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ABCD is a quadrilateral with AD=BC, AB=40, CD=20, and m∠A+m∠B=90∘.
What is the area of quadrilateral ABCD?
Hint: Consider how copies of ABCD can be constructed into another shape.
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Let x,y, and z be real numbers satisfying y+zx+z+xy+x+yz=1.
Find the maximum value of y+zx2+z+xy2+x+yz2.
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Tom is jumping around a 4×4 grid of circles with the following conditions:
The maximum number of circles that he can step on is m, and the number of ways of doing so is r.
Find the value of mr.
Note: The grid is fixed on the ground, so a method obtained by rotating another is considered different.
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128=27, but none of the other permutations of the digits of 128 form powers of 2: 182, 218, 281, 812, 821.
Is there any power of 2, 2n, such that at least one of its other permutations is also a power of 2?
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A uniform disk sits on a smooth floor with a rocket strapped to its perimeter. One second after the rocket ignites, how far is the disk's center from where it started, in meters?
Details and Assumptions:
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