Question Number 201949 by sonukgindia last updated on 16/Dec/23 Answered by Frix last updated on 17/Dec/23 $${n}^{{k}} \equiv{n}\mathrm{mod2024};\:{n}\in\left\{\mathrm{529},\:\mathrm{737},\:\mathrm{760},\:\mathrm{1265},\:\mathrm{1288},\:\mathrm{1496}\right\} \\ $$$$\Rightarrow \\ $$$$\Sigma{n}^{{n}} \equiv\mathrm{3mod2024} \\ $$…
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Question Number 201947 by Mingma last updated on 16/Dec/23 Answered by Frix last updated on 18/Dec/23 $$\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{cos}\:\left(\pi−\alpha−\beta\right)\:+ \\ $$$$\:\:\:\:\:+\mathrm{sin}\:\beta\:\mathrm{sin}\:\left(\pi−\alpha−\beta\right)\:\mathrm{cos}\:\alpha\:+ \\ $$$$\:\:\:\:\:+\mathrm{sin}\:\left(\pi−\alpha−\beta\right)\:\mathrm{sin}\:\alpha\:\mathrm{cos}\:\beta\:= \\ $$$$=\frac{\mathrm{3}−\left(\mathrm{cos}\:\mathrm{2}\alpha\:+\mathrm{cos}\:\mathrm{2}\beta\:+\mathrm{cos}\:\mathrm{2}\left(\alpha+\beta\right)\right.}{\mathrm{4}}= \\ $$$$\:\:\:\:\:\left[\mathrm{Let}\:\alpha={u}−{v}\wedge\beta={u}+{v}\right]…
Question Number 201956 by sonukgindia last updated on 16/Dec/23 Commented by mahdipoor last updated on 16/Dec/23 $$\mathrm{5}^{\mathrm{2}^{\mathrm{117}} } −\mathrm{1}=\left(\mathrm{5}^{\mathrm{2}^{\mathrm{116}} } −\mathrm{1}\right)\left(\mathrm{5}^{\mathrm{2}^{\mathrm{116}} } +\mathrm{1}\right)= \\ $$$$\left(\mathrm{5}^{\mathrm{2}^{\mathrm{115}}…
Question Number 201952 by mathlove last updated on 16/Dec/23 $$\left({gof}\right)_{{x}} =\mathrm{2}{x}−\mathrm{1}\:\: \\ $$$$\left({fog}\right)_{{x}} ^{−\mathrm{1}} =\mathrm{3}{x}+\mathrm{2} \\ $$$$\left({fof}\right)_{\mathrm{3}} =? \\ $$ Answered by cortano12 last updated…
Question Number 201917 by York12 last updated on 15/Dec/23 $$ \\ $$ Commented by York12 last updated on 15/Dec/23 $$\mathrm{please}\:\mathrm{help} \\ $$ Commented by York12…
Question Number 201912 by York12 last updated on 15/Dec/23 $$ \\ $$ Commented by York12 last updated on 15/Dec/23 Commented by York12 last updated on…
Question Number 201914 by Anonim_X last updated on 15/Dec/23 Commented by mr W last updated on 16/Dec/23 $${see}\:{Q}\mathrm{198828} \\ $$ Terms of Service Privacy Policy…
Question Number 201940 by Calculusboy last updated on 15/Dec/23 $$\boldsymbol{{tan}}^{\mathrm{3}} \left(\boldsymbol{{xy}}^{\mathrm{2}} +\boldsymbol{{y}}\right)=\boldsymbol{{x}}\:\:\boldsymbol{{find}}\:\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}} \\ $$ Answered by cortano12 last updated on 16/Dec/23 $$\:\:\Rightarrow\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\:\mathrm{tan}\:^{\mathrm{3}} \left(\mathrm{xy}^{\mathrm{2}} +\mathrm{y}\right)\:\right]\:=\:\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}\right) \\…
Question Number 201941 by ajfour last updated on 15/Dec/23 $${x}^{\mathrm{4}} −\frac{\mathrm{17}}{\mathrm{18}}{x}^{\mathrm{2}} +\frac{\mathrm{40}}{\mathrm{3}}{x}+\frac{\mathrm{1625}}{\mathrm{144}}=\mathrm{0} \\ $$$${Find}\:{roots}.\:\left({Two}\:{are}\:{real}\:{and}\:{two}\:\right. \\ $$$$\left.{are}\:{complex}\right)\bigstar \\ $$ Commented by Frix last updated on 17/Dec/23…