If Earth suddenly stopped spinning, mayhem would ensue.
What would happen to the objects on the surface?
For simplicity, assume that the objects start near the equator.
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\(A\) and \(B\) are positive real numbers such that \[A > B,\quad A^2+B^2=34,\quad AB=15.\] What is \(A^2-B^2?\)
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The orange points are the midpoints of the sides of a \(6\times 6\) square.
What is the area of the portion shaded blue?
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In a race run by A and B, runner A beats B by 10 meters. When runners B and C run the same lap, B beats C by 20 meters.
What happens when runners A and C run the lap?
Note: Assume each runner's speed is constant.
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\[\cos \theta^\circ + \cos (\theta^\circ+1^\circ) + \cos (\theta^\circ+2^\circ) +\cdots + \cos (\theta^\circ+359^\circ)\]
What is the value of this expression when \(\theta\) is an integer?
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