Question Number 91321 by M±th+et+s last updated on 29/Apr/20 $$\left.\mathrm{1}\right){find}\:{eigen}\:{values}\:{and}\:{corresponding} \\ $$$${eigen}\:{vector}\:{of}\:{the}\:{matrix} \\ $$$$ \\ $$$${A}=\begin{bmatrix}{{cos}\left(\theta\right)}&{−{sin}\left(\theta\right)}\\{{sin}\left(\theta\right)}&{\:\:\:\:\:{cos}\left(\theta\right)}\end{bmatrix} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){solve} \\ $$$$ \\ $$$$\mathrm{6}{y}^{\mathrm{2}} {dx}−{x}\left({y}+\mathrm{2}{x}^{\mathrm{2}}…
Question Number 156820 by tabata last updated on 15/Oct/21 $$\int\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\left(\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\right)} \\ $$ Commented by tabata last updated on 15/Oct/21 $$????? \\ $$ Commented…
Question Number 156795 by tabata last updated on 15/Oct/21 $${prove}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left({sinx}\right)^{\mathrm{2}{n}} ={sec}^{\mathrm{2}} {x}\:??? \\ $$ Answered by FongXD last updated on 15/Oct/21 $$\mathrm{we}\:\mathrm{have}:\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty}…
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Question Number 25700 by naka3546 last updated on 13/Dec/17 Commented by naka3546 last updated on 13/Dec/17 $${AB}\:=\:{AC}\:\:=\:\:\mathrm{2}\:\:{cm} \\ $$$${BC}\:\:=\:\:\mathrm{1}\:\:{cm} \\ $$$${How}\:\:{long}\:\:{the}\:\:{radius}\:\:{of}\:\:{small}\:\:{and}\:\:{big}\:\:{circle}\:\:? \\ $$ Terms of…
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Question Number 156754 by abdurehime last updated on 15/Oct/21 Answered by MathsFan last updated on 15/Oct/21 $$\sqrt{\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}}=\sqrt{\mathrm{5}+\sqrt{\mathrm{24}}}=\sqrt{\frac{\mathrm{5}+\sqrt{\mathrm{1}}}{\mathrm{2}}}+\sqrt{\frac{\mathrm{5}−\sqrt{\mathrm{1}}}{\mathrm{2}}}=\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}} \\ $$$$\:\:\sqrt{\mathrm{5}−\mathrm{2}\sqrt{\mathrm{6}}}=\sqrt{\frac{\mathrm{5}+\sqrt{\mathrm{1}}}{\mathrm{2}}}−\sqrt{\frac{\mathrm{5}−\sqrt{\mathrm{1}}}{\mathrm{2}}}=\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}} \\ $$$$\:{i}.\:\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}−\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}=\:\:\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$ \\ $$$$\boldsymbol{{ii}}.…
Question Number 156744 by joki last updated on 15/Oct/21 $$\mathrm{y}“+\mathrm{y}'=\mathrm{e}^{\mathrm{x}} +\mathrm{3x} \\ $$$$ \\ $$ Answered by qaz last updated on 15/Oct/21 $$\mathrm{y}_{\mathrm{p}} =\frac{\mathrm{1}}{\mathrm{D}^{\mathrm{2}} +\mathrm{D}}\left(\mathrm{e}^{\mathrm{x}}…
Question Number 25675 by naka3546 last updated on 12/Dec/17 Commented by moxhix last updated on 12/Dec/17 $$… \\ $$$$\mathrm{444}\left(\mathrm{2}{n}+\mathrm{887}\right)={k}^{\mathrm{2}} \\ $$$$\mathrm{444}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3}×\mathrm{37} \\ $$$${let}\:{k}=\mathrm{2}×\mathrm{3}×\mathrm{37}×{u}=\mathrm{222}{u}\:{u}\in\mathbb{N} \\…
Question Number 25667 by adityapratap2585@gmail.com last updated on 12/Dec/17 $$\mathrm{Deepak}\:\mathrm{srarts}\:\mathrm{a}\:\mathrm{work}\:\mathrm{and}\:\mathrm{work}\:\mathrm{for}\:\mathrm{12} \\ $$$$\mathrm{days}\:\mathrm{and}\:\mathrm{find}\:\mathrm{he}\:\mathrm{has}\:\mathrm{ompleted}\:\mathrm{10\%}\: \\ $$$$\mathrm{less}\:\mathrm{work}\:\mathrm{which}\:\mathrm{he}\:\mathrm{had}\:\mathrm{to}\:\mathrm{finish}\:\mathrm{in}\: \\ $$$$\mathrm{order}\:\mathrm{to}\:\mathrm{complete}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{24}\:\mathrm{days}\bar {,} \\ $$$$\mathrm{so}\:\mathrm{he}\:\mathrm{ask}\:\mathrm{Rahman}\:\mathrm{to}\:\mathrm{join}\:\mathrm{him}\:\mathrm{to}\:\mathrm{finish} \\ $$$$\mathrm{the}\:\mathrm{work}\:\mathrm{on}\:\mathrm{time}\:.\:\mathrm{If}\:\mathrm{Rahman}\:\mathrm{work}\: \\ $$$$\mathrm{half}\:\mathrm{day}\:\mathrm{only}\:\mathrm{for}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{days}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{efficiency}\:\mathrm{of}\:\mathrm{Rahman}\:\mathrm{is}\:\mathrm{what}…