Question Number 80145 by behi83417@gmail.com last updated on 31/Jan/20 $$\begin{cases}{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{a}}}+\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{b}}}=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} }\\{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}}\right]}\\{\boldsymbol{\mathrm{ab}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{y}}^{\mathrm{2}} \right)=\boldsymbol{\mathrm{xy}}\left(\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{b}}^{\mathrm{2}} \right)}\end{cases} \\ $$ Commented by john santu last updated on…
Question Number 80139 by M±th+et£s last updated on 31/Jan/20 Commented by M±th+et£s last updated on 31/Jan/20 $$\left[{Q}\mathrm{80131}\:{Reposted}\right] \\ $$ Commented by mr W last updated…
Question Number 145668 by mathdanisur last updated on 07/Jul/21 $${Compare}: \\ $$$${sin}\left(\mathrm{43}°\right)\:\:{and}\:\:{sin}\left(\mathrm{40}°\right)+{sin}\left(\mathrm{3}°\right) \\ $$ Answered by mr W last updated on 07/Jul/21 $$\mathrm{sin}\:\mathrm{43}°=\mathrm{sin}\:\left(\mathrm{40}+\mathrm{3}\right) \\ $$$$=\mathrm{cos}\:\mathrm{3}×\mathrm{sin}\:\mathrm{40}+\mathrm{cos}\:\mathrm{40}×\mathrm{sin}\:\mathrm{3}…
Question Number 145664 by qaz last updated on 07/Jul/21 $$\mathrm{S}=\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{k}} \mathrm{k}^{\mathrm{3}} =? \\ $$ Answered by mathmax by abdo last updated on 07/Jul/21…
Question Number 14594 by 1kanika# last updated on 02/Jun/17 Answered by Tinkutara last updated on 02/Jun/17 $${f}\left({x}\right)\:=\:{Q}\left({x}\:−\:\mathrm{2}\right)\left({x}\:−\:\mathrm{3}\right)\:+\:{ax}\:+\:{b} \\ $$$$\mathrm{3}{a}\:+\:{b}\:=\:\mathrm{2} \\ $$$$\mathrm{2}{a}\:+\:{b}\:=\:\mathrm{3} \\ $$$$\Rightarrow\:{a}\:=\:−\mathrm{1},\:{b}\:=\:\mathrm{5} \\ $$$$\mathrm{Remainder}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}…
Question Number 80131 by M±th+et£s last updated on 31/Jan/20 Commented by MJS last updated on 31/Jan/20 $$+\infty \\ $$$$\mathrm{e}^{\frac{\pi}{\mathrm{2}}} \approx\mathrm{4}.\mathrm{8} \\ $$$$\mathrm{4}.\mathrm{8}^{\mathrm{4}.\mathrm{8}} \approx\mathrm{1913} \\ $$$$……
Question Number 145666 by mathdanisur last updated on 07/Jul/21 Answered by Rasheed.Sindhi last updated on 07/Jul/21 $$\mid{x}+\mathrm{1}\mid+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{4}}+\mid{x}−{z}\mid+\mid{z}−\mathrm{3}\mid=\mathrm{4} \\ $$$$….. \\ $$$$…. \\ $$ Commented…
Question Number 145660 by imjagoll last updated on 07/Jul/21 Answered by Olaf_Thorendsen last updated on 08/Jul/21 $$!\mathrm{4}\:=\:\mathrm{4}!\left(\frac{\mathrm{1}}{\mathrm{0}!}−\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}\right) \\ $$$$!\mathrm{4}\:=\:\mathrm{9} \\ $$$$!\mathrm{5}\:=\:\mathrm{5}!\left(\frac{\mathrm{1}}{\mathrm{0}!}−\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}−\frac{\mathrm{1}}{\mathrm{5}!}\right) \\ $$$$!\mathrm{5}\:=\:\mathrm{44} \\ $$$$!\mathrm{7}\:=\:\mathrm{7}!\left(\frac{\mathrm{1}}{\mathrm{0}!}−\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}−\frac{\mathrm{1}}{\mathrm{5}!}+\frac{\mathrm{1}}{\mathrm{6}!}−\frac{\mathrm{1}}{\mathrm{7}!}\right)…
Question Number 80116 by mr W last updated on 31/Jan/20 $${Find} \\ $$$${S}_{{m}} =\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\underset{{k}=\mathrm{1}} {\overset{{m}} {\prod}}\left({n}+{k}\right)}=? \\ $$$$\left({m}\geqslant\mathrm{2}\right) \\ $$ Commented by mr…
Question Number 80108 by jagoll last updated on 31/Jan/20 $${a},{b},{c}\:\in\mathbb{R} \\ $$$$\frac{{b}+{c}+{d}}{{a}}=\frac{{a}+{c}+{d}}{{b}}=\frac{{a}+{b}+{c}}{{d}}=\frac{{a}+{b}+{d}}{{c}}={r} \\ $$$${what}\:{is}\:{r}? \\ $$ Commented by john santu last updated on 31/Jan/20 $$\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}\:=\:\mathrm{x}…