Question Number 180896 by mr W last updated on 18/Nov/22
$${find}\:{the}\:{maximum}\:{of}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\mathrm{sin}^{\mathrm{3}} \:{x}_{{i}} \\ $$$${if}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\mathrm{sin}\:{x}_{{i}} =\mathrm{0}. \\ $$
Commented by mr W last updated on 20/Nov/22
$${maximum}:\:\mathrm{33}−\frac{\mathrm{33}^{\mathrm{3}} }{\mathrm{67}^{\mathrm{2}} }=\frac{\mathrm{112}\:\mathrm{200}}{\mathrm{4}\:\mathrm{489}}\approx\mathrm{24}.\mathrm{994} \\ $$