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Home » 2x - \frac9611 = -6 \\ - Tacotoon

2x - \frac9611 = -6 \\ - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 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?

📌 Solution: The volume of the cylinder is $ V_{\text{cyl}} = \pi r^2 (6r) = 6\pi r^3 $. The volume of the cone is $ V_{\text{cone}} = \frac{1}{3} \pi (2r)^2 (3r) = \frac{1}{3} \pi (4r^2)(3r) = 4\pi r^3 $. The ratio is:

📌 \frac{V_{\text{cyl}}}{V_{\text{cone}}} = \frac{6\pi r^3}{4\pi r^3} = \frac{3}{2}.

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