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Category: Algebra

Question-82873

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}…

x-x-64-x-

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}…

cos40-1-2cos80-

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-148364

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)}}…