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Home » Transform Your Walkway: Discover the Revolutionary Power of Permeable Pavers! - Tacotoon

Transform Your Walkway: Discover the Revolutionary Power of Permeable Pavers! - Tacotoon

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 A rectangular garden measures 15 meters by 10 meters. If a path 1 meter wide is built inside along the perimeter, what is the area of the remaining garden space?

📌 The dimensions of the path-reduced garden are reduced by 2 meters in each dimension (1 meter on each side), resulting in dimensions of 13 meters by 8 meters. The area of the remaining garden is 13 * 8 = 104 square meters.

📌 A cylindrical tank with a radius of 3 meters and a height of 5 meters is filled with water. If a solid sphere with a radius of 2 meters is submerged in the tank, by how many cubic meters does the water level rise?

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📌 #### \(\frac{32}{3} \pi\)

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At $ u = \pm rac{\sqrt{6}}{4} $:
g = 3\left(rac{6}{16}
ight) - 4\left(rac{36}{256}
ight) = rac{18}{16} - rac{144}{256} = rac{9}{8} - rac{9}{16} = ra...
So maximum of $ \sin 3x \sin x $ is $ rac{9}{16} $, thus minimum of $...
But where: $ f(x) = 1 - \sin 3x \sin x $, so minimum of $ f $ is when...
f_{\min} = 1 - rac{9}{16} = rac{7}{16}
But earlier we saw $ f(x) = 1 - rac{1}{2}(\cos 2x - \cos 4x) $. Letâ...
$ \sin^2 rac{\pi}{2} = 1 $, $ \cos^2(2 \cdot rac{\pi}{2}) = \cos^2 \...
Wait: $ \cos(2x) = \cos \pi = -1 $, $ \cos^2(2x) = 1 $, $ \sin^2 x = 1...

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