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simplify-2-5-1-3-

Question Number 160831 by MathsFan last updated on 07/Dec/21 $$\mathrm{simplify}\:\:\sqrt[{\mathrm{3}}]{\mathrm{2}+\sqrt{\mathrm{5}}} \\ $$ Commented by mr W last updated on 07/Dec/21 $$\sqrt[{\mathrm{3}}]{\mathrm{2}+\sqrt{\mathrm{5}}} \\ $$$$=\frac{\sqrt[{\mathrm{3}}]{\mathrm{16}+\mathrm{8}\sqrt{\mathrm{5}}}}{\mathrm{2}} \\ $$$$=\frac{\sqrt[{\mathrm{3}}]{\mathrm{5}\sqrt{\mathrm{5}}+\mathrm{3}\sqrt{\mathrm{5}}+\mathrm{3}×\mathrm{5}+\mathrm{1}}}{\mathrm{2}}…

Question-160816

Question Number 160816 by 0731619 last updated on 07/Dec/21 Commented by mr W last updated on 07/Dec/21 $${f}\left({t}\right)={t}^{{t}^{{t}^{…} } } =\frac{{W}\left(−\mathrm{ln}\:{t}\right)}{−\mathrm{ln}\:{t}}\:{is}\:{defined}\:{only} \\ $$$${for}\:{t}>\mathrm{0}. \\ $$$${with}\:{t}=\mathrm{ln}\:{x},\:{so}\:\left({ln}\:{x}\right)^{\left({ln}\:{x}\right)^{…}…

If-log-x-3-y-3-x-3-y-3-then-dy-dx-

Question Number 160764 by ZiYangLee last updated on 06/Dec/21 $$\mathrm{If}\:\:\:\:\mathrm{log}\left(\frac{{x}^{\mathrm{3}} −{y}^{\mathrm{3}} }{{x}^{\mathrm{3}} +{y}^{\mathrm{3}} }\right),\:\mathrm{then}\:\frac{{dy}}{{dx}}=? \\ $$ Commented by cortano last updated on 06/Dec/21 $$\:\mathrm{do}\:\mathrm{you}\:\mathrm{meant}\:\mathrm{y}=\:\mathrm{ln}\:\left(\frac{\mathrm{x}^{\mathrm{3}} −\mathrm{y}^{\mathrm{3}}…

Question-160746

Question Number 160746 by Rokon last updated on 05/Dec/21 Answered by som(math1967) last updated on 06/Dec/21 $${if}\:\boldsymbol{\theta}=\mathrm{45}°\boldsymbol{{then}}\:\boldsymbol{{A}}=\sqrt{\mathrm{2}}\:\boldsymbol{{B}}=\mathrm{0} \\ $$$$\left.{ii}\right)\:{A}=\sqrt{\mathrm{2}}\left({cos}\theta+\boldsymbol{{sin}\theta}−{sin}\boldsymbol{\theta}\right) \\ $$$$\therefore\boldsymbol{{cos}\theta}+\boldsymbol{{sin}\theta}=\sqrt{\mathrm{2}}\boldsymbol{{cos}\theta} \\ $$$$\Rightarrow\boldsymbol{{sin}\theta}=\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\boldsymbol{{cos}\theta} \\ $$$$\Rightarrow\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\boldsymbol{{sin}\theta}=\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\boldsymbol{{cos}\theta}…

Question-95202

Question Number 95202 by mathocean1 last updated on 23/May/20 Commented by PRITHWISH SEN 2 last updated on 24/May/20 $$\mathrm{x}=\mathrm{2}\left(\mathrm{2cos}^{\mathrm{2}} \theta−\mathrm{1}\right)−\mathrm{1}=\mathrm{2cos2}\theta−\mathrm{1} \\ $$$$\therefore\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{2}\right)^{\mathrm{2}} =\:\mathrm{4}…\left(\mathrm{i}\right) \\…