Does there exist a quadrilateral with the side lengths and diagonal lengths as indicated above?
Note: We are working in \( \mathbb{R}^2 \) with the usual Euclidean geometry.
by
Calvin Lin
A rope of length \(\SI{90}{\centi\meter}\) 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 \(\text{m/s})\) of the rope (to 2 decimal places) at the instant it loses contact with the table?
Details: \(g = \SI[per-mode=symbol]{9.81}{\meter\per\second\squared}.\)
by
Denton Young
\(ABCD\) 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 \([AHF]+[FGED]+[ICE]?\)
by
Leonardo Joau
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.
by
Md Zuhair
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?
by
Kenneth Tan