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Author: Tinku Tara

x-2-3-x-3-1-3-1-x-3-1-3-1-3-x-5-6-x-3-1-3-1-2-x-3-1-3-1-3-5-

Question Number 197784 by cortano12 last updated on 28/Sep/23 $$\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}+\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\:\left(\mathrm{1}+\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\right)}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}+\mathrm{5}+\mathrm{6}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\left(\mathrm{1}+\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\:\right)}\:=\:\mathrm{5} \\ $$ Answered by Frix last updated on 28/Sep/23 $$\mathrm{Let}\:{x}={t}^{\mathrm{3}} +\mathrm{3} \\ $$$$\sqrt[{\mathrm{3}}]{\left({t}+\mathrm{1}\right)^{\mathrm{3}} }+\sqrt[{\mathrm{3}}]{{t}^{\mathrm{3}} +\mathrm{12}{t}^{\mathrm{2}}…

Question-197771

Question Number 197771 by sonukgindia last updated on 28/Sep/23 Answered by som(math1967) last updated on 28/Sep/23 $${B}=\frac{\mathrm{1}}{\mathrm{2}}×{r}^{\mathrm{2}} +\mathrm{2}×\frac{\mathrm{45}}{\mathrm{360}}×\pi{r}^{\mathrm{2}} \\ $$$$=\frac{{r}^{\mathrm{2}} }{\mathrm{2}}+\frac{\pi{r}^{\mathrm{2}} }{\mathrm{4}}=\frac{{r}^{\mathrm{2}} }{\mathrm{2}}\left(\mathrm{1}+\frac{\pi}{\mathrm{2}}\right){squnit} \\ $$$${A}=\frac{\mathrm{1}}{\mathrm{2}}\pi{r}^{\mathrm{2}}…

Question-197767

Question Number 197767 by AR19 last updated on 28/Sep/23 Commented by Frix last updated on 28/Sep/23 $$\int\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}{dx}={x}\:_{\mathrm{2}} {F}_{\mathrm{1}} \:\left(−\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{1}}{\mathrm{3}};\:\frac{\mathrm{4}}{\mathrm{3}};\:−{x}^{\mathrm{3}} \right)\:+{C} \\ $$ Terms of…

Solve-the-following-differential-equation-1-y-y-e-x-x-3-y-0-2-y-0-0-2-y-y-2y-x-sin2x-y-0-1-y-0-0-3-y-y-xe-x-y-0-2-y-0-1-Thank-

Question Number 197792 by Mastermind last updated on 28/Sep/23 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{y}''\:+\:\mathrm{y}\:=\:\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{x}^{\mathrm{3}} ,\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{2},\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{y}''\:+\:\mathrm{y}^{'} \:−\:\mathrm{2y}\:=\:\mathrm{x}\:+\:\mathrm{sin2x},\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1},\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{y}''\:−\:\mathrm{y}'\:=\:\mathrm{xe}^{\mathrm{x}} ,\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{2},\:\mathrm{y}'\left(\mathrm{0}\right)=\:\mathrm{1} \\ $$$$ \\ $$$$ \\…

if-x-log-tan-pi-4-y-2-prove-that-y-ilog-tan-ix-2-pi-4-here-i-1-

Question Number 197794 by universe last updated on 28/Sep/23 $$\:\:\:\:\mathrm{if}\:\mathrm{x}\:\:\:=\:\:\:\mathrm{log}\:\mathrm{tan}\left(\frac{\pi}{\mathrm{4}}+\frac{\mathrm{y}}{\mathrm{2}}\right),\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\mathrm{y}\:\:\:\:=\:\:\:−{i}\mathrm{log}\:\mathrm{tan}\left(\frac{{ix}}{\mathrm{2}}\:+\:\frac{\pi}{\mathrm{4}}\right)\:\:\:\:\:\mathrm{here}\:{i}\:\:=\:\sqrt{−\mathrm{1}} \\ $$ Answered by Frix last updated on 29/Sep/23 $${x}=\mathrm{ln}\:\mathrm{tan}\:\frac{\mathrm{2}{y}+\pi}{\mathrm{4}}\:\Leftrightarrow\:{y}=−\frac{\pi}{\mathrm{2}}+\mathrm{2tan}^{−\mathrm{1}} \:\mathrm{e}^{{x}} \\ $$$$−\frac{\pi}{\mathrm{2}}+\mathrm{2tan}^{−\mathrm{1}}…