Question Number 201343 by gabi last updated on 05/Dec/23 Answered by aleks041103 last updated on 05/Dec/23 $${A}^{\mathrm{3}} +{A}^{\mathrm{2}} +{A}=\mathrm{0} \\ $$$$\lambda\:{is}\:{eigenvalue} \\ $$$$\Rightarrow\lambda^{\mathrm{3}} +\lambda^{\mathrm{2}} +\lambda=\lambda\left(\lambda^{\mathrm{2}}…
Question Number 201388 by MrGHK last updated on 05/Dec/23 Answered by witcher3 last updated on 05/Dec/23 $$=\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}}\underset{\mathrm{m}\geqslant\mathrm{0}} {\sum}\int_{\mathrm{0}} ^{\mathrm{1}} \left(−\mathrm{1}\right)^{\mathrm{m}} \mathrm{x}^{\mathrm{n}+\mathrm{2m}} \mathrm{dx} \\…
Question Number 201408 by Ari last updated on 05/Dec/23 Answered by mr W last updated on 05/Dec/23 $$=\frac{\mathrm{1}×\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }×\frac{\mathrm{2}×\mathrm{4}}{\mathrm{3}^{\mathrm{2}} }×\frac{\mathrm{3}×\mathrm{5}}{\mathrm{4}^{\mathrm{2}} }×…×\frac{\mathrm{98}×\mathrm{100}}{\mathrm{99}^{\mathrm{2}} } \\ $$$$=\frac{\mathrm{1}×\cancel{\mathrm{3}}}{\mathrm{2}^{\cancel{\mathrm{2}}} }×\frac{\cancel{\mathrm{2}}×\cancel{\mathrm{4}}}{\cancel{\mathrm{3}^{\mathrm{2}}…
Question Number 201302 by hardmath last updated on 03/Dec/23 $$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{−\mathrm{2}} \:=\:\mathrm{4}}\\{\mathrm{x}^{−\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{5}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\:\frac{\mathrm{y}}{\mathrm{x}}\:=\:? \\ $$ Answered by witcher3 last updated on 03/Dec/23 $$\left(\mathrm{1}\right)\ast\left(\mathrm{2}\right)\Leftrightarrow\mathrm{2}+\left(\mathrm{xy}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\left(\mathrm{xy}\right)^{\mathrm{2}}…
Question Number 201282 by Supro last updated on 03/Dec/23 Answered by MM42 last updated on 03/Dec/23 $${x}=\frac{\begin{vmatrix}{{a}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:{b}}\\{{ab}\:\:\:\:\:\:−{a}}\end{vmatrix}}{\begin{vmatrix}{{a}\:\:\:\:\:\:\:{b}}\\{{b}\:\:\:\:\:−{a}}\end{vmatrix}}=\frac{−{a}^{\mathrm{3}} −{ab}^{\mathrm{2}} }{−{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }\:={a} \\ $$$${y}=\frac{\begin{vmatrix}{{a}\:\:\:\:\:\:\:\:{a}^{\mathrm{2}} }\\{{b}\:\:\:\:\:\:\:\:{ab}}\end{vmatrix}}{\begin{vmatrix}{{a}\:\:\:\:\:\:\:{b}}\\{{b}\:\:\:\:\:−{a}}\end{vmatrix}}=\frac{{a}^{\mathrm{2}}…
Question Number 201253 by mathlove last updated on 02/Dec/23 $${find}\:{the}\:{sum}\:{of}\:{n}\:{terms}\:{of}\:{the}\:{serice} \\ $$$${s}_{{n}} =\mathrm{5}+\mathrm{11}+\mathrm{19}+\mathrm{29}+\mathrm{41}+………. \\ $$ Answered by Rasheed.Sindhi last updated on 02/Dec/23 $$\left(\mathrm{4}+\mathrm{1}\right)+\left(\mathrm{9}+\mathrm{2}\right)+\left(\mathrm{16}+\mathrm{3}\right)+\left(\mathrm{25}+\mathrm{4}\right)+.. \\ $$$$\left(\mathrm{2}^{\mathrm{2}}…
Question Number 201237 by mnjuly1970 last updated on 02/Dec/23 $$ \\ $$$$\:\:\:\:{If}\:\:,\:\:\:{a}\:\mid\:\mathrm{5}{b}^{\:\mathrm{2}} −\mathrm{10}{b}\:+\mathrm{1}\: \\ $$$$\:\:\:\:\:\Rightarrow\:\:\:\left[\:{a}\:\:,\:\mathrm{5}{b}\:\right]_{\mathrm{lc}{m}} \:=\:\:?\: \\ $$$$ \\ $$$$ \\ $$ Commented by AST…
Question Number 201200 by Calculusboy last updated on 01/Dec/23 Commented by Rasheed.Sindhi last updated on 02/Dec/23 $$\left(\:\left({x}−\mathrm{1}\right)^{{x}−\mathrm{1}} \:\right)^{\mathrm{1}/\mathrm{3}} =\left({x}−\mathrm{1}\right)^{\left({x}−\mathrm{1}\right)^{\mathrm{1}/\mathrm{3}} } \\ $$ Commented by Rasheed.Sindhi…
Question Number 201162 by Calculusboy last updated on 01/Dec/23 Answered by Frix last updated on 01/Dec/23 $${x}={y}={z}=\mathrm{1} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 201190 by Calculusboy last updated on 01/Dec/23 Answered by mr W last updated on 01/Dec/23 $$\frac{\mathrm{1}}{\left(−{x}\right)^{\left(−{x}\right)} }=\frac{\mathrm{1}}{\mathrm{1000}} \\ $$$$\left(−{x}\right)^{\left(−{x}\right)} =\mathrm{1000} \\ $$$$\Rightarrow{x}=−\frac{\mathrm{4ln}\:\mathrm{10}}{{W}\left(\mathrm{4ln}\:\mathrm{10}\right)}\approx−\mathrm{5}.\mathrm{438583} \\…