Question Number 173373 by AgniMath last updated on 10/Jul/22 Answered by mahdipoor last updated on 10/Jul/22 $${p}^{\mathrm{2}} −{rq}={p}^{\mathrm{2}} −\left(−{rp}−{pq}\right)={p}\left({p}+{r}+{q}\right) \\ $$$$\Rightarrow{q}^{\mathrm{2}} −{rp}={q}\left({p}+{r}+{q}\right) \\ $$$$\Rightarrow{r}^{\mathrm{2}} −{pq}={r}\left({p}+{r}+{q}\right)…
Question Number 173369 by AgniMath last updated on 10/Jul/22 Answered by mr W last updated on 10/Jul/22 $$\frac{{by}+{cz}}{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }=\frac{{cz}+{ax}}{{c}^{\mathrm{2}} +{a}^{\mathrm{2}} }=\frac{{ax}+{by}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }={k},\:{say} \\…
Question Number 42296 by maxmathsup by imad last updated on 22/Aug/18 $${solve}\:{in}\:{Z}^{\mathrm{2}} \:\:\:\:\:\:\:\mathrm{2}{x}+\mathrm{3}{y}\:=\mathrm{7} \\ $$ Commented by math khazana by abdo last updated on 22/Aug/18…
Question Number 42285 by maxmathsup by imad last updated on 22/Aug/18 $${let}\:\:{S}_{{p}} =\sum_{{n}=\mathrm{0}} ^{\infty} \:\:{cos}\left(\frac{{n}\pi}{{p}}\right)\:\:{and}\:\:{W}_{{p}} \:=\sum_{{n}=\mathrm{0}} ^{\infty} \:{sin}\left(\frac{{n}\pi}{{p}}\right)\:{with}\:{p}\:{natural}\:{integr}\:{not}\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{S}_{{p}} \:{and}\:{W}_{{p}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{cos}\left(\frac{{n}\pi}{\mathrm{3}}\right)\:{and}\:\sum_{{n}=\mathrm{0}}…
Question Number 173339 by AgniMath last updated on 10/Jul/22 Commented by som(math1967) last updated on 10/Jul/22 $$\:{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…