Question Number 110246 by Her_Majesty last updated on 28/Aug/20 $${solve}\:{for}\:{z}\in\mathbb{C}:\:\left({a}+{bi}\right)^{{z}} ={b}+{ai} \\ $$ Answered by mr W last updated on 28/Aug/20 $$\theta=\mathrm{tan}^{−\mathrm{1}} \frac{{b}}{{a}} \\ $$$${z}\mathrm{ln}\:\left({a}+{bi}\right)=\mathrm{ln}\:\left({b}+{ai}\right)…
Question Number 175770 by mnjuly1970 last updated on 06/Sep/22 $$ \\ $$$$\:\:\:\mathrm{P}_{{n}} \:=\:{e}^{\:\left(\frac{\mathrm{1}}{\mathrm{1}}\:−\frac{\mathrm{1}}{\mathrm{2}}\right)\:+\left(\frac{\mathrm{1}}{\mathrm{3}}\:−\frac{\mathrm{1}}{\mathrm{4}}\right)\:+…+\left(\frac{\mathrm{1}}{{n}−\mathrm{1}}\:−\frac{\mathrm{1}}{{n}}\right)} \\ $$$$\:\:\:\:\:\:\:\:=\:{e}^{\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}}\:−\frac{\mathrm{1}}{\mathrm{4}}\:\:+…+\frac{\mathrm{1}}{{n}−\mathrm{1}}\:−\frac{\mathrm{1}}{{n}}\right)} \\ $$$$\:\:\:\:\:\:\:\:=\:{e}^{\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\:\left(−\mathrm{1}\:\right)^{\:{k}+\mathrm{1}} }{{k}}} \\ $$$$\:\:\:\:\:\:\:\:\:\therefore\:\:\mathrm{P}\:=\:{lim}_{\:{n}\rightarrow\infty} \left({e}^{\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\:{k}+\mathrm{1}}…
Question Number 44691 by ajfour last updated on 03/Oct/18 Commented by ajfour last updated on 03/Oct/18 $${Find}\:{equation}\:{of}\:{the}\:{biquadratic} \\ $$$${curve}. \\ $$ Answered by ajfour last…
Question Number 110219 by mohammad17 last updated on 27/Aug/20 $${let}\:{A}\:{and}\:{C}\:{be}\:{two}\:{none}\:{empety}\:{set}\:{prove}\:{that} \\ $$$${A}\subseteq{B}\:\wedge\:{C}\:\subseteq{D}\:{iff}\:{A}×{C}\:\subseteq{B}×{D}? \\ $$$${help}\:{me}\:{sir} \\ $$ Commented by kaivan.ahmadi last updated on 27/Aug/20 $${if}\:{A}\subseteq{B}\wedge{C}\subseteq{D}\Rightarrow{A}×{C}\subseteq{B}×{D} \\…
Question Number 175750 by Shrinava last updated on 06/Sep/22 Answered by mr W last updated on 06/Sep/22 $$\mathrm{1}\:{time}\:\mathrm{1} \\ $$$$\mathrm{2}\:{times}\:\mathrm{2} \\ $$$$\mathrm{3}\:{times}\:\mathrm{3} \\ $$$$… \\…
Question Number 175739 by cortano1 last updated on 06/Sep/22 $$\:\mathrm{x}^{\mathrm{3}} −\mathrm{5x}−\mathrm{6}=\mathrm{0} \\ $$$$\:\mathrm{x}=? \\ $$ Commented by mr W last updated on 06/Sep/22 $$\boldsymbol{{cortano}}\:{should}\:{know}\:\boldsymbol{{cardano}}: \\…
Question Number 110182 by udaythool last updated on 27/Aug/20 $$\mathrm{Solve}\:{x}^{\mathrm{3}} +\mathrm{15}{x}−\mathrm{92}=\mathrm{0} \\ $$ Commented by mr W last updated on 27/Aug/20 $${let}\:{x}={u}+{v} \\ $$$$\left({u}+{v}\right)^{\mathrm{3}} +\mathrm{15}\left({u}+{v}\right)−\mathrm{92}=\mathrm{0}…
Question Number 175715 by zaheen last updated on 05/Sep/22 $${how}\:{is}\:{the}\:{solution}\:{of}\:{this}\:{qution} \\ $$$$ \\ $$$$\sqrt{\left({x}\right)\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)+\mathrm{1}} \\ $$$${when}\:\:\:\:\:\begin{array}{|c|}{{x}=\mathrm{50}}\\\hline\end{array}\begin{array}{|c|c|}\\\\\hline\end{array} \\ $$ Commented by Frix last updated on 05/Sep/22…
Question Number 175709 by Shrinava last updated on 05/Sep/22 Answered by mr W last updated on 05/Sep/22 $${r}={radius}\:{of}\:{small}\:{circle} \\ $$$${R}={radius}\:{of}\:{big}\:{semicircle} \\ $$$$\pi{r}^{\mathrm{2}} =\mathrm{4}\pi\:\Rightarrow{r}=\mathrm{2} \\ $$$${R}=\frac{\mathrm{3}+{x}}{\mathrm{2}}…
Question Number 110173 by ajfour last updated on 27/Aug/20 $${If}\:\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{t}_{{r}} =\frac{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}{\mathrm{8}} \\ $$$${then}\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{t}_{{r}} }\:=\:? \\ $$$$ \\ $$ Answered by…