Question Number 212457 by 281981 last updated on 14/Oct/24 Answered by som(math1967) last updated on 14/Oct/24 $$\:\begin{vmatrix}{{a}}&{{b}}&{{c}}\\{{b}}&{{c}}&{{a}}\\{{c}}&{{a}}&{{b}}\end{vmatrix}=\mathrm{0} \\ $$$$\Rightarrow{a}\left({bc}−{a}^{\mathrm{2}} \right)−{b}\left({b}^{\mathrm{2}} −{ca}\right)+{c}\left({ab}−{c}^{\mathrm{2}} \right)=\mathrm{0} \\ $$$$\Rightarrow{a}^{\mathrm{3}} +{b}^{\mathrm{3}}…
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Question Number 212445 by ChantalYah last updated on 13/Oct/24 Commented by Frix last updated on 13/Oct/24 $$\mathrm{80cos}\:{A}\:?\:\mathrm{150sin}\:{A}\:=\mathrm{13} \\ $$$$ \\ $$$$\mathrm{80cos}\:{A}\:−\mathrm{150sin}\:{A}\:=\mathrm{13} \\ $$$$−\mathrm{170sin}\:\left({A}−\mathrm{tan}^{−\mathrm{1}} \:\frac{\mathrm{8}}{\mathrm{15}}\right)\:=\mathrm{13} \\…
Question Number 212415 by MrGaster last updated on 13/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{2}^{\frac{{k}}{{n}}} }{{n}+\frac{\mathrm{1}}{{k}}} \\ $$$$ \\ $$ Answered by Frix last updated on 13/Oct/24…
Question Number 212405 by mathlove last updated on 13/Oct/24 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{{e}^{{x}} −{e}^{\mathrm{3}} }{{x}−\mathrm{3}}=? \\ $$ Answered by som(math1967) last updated on 13/Oct/24 $$\underset{{x}\rightarrow\mathrm{3}} {\:{lim}}\frac{{e}^{\mathrm{3}} \left({e}^{{x}−\mathrm{3}}…
Question Number 212432 by hardmath last updated on 13/Oct/24 $$\frac{\mathrm{9}}{\mathrm{2}\centerdot\mathrm{4}}\:+\:\frac{\mathrm{9}}{\mathrm{4}\centerdot\mathrm{6}}\:+…+\:\frac{\mathrm{9}}{\mathrm{4n}\centerdot\left(\mathrm{n}\:+\:\mathrm{1}\right)}\:=\:\frac{\mathrm{15}}{\mathrm{8}} \\ $$$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{n}}\:=\:? \\ $$ Answered by Ar Brandon last updated on 13/Oct/24 $$\mathrm{9}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{4}{n}\left({n}+\mathrm{1}\right)}=\frac{\mathrm{15}}{\mathrm{8}}…
Question Number 212435 by Ar Brandon last updated on 13/Oct/24 Answered by mr W last updated on 13/Oct/24 $${y}'=−\frac{\mathrm{2}{y}^{\mathrm{2}} +{xy}}{{x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} } \\ $$$${let}\:{y}={px} \\…
Question Number 212428 by Spillover last updated on 13/Oct/24 Answered by Yassine84 last updated on 13/Oct/24 $${let}\:{f}\left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)\:{then} \\ $$$${li}\underset{\mathrm{1}} {{m}}\:\frac{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}}…
Question Number 212430 by Ismoiljon_008 last updated on 13/Oct/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212424 by hardmath last updated on 13/Oct/24 $$\begin{cases}{\mathrm{x}\:+\:\mathrm{2y}\:−\:\mathrm{3z}\:=\:\mathrm{1}}\\{\mathrm{2x}\:−\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{4}}\\{\mathrm{3x}\:+\:\mathrm{y}\:+\:\mathrm{2z}\:=\:\mathrm{7}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\mathrm{x},\mathrm{y},\mathrm{z}\:=\:? \\ $$ Answered by A5T last updated on 13/Oct/24 $$\left({ii}\right)+\left({iii}\right)\Rightarrow\mathrm{5}{x}+\mathrm{3}{z}=\mathrm{11}…\left({iv}\right) \\ $$$$\mathrm{2}\left({iii}\right)−\left({i}\right)\Rightarrow\mathrm{5}{x}+\mathrm{7}{z}=\mathrm{13}…\left({v}\right) \\ $$$$\left({v}\right)−\left({iv}\right)\Rightarrow\mathrm{4}{z}=\mathrm{2}\Rightarrow{z}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow{x}=\frac{\mathrm{19}}{\mathrm{10}}\Rightarrow{y}=\frac{\mathrm{3}}{\mathrm{10}} \\…