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Question-65366

Question Number 65366 by Tawa1 last updated on 29/Jul/19 Commented by Prithwish sen last updated on 29/Jul/19 $$\mathrm{the}\:\mathrm{length}\:\mathrm{is} \\ $$$$=\:\mathrm{3}\:+\:\mathrm{2}×\mathrm{2}\:+\mathrm{2}×\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{3}}\:+\:\mathrm{2}×\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{3}^{\mathrm{2}} }\:+\:\mathrm{2}×\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{3}^{\mathrm{3}} }\:+\:…….…

There-are-20-persons-at-a-party-Maria-dansed-with-7-boys-Stacy-dansed-with-8-boys-Monia-dansed-with-9-boys-and-Eve-dansed-with-all-the-boys-at-the-party-How-many-girls-are-there-at-the-party-

Question Number 130899 by greg_ed last updated on 30/Jan/21 $$\mathrm{There}\:\mathrm{are}\:\mathrm{20}\:\mathrm{persons}\:\mathrm{at}\:\mathrm{a}\:\mathrm{party}. \\ $$$$\mathrm{Maria}\:\mathrm{dansed}\:\mathrm{with}\:\mathrm{7}\:\mathrm{boys}, \\ $$$$\mathrm{Stacy}\:\mathrm{dansed}\:\mathrm{with}\:\mathrm{8}\:\mathrm{boys}, \\ $$$$\mathrm{Monia}\:\mathrm{dansed}\:\mathrm{with}\:\mathrm{9}\:\mathrm{boys}\:\mathrm{and} \\ $$$$\mathrm{Eve}\:\mathrm{dansed}\:\mathrm{with}\:\mathrm{all}\:\mathrm{the}\:\mathrm{boys}\:\mathrm{at}\:\mathrm{the}\:\mathrm{party}. \\ $$$$\boldsymbol{\mathrm{How}}\:\boldsymbol{\mathrm{many}}\:\boldsymbol{\mathrm{girls}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{party}}\:? \\ $$ Commented by mr…

Question-65356

Question Number 65356 by aliesam last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 29/Jul/19 $${let}\:{A}\left({x}\right)\:=\frac{\sqrt{{cos}^{\mathrm{4}} {x}−{cos}\left(\mathrm{2}{x}\right)}}{{ln}\left(\mathrm{1}+\mathrm{3}{x}\right)}\:\:\:\:{we}\:{have}\: \\ $$$${cos}^{\mathrm{4}} {x}\:−{cos}\left(\mathrm{2}{x}\right)\:=\left(\frac{\mathrm{1}+{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}\right)^{\mathrm{2}} −{cos}\left(\mathrm{2}{x}\right) \\…

find-dx-x-1-x-2-x-3-

Question Number 65355 by mathmax by abdo last updated on 28/Jul/19 $${find}\:\int\:\:\:\frac{{dx}}{\:\sqrt{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)}} \\ $$ Commented by Prithwish sen last updated on 29/Jul/19 $$\int\frac{\mathrm{dx}}{\:\sqrt{\left\{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} −\mathrm{1}\right\}\left(\mathrm{x}+\mathrm{2}\right)}}\:\:\:\mathrm{putting}\:\left(\mathrm{x}+\mathrm{2}\right)=\mathrm{a} \\…