Find the point in the interior of a triangle for which the product of the distances from that point to the sides of the triangle is maximized.
Archive for June, 2014
Find the values of x,y,z≥0 that maximize the value of f(x,y,z)=xyz, subject to the constraint ax+by+cz=d, where a, b, c and d are positive real numbers.
1) That all three medians of a triangle intersect at a single point (the centroid of the triangle), and that this point divides the medians into segments with a 2:1 length ratio.
2) That the six smaller triangles into which a triangle is divided by its medians have equal area.
In the recent Hall v. Florida decision, the US Supreme Court (besides demonstrating a limited understanding of statistics; but what do you expect, they went to law school) has effectively raised the IQ threshold with regards to the level of mental handicap to bar execution to 75. However, when one consideres that the median black American IQ is 85, with standard deviation 13.5 (here), this cutoff has a z-score of (75-85)/13.5≈0.74, which corresponds to a percentile of 23%. Thus, SCOTUS has effectively called almost a quarter of American blacks retarded.
The opposite of “discriminate” is “indiscriminate”.