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A and B are distinct numbers such that An−Bn is an integer for all positive integers n.
Do both A and B have to be integers?
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Steph Curry regularly wows crowds with his incredible 3-point shooting, as he did in Game 1 of the 2018 NBA championship last Thursday when he made a shot from half-court right at the buzzer.
When he shoots, he aims the ball at the center of the rim, horizontal distance d ahead of him and vertical distance h above. There is some freedom in making the shot — there are an infinite number of pairs of shot velocity and shot angle that will result in the ball passing through the target point (d,h). But the key to a consistent shot is minimizing the effect of small errors in execution. In fact, there's a magic angle at which the variation in both d and h with respect to θ is minimized.
At what angle (in degrees) should he take his shots for the most reproducible three-pointer?
Assumptions and Details:
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f(x)=x+sin(x).
What is the area of one of the infinitely many closed regions between the curves y=f(x) and its inverse function y=f−1(x)?
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Triangle ABC has vertices A=(0,1), B=(1,0), and C=(0,0) in the coordinate plane.
The insides of the sides are lined with mirrors, and then a laser beam is fired from the origin with a slope of 379314.
Which corner of the triangle will the laser beam hit first?
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Two unit circles are joined by many equally spaced strings of length 2 to form a cylinder.
The upper circle is rotated by 90 degrees while the lower is fixed. If there were infinitely many strings, they would serve as the surface of a 3D figure, together with the two circles.
What is the volume inside this 3D figure?
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