Space base
Astronauts travel to the planet Oobleck and find ruins of civilisation. There is a board with an equation and a graph on it. the astronauts see that the graph uses markings of base 10 but the equations of the graph don’t make sense. Scientists think that it is because Oobleck uses a different number base for equations.
What number base does Oobleck use for equations?
P.S. the figure is a circle, which has horizontal limits -8 & -20, & vertical limits -1 & 11. The equation is the expression of the graph.
The answer is 6.
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1 solution
The expression of a circle is ( x + a ) 2 + ( y + b ) 2 = c 2 ,
Where its centre is ( − a , − b ) and its radii is c .
So the expression for the above graph in base 10 is: ( x + 1 4 ) 2 + ( y − 5 ) 2 = 3 6 .
Using the definition of bases , if the polynomial is expressed in base n , we have 2 n + 2 = 1 4 , n > 5 , n 2 = 3 6 .
So n = 6 .