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The lotus flower is self-cleaning. Water slides off with ease, and even incredibly viscous substances like honey and glue will come right off.
Like other leaves, the lotus leaf has a waxy cuticle. However, the lotus leaf is significantly more hydrophobic.
Below are illustrations of leaf surfaces. Which surface is most likely to resemble that of a real lotus leaf?
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A unit square is rotated 45∘ counterclockwise about one of its vertices, A.
What is the green area?
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Krishna and Satvik are playing a game called 3-Point Shattering, which has the following rules:
Krishna wins if he can do Step 3. Otherwise, Satvik wins. Here are some examples of how Krishna can win:
Notice that Krishna can still win if Satvik marks all the points the same color.
However, if they played a slightly different game, 4-Point Shattering, where Krishna starts by placing 4 points, who has a winning strategy?
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Below is a multiplication table up to y×y. Find y such that the sum of all the products in the blue square equals 90000.
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Below is the graph of the equation 4x2=y(1−y)(2−y)2 rotated about the y-axis.
Find the volume of the egg.
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