Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
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including olympiad champions, researchers, and professionals.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, interactive explorations.
Used and loved by over 6 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
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The area of the large square is 100 and all of the small, blue squares are congruent.
What is the total area shaded blue?
by
Janae Pritchett
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Which is larger, \[\sqrt{ 5 + \frac5{24} }\quad \text{ or }\quad 5 \times \sqrt{\frac5{24} }\,?\]
by
Áron Bán-Szabó
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A wrecking ball is a heavy metal mass that's swung, from a crane, into structures to demolish them. Suppose we release a ball of mass \(M\) from initial angle \(\theta\) and measure the speed at the lowest point in its swing to be \(v_\textrm{max}.\)
If we replace the wrecking ball with one of mass \(2M,\) keeping the length of the chain and the angle \(\theta\) at which the ball is released constant, how will \(v_\textrm{max}\) be affected?
\(\)
Details and Assumptions:
- Neglect air resistance.
- The mass of the chain is zero.
by
Rohit Gupta
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Two players are playing a shortened version of badminton: a 6-point, 3-game match with no deuce. Specifically, in each game, the player who first scores 6 points wins. The winner of the match is the player who first wins 2 out of 3 games.
Is it possible for the loser to have accumulated more points than the winner?
by
Christopher Boo
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\[\large 1 \; \square \; \dfrac{1}{2} \; \square \; \dfrac{1}{3}\; \square \; \dfrac{1}{4}\; \square \; \dfrac{1}{5} \; \square \; \dfrac{1}{6} \; \square \; \dfrac{1}{7} \; \square \; \dfrac{1}{8} \; \square \; \dfrac{1}{9} \; \square \; \dfrac{1}{10} \; \square \; \dfrac{1}{11} \; \square \; \dfrac{1}{12}= 0\]
Can you fill the boxes with \(+ \text{ and } -\) to make this equation true?
by
Áron Bán-Szabó
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