Question Number 70385 by ®Ëƒ ¬Ë°¹¾¨ ‰¦Í¦¿¨ ¸Ë¹Ç² last updated on 04/Oct/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{determinant} \\ $$$$\begin{vmatrix}{{x}+\mathrm{2}}&{\:{x}+\mathrm{3}}&{{x}+\mathrm{5}}\\{{x}+\mathrm{4}}&{\:{x}+\mathrm{6}}&{{x}+\mathrm{9}}\\{{x}+\mathrm{8}}&{{x}+\mathrm{11}}&{{x}+\mathrm{15}}\end{vmatrix}\:\mathrm{is} \\ $$ Answered by $@ty@m123 last updated on 04/Oct/19 $$=\begin{vmatrix}{−\mathrm{1}}&{\:−\mathrm{2}}&{{x}+\mathrm{5}}\\{−\mathrm{2}}&{\:−\mathrm{3}}&{{x}+\mathrm{9}}\\{−\mathrm{3}}&{−\mathrm{4}}&{{x}+\mathrm{15}}\end{vmatrix}\begin{cases}{{by}\:{C}_{\mathrm{1}}…
Question Number 70383 by ®Ëƒ ¬Ë°¹¾¨ ‰¦Í¦¿¨ ¸Ë¹Ç² last updated on 04/Oct/19 $$\mathrm{If}\:\mathrm{a}\:\mathrm{matrix}\:{A}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that}\:\mathrm{3}{A}^{\mathrm{3}} +\mathrm{2}{A}^{\mathrm{2}} +\mathrm{5}{A}+{I}=\mathrm{0}, \\ $$$$\mathrm{then}\:{A}^{−\mathrm{1}} \mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Commented by mathmax by abdo…
Question Number 69734 by mhmd last updated on 27/Sep/19 $$\mathrm{If}\:{I}_{{n}} =\:\underset{\mathrm{0}\:} {\overset{\pi/\mathrm{4}} {\int}}\mathrm{tan}^{{n}} {x}\:{dx},\:{n}\:\in\:{N},\:\mathrm{then}\:{I}_{{n}+\mathrm{2}} +{I}_{{n}} = \\ $$ Commented by mathmax by abdo last updated…
Question Number 69735 by mhmd last updated on 27/Sep/19 $$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{3}+\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\:= \\ $$ Commented by mathmax by abdo last updated on 27/Sep/19 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…
Question Number 69328 by mhmd last updated on 22/Sep/19 $$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\phi\left({x}\right)}{\phi\left({x}\right)+\phi\left(\frac{\pi}{\mathrm{2}}\:−{x}\right)}\:{dx}\:= \\ $$ Commented by mathmax by abdo last updated on 22/Sep/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 69327 by mhmd last updated on 22/Sep/19 $$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\frac{\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}} −\:\mathrm{5}^{\mathrm{2}{x}−\mathrm{1}} }{\mathrm{10}^{{x}} }\:{dx}\:=\: \\ $$ Answered by MJS last updated on 22/Sep/19 $$\int\frac{\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}}…
Question Number 68352 by mhmd last updated on 09/Sep/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\frac{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \mathrm{15}°}{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \mathrm{15}°}\:\:\mathrm{is} \\ $$ Answered by $@ty@m123 last updated on 09/Sep/19 $$\frac{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \theta}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \theta}=\mathrm{cos}\:\mathrm{2}\theta \\…
Question Number 68353 by mhmd last updated on 09/Sep/19 $$\mathrm{If}\:\mathrm{sin}\:{x}+\mathrm{sin}^{\mathrm{2}} {x}=\mathrm{1},\:\mathrm{then}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{cos}^{\mathrm{4}} {x}\:\:\mathrm{is} \\ $$ Answered by $@ty@m123 last updated on 09/Sep/19 $${Given}\:,\:\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}}…
Question Number 68351 by mhmd last updated on 09/Sep/19 $$\mathrm{If}\:\mathrm{2}{x}^{\mathrm{2}} +\left(\mathrm{2}{p}−\mathrm{13}\right){x}+\mathrm{2}=\mathrm{0}\:\mathrm{is}\:\mathrm{exactly}\:\mathrm{divisible} \\ $$$$\mathrm{by}\:{x}−\mathrm{3},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{p}\:\mathrm{is} \\ $$ Answered by $@ty@m123 last updated on 09/Sep/19 $${f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} +\left(\mathrm{2}{p}−\mathrm{13}\right){x}+\mathrm{2} \\…
Question Number 68151 by mhmd last updated on 06/Sep/19 $$\mathrm{If}\:\mid{a}\mid<\:\mathrm{1}\:\mathrm{and}\:\mid{b}\mid<\:\mathrm{1},\:\mathrm{then}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\mathrm{1}+\left(\mathrm{1}+{a}\right){b}+\left(\mathrm{1}+{a}+{a}^{\mathrm{2}} \right){b}^{\mathrm{2}} +\left(\mathrm{1}+{a}+{a}^{\mathrm{2}} +{a}^{\mathrm{3}} \right){b}^{\mathrm{3}} +… \\ $$$$\mathrm{is} \\ $$ Commented by ~ À…