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2018-05-14 Basic

         

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.

AA and BB are positive real numbers such that A>B,A2+B2=34,AB=15.A > B,\quad A^2+B^2=34,\quad AB=15. What is A2B2?A^2-B^2?

The orange points are the midpoints of the sides of a 6×66\times 6 square.

What is the area of the portion shaded blue?

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.

cosθ+cos(θ+1)+cos(θ+2)++cos(θ+359)\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 θ\theta is an integer?

A certain theta value is shown here, but theta can be any integer. Consider how the cosine changes as the angle increases. A certain theta value is shown here, but theta can be any integer. Consider how the cosine changes as the angle increases.

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