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Question Number 226246 by ajfour last updated on 23/Nov/25 Commented by fantastic2 last updated on 23/Nov/25 $$\alpha\:{is}\:\mathrm{30}^{\mathrm{0}} \\ $$ Commented by fantastic2 last updated on…
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Question Number 226173 by sonukgindia last updated on 22/Nov/25 Answered by A5T last updated on 22/Nov/25 $$\mathrm{x}^{\mathrm{2013}} +\left(\mathrm{2014}−\mathrm{x}\right)^{\mathrm{2013}} \:\equiv\:\mathrm{x}^{\mathrm{2013}} +\left(−\mathrm{x}\right)^{\mathrm{2013}} \equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{2014}\right) \\ $$$$\mathrm{1}^{\mathrm{2013}} +\mathrm{2}^{\mathrm{2013}} +\mathrm{3}^{\mathrm{2013}}…
Question Number 226217 by mr W last updated on 22/Nov/25 Commented by mr W last updated on 22/Nov/25 Commented by fantastic2 last updated on 22/Nov/25…
Question Number 226176 by Spillover last updated on 22/Nov/25 Commented by fantastic2 last updated on 22/Nov/25 $${you}\:{forgot}\:{dx} \\ $$ Answered by Spillover last updated on…
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Question Number 226194 by fantastic2 last updated on 22/Nov/25 Answered by gregori last updated on 22/Nov/25 $$\:\:\measuredangle\: =\:\mathrm{60}°\: \\ $$$$\:\:\measuredangle\: =\:\mathrm{60}°\: \\ $$$$\:\:\measuredangle\: =\:\mathrm{360}°−\left(\mathrm{2}×\mathrm{120}°+\mathrm{60}°\right)\:=\:\mathrm{60}°\: \\…
Question Number 226178 by Spillover last updated on 22/Nov/25 Answered by mr W last updated on 22/Nov/25 $$=\int\frac{\mathrm{1}+\frac{\mathrm{1}}{{x}}}{{x}+\frac{\mathrm{1}}{{x}}}{dx} \\ $$$$=\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{d}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}+\int\frac{\mathrm{1}}{{x}^{\mathrm{2}}…