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Does there exist a quadrilateral with the side lengths and diagonal lengths as indicated above?
Note: We are working in R2 with the usual Euclidean geometry.
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A rope of length 90 cm lies in a straight line on a frictionless table, except for a very small piece at one end which hangs down through a hole in the table.
This piece is released, and the rope slides down through the hole. What is the speed (in m/s) of the rope (to 2 decimal places) at the instant it loses contact with the table?
Details: g=9.81 m/s2.
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ABCD is a square with points E and F lying on sides CD and AD, respectively. If the purple area is [BHGI]=120, what is the sum of the pink areas [AHF]+[FGED]+[ICE]?
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A particle moves in 1-dimension. If we plot its velocity and displacement over time, the trajectory forms a circle that's centered at the origin.
Which of the following relations is true regarding its acceleration (a), velocity (v), and displacement (x)?
Note: In the options, k is a positive constant.
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There are n people in a room, who each wear a hat of a specific color. They are able to see other people's hats but not their own.
One of them shouted, "If you can see at least 5 red hats and at least 5 white hats, raise your hand!"
Exactly 10 people raised their hands.
What is the minimum value of n that fits this scenario?
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