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Which is larger?
$\begin{aligned} A &= \sqrt{2} + \sqrt{4} + \cdots + \sqrt{98} + \sqrt{100} \\\\ B &= \sqrt{1} + \sqrt{3} + \cdots + \sqrt{97} + \sqrt{99} + \sqrt{101} \end{aligned}$
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Two plane mirrors (shown to the right) both stand perpendicular to the floor and meet at the angle $\theta = 17^\circ.$ A laser beam is pointed at one of the mirrors such that the beam travels parallel to the other mirror and to the floor.
At how many points will the light be reflected by the two mirrors?
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Clarification: The figure shows the top view of the two mirrors and the laser beam.
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A tennis ball hits the court with angle of incidence $30^\circ,$ and the ball has such a perfect top spin that even after it bounces, it is still spinning fast.
At what angle (in degrees relative to the horizontal) will the ball emerge after the collision?
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Details and Assumptions:
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I've partitioned a unit square into 4 rectangles and each rectangle has perimeter 2, as illustrated in the diagram. I can also cut this unit square into all of the following numbers of rectangles, each with perimeter 2, except for one number.
Which one is it?
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A small ball undergoes a partially elastic collision with a rough horizontal surface. Assume that friction $f=\mu N$ during the contact period, where $N$ is the normal reaction and $\mu$ is the coefficient of friction.
Find the value of the incoming angle $\theta$ (in degrees) such that the horizontal range of the ball after hitting the surface is maximized.
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Details and Assumptions:
Inspired from Rajdeep Brahma
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