Question Number 155182 by mathdanisur last updated on 26/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155183 by mathdanisur last updated on 26/Sep/21 Answered by aleks041103 last updated on 26/Sep/21 $$\mathrm{1}−{tan}^{\mathrm{2}} \frac{{x}}{\mathrm{2}^{{k}} }=\frac{{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}^{{k}} }−{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}^{{k}} }}{{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}^{{k}} }}=\frac{{cos}\frac{{x}}{\mathrm{2}^{{k}−\mathrm{1}}…
Question Number 155164 by mnjuly1970 last updated on 26/Sep/21 $$\:\:\:{solve}.. \\ $$$$\:\:\:\:\:\:\:\:\:\lfloor\:\frac{\:{x}}{\mathrm{2}+\:\sqrt{{x}}}\:\rfloor\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\left(\:{x}\in\:\mathbb{Z}\:\right) \\ $$$$ \\ $$ Answered by MJS_new last updated on 26/Sep/21 $$\frac{{x}}{\mathrm{2}+\sqrt{{x}}}=\mathrm{3}\:\Rightarrow\:{x}\approx\mathrm{19}.\mathrm{11} \\…
Question Number 155154 by mathdanisur last updated on 26/Sep/21 $$\mathrm{let}\:\:\mathrm{n}\in\mathbb{N}^{+} \:\:\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{3}\boldsymbol{\mathrm{n}}} \:-\:\mathrm{y}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{y}^{\mathrm{3}\boldsymbol{\mathrm{n}}} \:-\:\mathrm{x}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{4} \\ $$ Answered by MJS_new last updated on…
Question Number 155153 by mathdanisur last updated on 26/Sep/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{in}\:\mathbb{R} \\ $$$$\sqrt{\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{x}\:+\:\mathrm{1}\right)}\:=\:\mathrm{1}\:+\:\sqrt{\mathrm{x}}\:-\:\mathrm{x} \\ $$ Answered by MJS_new last updated on 26/Sep/21 $$\sqrt{{x}}\in\mathbb{R}\:\Rightarrow\:{x}\geqslant\mathrm{0}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{see}\:{x}\neq\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{lhs}>\mathrm{0}\:\Rightarrow\:\mathrm{1}+\sqrt{{x}}−{x}>\mathrm{0}…
Question Number 155144 by mnjuly1970 last updated on 26/Sep/21 $$ \\ $$$$\:\:{how}\:{many}\:{integer}\:{solutions}\: \\ $$$$\:\:\:\:{are}\:{there}\:: \\ $$$$\:\:\:\:\lfloor\:\frac{\mathrm{1}}{\mathrm{2}+\sqrt{{x}}}\rfloor\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\:\blacksquare \\ $$$$ \\ $$ Commented by mr W last…
Question Number 155136 by amin96 last updated on 25/Sep/21 $$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\frac{\boldsymbol{\mathrm{log}}^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{2}}\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left(\boldsymbol{{n}}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{2}} \mathrm{2}^{\boldsymbol{{n}}} }+\boldsymbol{\mathrm{log}}\left(\mathrm{2}\right)\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left({n}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{3}} \mathrm{2}^{\boldsymbol{{n}}} }+\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left({n}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{4}} \mathrm{2}^{\boldsymbol{{n}}} }=…
Question Number 24069 by Joel577 last updated on 12/Nov/17 $$\mathrm{Simplify} \\ $$$$\frac{\left(\mathrm{log}_{\mathrm{2}} \:\sqrt{\mathrm{5}}\:.\:\mathrm{log}_{\mathrm{25}} \:\mathrm{20}\right)\:+\:\mathrm{log}_{\mathrm{4}} \:\sqrt{\mathrm{50}}\:\:}{\mathrm{log}_{\mathrm{4}} \:\mathrm{70}\:−\:\mathrm{log}_{\mathrm{15}} \:\mathrm{49}} \\ $$ Answered by $@ty@m last updated on…
Question Number 155132 by mathdanisur last updated on 25/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89592 by M±th+et£s last updated on 18/Apr/20 $${cos}\left({x}\right)={k}\: \\ $$$$\left\{−\mathrm{1}\leqslant{k}<\mathrm{0}\right\} \\ $$ Commented by mr W last updated on 18/Apr/20 $${i}\:{don}'{t}\:{understand}\:{what}'{s}\:{your}\:{problem}. \\ $$$$…