Category: Arithmetic

Question Number 47111 by peter frank last updated on 04/Nov/18 Commented by MrW3 last updated on 04/Nov/18 $$\frac{\mathrm{4}!/\mathrm{2}!}{\mathrm{7}!/\mathrm{3}!/\mathrm{2}!}=\frac{\mathrm{4}!\mathrm{3}!}{\mathrm{7}!}=\frac{\mathrm{3}×\mathrm{2}×\mathrm{1}}{\mathrm{7}×\mathrm{6}×\mathrm{5}}=\frac{\mathrm{1}}{\mathrm{35}} \\ $$ Commented by peter frank last…

Question Number 46860 by 786786AM last updated on 01/Nov/18 $$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{infinity}\:\mathrm{whose}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:\frac{\mathrm{n}}{\mathrm{2}^{\mathrm{n}−\mathrm{1}} }\:. \\ $$ Commented by maxmathsup by imad last updated on 01/Nov/18 $${let}\:{s}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty}…

Question Number 46829 by peter frank last updated on 01/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Nov/18 $${eqn}\:{of}\:{focal}\:{chord}\:{is} \\ $$$${y}={tan}\theta\left({x}−\sqrt{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }\:\right)\:{focaus}\left(\sqrt{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }\:,\mathrm{0}\right) \\…

Question Number 46816 by peter frank last updated on 31/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Nov/18 $${slope}\:{M}_{\mathrm{1}} =\frac{\frac{{a}}{{m}_{\mathrm{2}\:} }−\frac{{a}}{{m}_{\mathrm{1}} }}{{a}\left({m}_{\mathrm{2}} −{m}_{\mathrm{1}} \right)} \\ $$$$\:\:\:\:\:{M}_{\mathrm{1}}…

Question Number 46814 by peter frank last updated on 31/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Nov/18 $${cos}\theta=\frac{{OP}^{\mathrm{2}} +{OQ}^{\mathrm{2}} −{PQ}^{\mathrm{2}} }{\mathrm{2}×{OP}×{OQ}} \\ $$$$\:\:\:=\frac{\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)+\left({c}^{\mathrm{2}}…