Question Number 173339 by AgniMath last updated on 10/Jul/22 Commented by som(math1967) last updated on 10/Jul/22 $$\:{if}\:{it}\:\frac{{x}}{{a}+{x}}\:+\frac{{y}}{{b}+{y}}\:+\frac{{z}}{{c}+{z}} \\ $$$$=\frac{{ax}}{{a}^{\mathrm{2}} +{ax}}\:+\frac{{by}}{{b}^{\mathrm{2}} +{by}}\:+\frac{{cz}}{{c}^{\mathrm{2}} +{cz}} \\ $$$$=\frac{{ax}}{{by}+{cz}+{ax}}\:+\frac{{by}}{{ax}+{cz}+{by}}+\frac{{cz}}{{ax}+{by}+{cz}} \\…
Question Number 173332 by pete last updated on 09/Jul/22 $$\mathrm{A}\:\mathrm{shop}\:\mathrm{keeper}\:\mathrm{gave}\:\mathrm{a}\:\mathrm{bill}\:\mathrm{to}\:\mathrm{a}\:\mathrm{customer}. \\ $$$$\mathrm{The}\:\mathrm{bill}\:\mathrm{was}\:\mathrm{in}\:\mathrm{two}\:\mathrm{digits}\:\mathrm{but}\:\mathrm{was}\:\mathrm{mistakenly} \\ $$$$\mathrm{interchanged}\:\mathrm{thereby}\:\mathrm{undercharging}\:\mathrm{the} \\ $$$$\mathrm{customer}\:\mathrm{by}\:\$\mathrm{45}.\mathrm{00}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{is}\: \\ $$$$\mathrm{9},\:\mathrm{find}\:\mathrm{the}\:\mathrm{actual}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bill}. \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 107794 by udaythool last updated on 12/Aug/20 Answered by arcana last updated on 12/Aug/20 $$\mathrm{Considere} \\ $$$${f}\left({x}\right)={x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$$$\Rightarrow{f}\:'\left({x}\right)=\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }−\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}=\mathrm{0},…
Question Number 107779 by ajfour last updated on 12/Aug/20 Commented by ajfour last updated on 12/Aug/20 $${y}=\left({x}−{p}\right)\left({x}^{\mathrm{3}} −\mathrm{39}{x}−\mathrm{70}\right) \\ $$$${Find}\:{p}. \\ $$ Commented by Sarah85…
Question Number 173321 by pete last updated on 09/Jul/22 $$\mathrm{The}\:\mathrm{diagonal}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rectangualar}\:\mathrm{field}\:\mathrm{is}\:\mathrm{169m}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lengh}\:\mathrm{to}\:\mathrm{the}\:\mathrm{width}\:\mathrm{is} \\ $$$$\mathrm{12}:\mathrm{5},\:\mathrm{find}\:\mathrm{its}\:\mathrm{dimensions}. \\ $$ Answered by Rasheed.Sindhi last updated on 09/Jul/22 $${Length}:\:\mathrm{12}{k}\:,\:{Width}:\:\mathrm{5}{k} \\…
Question Number 173311 by mnjuly1970 last updated on 09/Jul/22 Commented by Rasheed.Sindhi last updated on 09/Jul/22 $$\mathrm{18} \\ $$ Commented by Ar Brandon last updated…
Question Number 173303 by dragan91 last updated on 09/Jul/22 Answered by Frix last updated on 09/Jul/22 $$\mathrm{5}{a}^{\mathrm{6}} +\mathrm{15}{a}^{\mathrm{4}} +\mathrm{1}\geqslant\mathrm{16}{a}^{\mathrm{5}} +\mathrm{5}{a}^{\mathrm{2}} \\ $$$$\Leftrightarrow \\ $$$$\mathrm{5}{a}^{\mathrm{6}} −\mathrm{16}{a}^{\mathrm{5}}…
Question Number 173302 by AgniMath last updated on 09/Jul/22 Commented by mr W last updated on 10/Jul/22 $${nice}\:{solution}! \\ $$ Commented by dragan91 last updated…
Question Number 173298 by mnjuly1970 last updated on 09/Jul/22 $$\mathrm{Q}: \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:{e}^{\:{x}} +\:{x}\:−\mathrm{4}\:{is}\:{given} \\ $$$$\:\:\:\:\:{put}\::\:\:\:\:\:{h}\left({x}\right)=\:{ln}\left({x}−{f}^{\:−\mathrm{1}} \left({x}\right)\right) \\ $$$$\:\:\:\:\:\:{find}\::\:\:\:\:\mathrm{D}_{\:{h}\:} \:=\:\left({domain}\:{of}\:\:\:\:{h}\:\right) \\ $$$$ \\ $$$$ \\ $$$$…
Question Number 107761 by Algoritm last updated on 12/Aug/20 Commented by mr W last updated on 12/Aug/20 $${all}\:{can}\:{be}\:{correct}\:{and}\:{all}\:{can}\:{be}\:{wrong}! \\ $$ Commented by Sarah85 last updated…