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Author: Tinku Tara

Question-153407

Question Number 153407 by liberty last updated on 07/Sep/21 Answered by Rasheed.Sindhi last updated on 08/Sep/21 $${x}\equiv\mathrm{2}\:\left({mod}\:\mathrm{5}\right)……..\left({i}\right) \\ $$$${x}\equiv\mathrm{1}\:\left({mod}\:\mathrm{3}\right)……..\left({ii}\right) \\ $$$${x}\equiv\mathrm{6}\:\left({mod}\:\mathrm{14}\right)……\left({iii}\right) \\ $$$$\underset{\underset{} {−}} {{x}\equiv\mathrm{5}\underline{\:\left({mod}\:\mathrm{11}\right)…….\left({iv}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\:\:\:\:\:\:\:\:\:}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…

Question-22332

Question Number 22332 by A1B1C1D1 last updated on 15/Oct/17 Answered by ajfour last updated on 15/Oct/17 $$\frac{{d}\left[{f}\left({x}\right)\right]}{{dx}}=\mathrm{1}+\mathrm{2cos}\:{x}=\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{cos}\:{x}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:{x}=\mathrm{2}{n}\pi\pm\frac{\mathrm{2}\pi}{\mathrm{3}}\:\:{where}\:{n}\in\mathbb{Z}\:. \\ $$$$\:\:\:\:{which}\:{is}\:{equivalent}\:{to} \\ $$$$\:\:\:\:{x}=\left(\mathrm{2}{n}+\mathrm{1}\right)\pi\pm\frac{\pi}{\mathrm{3}}\:.…

Evaluate-1-1-1-x-1-dx-

Question Number 87862 by Rio Michael last updated on 06/Apr/20 $$\mathrm{Evaluate}\:\:\:\:\overset{\mathrm{1}} {\int}_{−\mathrm{1}} \frac{\mathrm{1}}{{x}−\mathrm{1}}\:{dx}\: \\ $$ Commented by MJS last updated on 06/Apr/20 $$\mathrm{doesn}'\mathrm{t}\:\mathrm{exist} \\ $$$$\int\frac{{dx}}{{x}−\mathrm{1}}=\mathrm{ln}\:\mid{x}−\mathrm{1}\mid\:+{C}…

Question-87860

Question Number 87860 by naka3546 last updated on 06/Apr/20 Commented by MJS last updated on 06/Apr/20 $$\mathrm{again},\:\mathrm{there}'\mathrm{s}\:\mathrm{no}\:\mathrm{unique}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{such} \\ $$$$\mathrm{questions} \\ $$$$\mathrm{my}\:\mathrm{answer}\:\mathrm{is}\:{x}=\sqrt{\frac{\mathrm{e}^{\mathrm{3}} −\pi}{\pi^{\mathrm{5}} +\mathrm{e}}} \\ $$$$\mathrm{do}\:\mathrm{you}\:\mathrm{want}\:\mathrm{my}\:\mathrm{equation}?…

If-separate-samples-of-argon-methane-nitrogen-and-carbon-dioxide-all-at-the-same-initial-temperature-and-pressure-and-expanded-adiabatically-reversibally-to-double-their-original-volumes-then-whic

Question Number 22325 by Tinkutara last updated on 15/Oct/17 $$\mathrm{If}\:\mathrm{separate}\:\mathrm{samples}\:\mathrm{of}\:\mathrm{argon},\:\mathrm{methane}, \\ $$$$\mathrm{nitrogen}\:\mathrm{and}\:\mathrm{carbon}\:\mathrm{dioxide},\:\mathrm{all}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{initial}\:\mathrm{temperature}\:\mathrm{and}\:\mathrm{pressure} \\ $$$$\mathrm{and}\:\mathrm{expanded}\:\mathrm{adiabatically}\:\mathrm{reversibally} \\ $$$$\mathrm{to}\:\mathrm{double}\:\mathrm{their}\:\mathrm{original}\:\mathrm{volumes},\:\mathrm{then} \\ $$$$\mathrm{which}\:\mathrm{one}\:\mathrm{of}\:\mathrm{these}\:\mathrm{gases}\:\mathrm{will}\:\mathrm{have}\:\mathrm{high} \\ $$$$\mathrm{temperature}\:\mathrm{as}\:\mathrm{final}\:\mathrm{temperature}? \\ $$ Terms…

0-pi-4-tanh-2x-dx-

Question Number 87861 by Rio Michael last updated on 06/Apr/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\:\mathrm{tanh}\:\mathrm{2}{x}\:{dx} \\ $$ Commented by MJS last updated on 06/Apr/20 $$\mathrm{tanh}\:\mathrm{2}{x}\:=\frac{\mathrm{e}^{\mathrm{4}{x}} −\mathrm{1}}{\mathrm{e}^{\mathrm{4}{x}} +\mathrm{1}}…