Prove that given an unlimited supply of 6-cent coins, 10-cent coins, and 15-cent coins, one can make any amount of change larger
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The third coordinate of the equilateral triangle is . Ir can be obtained by distance formula.
What is distance formula?
It gives the distance between two coordinates.
Distance formula is given by the following expression:
Consider the third cordinate is (x,0) and x is positive because it is on tight side on the x axis.
Now, since the triangle is equilateral hence, the distance of (x,0) from (0, -a) and (0, a) should be equal to distance between (0, -a) and (0, a).
Now, caculate the distance between (0,-a) and (0, a).
Now, distance between (x,0) and (0, a) should be 2a.
Now, square on both the sides.
and
But the negative value of x is not possible because the coordinate lies on the right side.
Hence, the third coordinate of equilateral triangle is .
Learn more about distance formula from the following link:
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