Question Number 82877 by M±th+et£s last updated on 25/Feb/20 $$\left.\mathrm{1}\right){find}\:{xy}\in{R} \\ $$$$\left.\mathrm{2}\right){find}\:{x},{y}\in{Z} \\ $$$$\left({x}+\mathrm{2}{yi}\right)^{\mathrm{6}} =\mathrm{8}{i} \\ $$ Commented by mr W last updated on 25/Feb/20…
Question Number 82873 by mr W last updated on 25/Feb/20 Commented by mr W last updated on 25/Feb/20 $${A}\:{rope}\:{with}\:{length}\:\boldsymbol{{l}}\:{and}\:{mass}\:\boldsymbol{{m}}\:{is} \\ $$$${fixed}\:{at}\:{one}\:{end}\:{on}\:{the}\:{top}\:{of}\:{a}\:{roller} \\ $$$${with}\:{diameter}\:{h}\:{as}\:{shown}.\:{Find}\:{the} \\ $$$${maximal}\:{possible}\:{horizontal}\:{distance}…
Question Number 148395 by mathdanisur last updated on 27/Jul/21 $$\boldsymbol{{x}}^{\boldsymbol{{x}}} \:=\:\mathrm{64} \\ $$$$\Rightarrow\:\boldsymbol{{x}}\:=\:? \\ $$ Answered by Math_Freak last updated on 27/Jul/21 $${if}\:{x}>\mathrm{0} \\ $$$${xlnx}\:=\:{ln}\mathrm{64}…
Question Number 148388 by mathdanisur last updated on 27/Jul/21 $${cos}\mathrm{40}°\left(\mathrm{1}\:-\:\mathrm{2}{cos}\mathrm{80}°\right)\:=\:? \\ $$ Answered by liberty last updated on 27/Jul/21 $$\mathrm{cos}\:\mathrm{40}°\left(\mathrm{1}−\mathrm{2}\left(\mathrm{2cos}\:^{\mathrm{2}} \mathrm{40}°−\mathrm{1}\right)\right) \\ $$$$=\:\mathrm{cos}\:\mathrm{40}°\left(\mathrm{3}−\mathrm{4cos}\:^{\mathrm{2}} \mathrm{40}°\right) \\…
Question Number 82843 by M±th+et£s last updated on 24/Feb/20 $${show}\:{that} \\ $$$$\frac{\left(\mathrm{1}+\sqrt{\mathrm{3}}\:{i}\right)^{\mathrm{4}} \left(\mathrm{1}+{i}\right)^{\mathrm{8}} }{\left({cos}\mathrm{100}°−{i}\:{sin}\mathrm{100}\right)^{\mathrm{3}} }=−\mathrm{256} \\ $$ Answered by mind is power last updated on…
Question Number 148374 by mathdanisur last updated on 27/Jul/21 $${Solve}\:{the}\:{equation}\:{on}\:{the}\:{set}\:{of}\:{real} \\ $$$${number}:\:\:\:\frac{\mathrm{8}}{\:\sqrt{\mathrm{6}\:-\:\mathrm{2}{z}}}\:+\:\frac{\mathrm{2}}{\:\sqrt{{z}}}\:=\:{z}^{\mathrm{2}} \:-\:\mathrm{2}{z}\:+\:\mathrm{7} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 148364 by mathdanisur last updated on 27/Jul/21 Commented by dumitrel last updated on 27/Jul/21 $$\Leftrightarrow\left({ae}^{\frac{{x}}{\mathrm{2}}} +{be}^{\frac{{y}}{\mathrm{2}}} \right)^{\mathrm{2}} \geqslant{e}^{\frac{{ax}+{by}}{{a}+{b}}} \Leftrightarrow \\ $$$${ae}^{\frac{{x}}{\mathrm{2}}} +{be}^{\frac{{y}}{\mathrm{2}}} \geqslant{e}^{\frac{{ax}+{by}}{\mathrm{2}\left({a}+{b}\right)}}…
Question Number 148356 by mathdanisur last updated on 27/Jul/21 Commented by Rasheed.Sindhi last updated on 27/Jul/21 $$\mathcal{T}{wo}\:{integer}-{parts}\:{of}\:{a}\:{single} \\ $$$$\:{number}? \\ $$ Commented by mathdanisur last…
Question Number 148362 by mathdanisur last updated on 27/Jul/21 $${Show}\:{that}\:{the}\:{equation}\:\:\mathrm{4}{xy}-{x}-{y}={z}^{\mathrm{2}} \\ $$$${has}\:{no}\:{solution}\:{in}\:{natural}\:{numbers}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 17279 by tawa tawa last updated on 03/Jul/17 $$\mathrm{Is}\:\:\mathrm{cosh}^{\mathrm{2}} \left(\mathrm{3x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{1}\:+\:\mathrm{cos}\left(\mathrm{6x}\right)\right]\:\:?????? \\ $$ Commented by mrW1 last updated on 03/Jul/17 $$\mathrm{cosh}^{\mathrm{2}} \:\mathrm{3x}=\left(\frac{\mathrm{e}^{\mathrm{3x}} +\mathrm{e}^{−\mathrm{3x}} }{\mathrm{2}}\right)^{\mathrm{2}}…