Question Number 127369 by liberty last updated on 29/Dec/20 $$\:\left({x}−\mathrm{3}{y}+\mathrm{5}\right){dx}\:+\left(\mathrm{2}{x}+\mathrm{5}{y}+\mathrm{4}\right){dy}\:=\:\mathrm{0} \\ $$ Answered by bemath last updated on 29/Dec/20 Terms of Service Privacy Policy Contact:…
Question Number 192901 by cortano12 last updated on 30/May/23 Answered by Frix last updated on 30/May/23 $$\mathrm{Assuming}\:{a},\:{b}\:>\mathrm{0} \\ $$$${z}=\frac{{x}}{{a}+\frac{{x}}{{b}+{z}}}\:\Rightarrow\:{z}=\frac{−{b}+\sqrt{\left(\mathrm{4}{x}+{ab}\right){b}}}{\mathrm{2}} \\ $$$${y}={x}+{z}\:\Rightarrow\:{y}={x}+\frac{−{b}+\sqrt{\left(\mathrm{4}{x}+{ab}\right){b}}}{\mathrm{2}} \\ $$$$\frac{{d}\left[{x}+\frac{−{b}+\sqrt{\left(\mathrm{4}{x}+{ab}\right){b}}}{\mathrm{2}}\right]}{{dx}}=\mathrm{1}+\frac{\sqrt{{b}}}{\:\sqrt{\left(\mathrm{4}{x}+{ab}\right){a}}} \\ $$…
Question Number 127366 by mohammad17 last updated on 29/Dec/20 $${Appointed}\:{at}\:{the}\:{nodal}\:{level}\:{of}\:{the}\:{group} \\ $$$$ \\ $$$$\mid{z}+\overset{−} {{z}}\mid^{\mathrm{2}} +\left({z}−\overset{−} {{z}}\right)=\mathrm{4}? \\ $$ Commented by JDamian last updated on…
Question Number 127364 by mohammad17 last updated on 29/Dec/20 $${prove}\:{that}:\:{Arg}\left({log}\left(\mathrm{3}−\mathrm{4}{i}\right)\right)=\frac{\mathrm{1}}{{i}}{log}\left(\frac{\mathrm{3}−\mathrm{4}{i}}{\mathrm{5}}\right) \\ $$$$ \\ $$$${help}\:{me}\:{sir}\:{please} \\ $$ Commented by mohammad17 last updated on 29/Dec/20 $${pleas}\:{help}\:{me}\:? \\…
Question Number 127363 by mohammad17 last updated on 29/Dec/20 $${prove}\:{that}\:{log}\left(−\mathrm{1}\right)^{\mathrm{3}} =\mathrm{3}{log}\left(−\mathrm{1}\right)\:? \\ $$ Commented by mohammad17 last updated on 29/Dec/20 $$????? \\ $$ Commented by…
Question Number 127360 by bemath last updated on 29/Dec/20 Answered by liberty last updated on 29/Dec/20 $${let}\::\:{a}−\mathrm{7}{b},{a}−\mathrm{6}{b},{a}−\mathrm{5}{b},…,\:{a}+\mathrm{5}{b},\:{a}+\mathrm{6}{b},\:{a}+\mathrm{7}{b}\:{is}\:{AP} \\ $$$${given}\:{condition}\:\rightarrow\begin{cases}{\mathrm{3}{a}−\mathrm{18}{b}=−\mathrm{60};\:{a}−\mathrm{6}{b}=−\mathrm{20}\:\left({the}\:{first}\:\mathrm{3}\:{terms}\right)}\\{\mathrm{3}{a}+\mathrm{18}{b}=\mathrm{84};\:{a}+\mathrm{6}{b}\:=\:\mathrm{28}\:\left({the}\:{last}\:\mathrm{3}\:{terms}\right)}\end{cases} \\ $$$${we}\:{get}\:\begin{cases}{{a}=\mathrm{4}}\\{{b}=\mathrm{4}}\end{cases}.\:{we}\:{want}\:{to}\:{compute}\:{the} \\ $$$${sum}\:{of}\:{the}\:{middle}\:\mathrm{3}\:{terms}\:\Rightarrow{T}_{\mathrm{7}} +{T}_{\mathrm{8}} +{T}_{\mathrm{9}}…
Question Number 61825 by Tawa1 last updated on 09/Jun/19 Answered by mr W last updated on 10/Jun/19 Commented by mr W last updated on 10/Jun/19…
Question Number 192898 by Red1ight last updated on 30/May/23 $$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}^{\mathrm{3}} −\mathrm{7}{x}−\mathrm{2}=\mathrm{0} \\ $$ Commented by Frix last updated on 30/May/23 $$\mathrm{You}\:\mathrm{need}\:\mathrm{the}\:{Trigonometric}\:{Solution}\:\mathrm{to} \\ $$$$\mathrm{get}\:\mathrm{exact}\:\mathrm{solutions}:…
Question Number 192893 by mnjuly1970 last updated on 30/May/23 $$ \\ $$$$\:\:\:\:\:\:\mathrm{Q}\::\:\mathrm{Find}\:\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{of}\:\:\mathrm{dividing} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{number}\:\mathrm{by}\:\:\mathrm{7}\:. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{N}\:=\:\mathrm{3}^{\:\mathrm{10}^{\:\mathrm{1}} } \:+\:\mathrm{3}^{\:\mathrm{10}^{\:\mathrm{2}} \:} \:+\:\mathrm{3}^{\:\mathrm{10}^{\:\mathrm{3}} \:} \:+\:…\:+\:\mathrm{3}^{\:\mathrm{10}^{\:\mathrm{10}} }…
Question Number 127358 by Fareed last updated on 29/Dec/20 $$ \\ $$$$\mathrm{lim}\left(\frac{\mathrm{a}^{\mathrm{x}+\mathrm{1}} +\mathrm{b}^{\mathrm{x}+\mathrm{1}} +\mathrm{c}^{\mathrm{x}+\mathrm{1}} }{\mathrm{a}+\mathrm{b}+\mathrm{c}}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} =? \\ $$$$\mathrm{x}\Rightarrow\mathrm{0} \\ $$ Answered by Ar Brandon last…