Question Number 71729 by peter frank last updated on 19/Oct/19 $${find}\:{dU}\:\:\:{if}\:\:\:{U}={x}^{\mathrm{2}} {e}^{\frac{{x}}{{y}}} \\ $$$$ \\ $$ Commented by peter frank last updated on 19/Oct/19 $${thank}\:{you}…
Question Number 137269 by mohssinee last updated on 31/Mar/21 Commented by mohssinee last updated on 31/Mar/21 $${n}\in\mathbb{N}^{\ast} \\ $$ Answered by aleks041103 last updated on…
Question Number 71696 by TawaTawa last updated on 18/Oct/19 $$\mathrm{The}\:\mathrm{side}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{is}\:\mathrm{measured}\:\mathrm{to}\:\mathrm{be}\:\:\mathrm{12cm}\:\mathrm{long}\:\mathrm{cofrect} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\:\mathrm{cm}.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{absolute}\:\mathrm{error} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{percentage}\:\mathrm{error}\:\mathrm{for} \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\:\:\:\:\left(\mathrm{Answer}:\:\:\mathrm{0}.\mathrm{5cm},\:\:\mathrm{4}.\mathrm{17\%}\right) \\ $$$$\left(\mathrm{b}\right)\:\:\:\:\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}.\:\:\:\:\:\:\left(\mathrm{Answer}:\:\:\:\:\mathrm{12}.\mathrm{25cm},\:\:\:\mathrm{8}.\mathrm{5\%}\right) \\ $$ Answered by MJS last updated…
Question Number 6154 by Rasheed Soomro last updated on 16/Jun/16 $${Prove}\:{or}\:{disprove} \\ $$$$\left(\frac{\mathrm{2}\boldsymbol{{ab}}+\mathrm{2}\boldsymbol{{bc}}+\boldsymbol{{ca}}}{\mathrm{5}}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} \geqslant\:\:\boldsymbol{{abc}}\:\:\:\forall\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}>\mathrm{0} \\ $$ Commented by Yozzii last updated on 18/Jun/16 $$\frac{\mathrm{5}\sqrt{\mathrm{5}}}{\left(\frac{\mathrm{2}}{{c}}+\frac{\mathrm{2}}{{a}}+\frac{\mathrm{1}}{{b}}\right)\sqrt{\mathrm{2}{ab}+\mathrm{2}{bc}+{ca}}}\leqslant\mathrm{1} \\…
Question Number 137208 by bemath last updated on 31/Mar/21 $$\mathrm{If}\:\mathrm{x},\mathrm{y}\:>\:\mathrm{0}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\:\mathrm{3}\sqrt{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }{\mathrm{2}}}\:+\:\sqrt{\mathrm{xy}}\:\geqslant\:\mathrm{2}\left(\mathrm{x}+\mathrm{y}\right)\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 71674 by TawaTawa last updated on 18/Oct/19 Answered by mind is power last updated on 18/Oct/19 $$\mathrm{what}\:\mathrm{de}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{by}\:\mathrm{n}^{\mathrm{n}^{\mathrm{n}^{\mathrm{n}^{\mathrm{0}} } } } ? \\ $$$$…
Question Number 137209 by JulioCesar last updated on 31/Mar/21 Answered by bemath last updated on 31/Mar/21 $$\int\:\left(\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} \mathrm{sec}\:\mathrm{x}\:\mathrm{dx} \\ $$$$=\int\left(\mathrm{sec}\:^{\mathrm{5}} \mathrm{x}−\mathrm{2sec}\:^{\mathrm{3}} \mathrm{x}+\mathrm{sec}\:\mathrm{x}\:\right)\mathrm{dx} \\ $$$$\mathrm{now}\:\mathrm{it}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{solve}…
Question Number 71666 by aliesam last updated on 18/Oct/19 $${f}:{z}\rightarrow{z} \\ $$$$ \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+\mathrm{3}\left(\mathrm{4}{xy}−\mathrm{1}\right) \\ $$$$ \\ $$$$,{f}\left(\mathrm{1}\right)=\mathrm{0} \\ $$$$ \\ $$$$\forall{x},{y}\:\in{z} \\ $$$${evaluate}\:{f}\left(\mathrm{19}\right) \\…
Question Number 6115 by Rasheed Soomro last updated on 14/Jun/16 $${Solve}\:{the}\:{system}\:{of}\:{following}\:{equations} \\ $$$${a}^{\mathrm{3}} −{bcd}=−\mathrm{32} \\ $$$${b}^{\mathrm{3}} −{acd}=−\mathrm{79} \\ $$$${c}^{\mathrm{3}} −{abd}=\mathrm{109} \\ $$$${d}^{\mathrm{3}} −{abc}=\mathrm{502} \\ $$…
Question Number 137173 by JulioCesar last updated on 30/Mar/21 Commented by mathmax by abdo last updated on 31/Mar/21 $$\mathrm{not}\:\mathrm{defined}\:\:\:\mathrm{arcsin}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{on}\:\left[−\mathrm{1},\mathrm{1}\right]\:\:\mathrm{but}\:\mathrm{x}^{\mathrm{2}} −\mathrm{1}\leqslant\mathrm{0}\:! \\ $$ Answered by Ñï=…