Question Number 204499 by DeArtist last updated on 19/Feb/24 $$\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{directional}\:\mathrm{derivative}\:\mathrm{of}\: \\ $$$${F}\left({x},{y},{z}\right)\:=\:\mathrm{2}{xy}−{z}^{\mathrm{2}} \:\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},−\mathrm{1},\mathrm{1}\right)\:\mathrm{in} \\ $$$$\mathrm{a}\:\mathrm{direction}\:\mathrm{towards}\:\left(\mathrm{3},\mathrm{1},−\mathrm{1}\right)\: \\ $$$$\mathrm{in}\:\mathrm{what}\:\mathrm{direction}\:\mathrm{is}\:\mathrm{the}\:\mathrm{directional}\:\mathrm{derivative} \\ $$$$\mathrm{maximum}?\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{this}\:\mathrm{maximum}? \\ $$ Answered by TonyCWX08 last…
Question Number 204461 by MATHEMATICSAM last updated on 18/Feb/24 $$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$$\left({x}\:−\:\mathrm{12}\right)\left({x}\:−\:\mathrm{13}\right)\:=\:\frac{\mathrm{34}}{\mathrm{33}^{\mathrm{2}} } \\ $$ Answered by TonyCWX08 last updated on 18/Feb/24 $${x}^{\mathrm{2}} −\mathrm{25}{x}+\mathrm{156}\:=\:\frac{\mathrm{34}}{\mathrm{1089}} \\…
Question Number 204480 by EJJDJX last updated on 18/Feb/24 $${x}\:+\:\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{2}.\mathrm{05} \\ $$$${x}\:=\:? \\ $$ Commented by TonyCWX08 last updated on 19/Feb/24 $$ \\ $$$${x}^{\mathrm{2}} +\mathrm{1}=\:\mathrm{2}.\mathrm{05}{x}…
Question Number 204437 by SANOGO last updated on 17/Feb/24 $$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} {sin}\left({t}\right){ln}\left({sint}\right){dt} \\ $$ Answered by TonyCWX08 last updated on 18/Feb/24 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{ln}\left({sin}\left({t}\right)\right){sin}\left({t}\right){dt} \\…
Question Number 204421 by necx122 last updated on 17/Feb/24 $${x}^{\mathrm{3}} +{y}^{\mathrm{3}} \:=\:\mathrm{35} \\ $$$$\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}\:=\frac{\mathrm{5}}{\mathrm{6}} \\ $$$${solve}\:{for}\:{all}\:{possible}\:{values}\:{of}\:{x}\:{and}\:{y} \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 204397 by Abdullahrussell last updated on 16/Feb/24 Answered by MM42 last updated on 16/Feb/24 $$\left({y}−\mathrm{1}\right)\left({y}+\mathrm{1}\right)\left({y}^{\mathrm{2}} +\mathrm{1}\right)={x}\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right) \\ $$$$\Rightarrow{y}={x}\Rightarrow\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}+\mathrm{1}\right)=\mathrm{0} \\ $$$$\Rightarrow{x}={y}=−\mathrm{1}\:\checkmark \\…
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Question Number 204417 by Frix last updated on 16/Feb/24 $$\mathrm{Solve}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{e}^{{z}} =\mathrm{ln}\:{z} \\ $$ Answered by mr W last updated on 17/Feb/24…
Question Number 204384 by Abdullahrussell last updated on 15/Feb/24 Commented by Frix last updated on 15/Feb/24 $$\mathrm{35}^{\mathrm{36}} =\mathrm{10}{m}+\mathrm{5} \\ $$$$\mathrm{36}^{\mathrm{35}} =\mathrm{10}{n}+\mathrm{6} \\ $$$$\mathrm{4}^{\mathrm{10}{m}+\mathrm{5}} =\mathrm{100}{k}+\mathrm{24} \\…