms, not the value. Since the sequence starts at $n = 1$ and ends at $n = 20$, there are $\boxed{20}$ numbers.Question: A square has a perimeter of $ 40 \, \text{cm} $. If each side is increased by $ 2 \, \text{cm} $, by how many square centimeters does the area increase?

📌 Solution: The original side length of the square is $ \frac{40}{4} = 10 \, \text{cm} $. The original area is $ 10^2 = 100 \, \text{cm}^2 $. After increasing each side by $ 2 \, \text{cm} $, the new side length is $ 12 \, \text{cm} $, and the new area is $ 12^2 = 144 \, \text{cm}^2 $. The increase in area is $ 144 - 100 = 44 \, \text{cm}^2 $.

📌 \boxed{44}

📌 Question: Compute $ \cos 360^\circ $.

📌 Solution: The cosine of $ 360^\circ $ corresponds to the x-coordinate of the point on the unit circle at a full rotation from the positive x-axis. This point is $ (1, 0) $, so $ \cos 360^\circ = 1 $.

📌 Question: A cylinder has radius $ r $ and height $ 6r $. A cone has radius $ 2r $ and height $ 3r $. What is the ratio of the volume of the cylinder to the volume of the cone?

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