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What is the sum of the digits of the sum of all the integers xxx such that x+123x+123x+123 and x+456x+456x+456 are both square numbers?
Given the circular sector BOABOABOA, where OOO is its center, can we divide it into two parts of even area, using only the compass and the ruler?
Note: This problem …
Consider an equilateral triangle wire loop with a side length S=3S = \sqrt{3}S=3 and a wire radius R=0.01R = 0.01R=0.01. Calculate the self inductance of the wire loop by making …
As shown above, the cyan polygon is surrounded by 10 unit regular heptagons. If the area of the cyan polygon can be expressed as
Asinπ7+Bsin2π7+Csin3π7A\sin\dfrac{\pi}{7} + B\sin\dfrac{2\pi}{7} + C\sin\dfrac{3\pi}{7}Asin7π+Bsin72π+Csin73π
where …
Given a tetrahedron ABCD ABCD ABCD with A(0,0,0),B(10,0,0),C(0,10,0),D(1,1,10) A(0, 0, 0), B(10, 0, 0), C(0, 10, 0) , D(1, 1, 10) A(0,0,0),B(10,0,0),C(0,10,0),D(1,1,10), you select a point ...
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