Question Number 5321 by qw last updated on 07/May/16 $$\:\underset{\:\mathrm{0}} {\overset{\mathrm{sin}^{\mathrm{2}} {x}} {\int}}\:\mathrm{sin}^{−\mathrm{1}} \sqrt{{t}}\:{dt}\:+\underset{\:\mathrm{0}} {\overset{\mathrm{cos}^{\mathrm{2}} {x}} {\int}}\mathrm{cos}^{−\mathrm{1}} \sqrt{{t}}\:{dt}\:= \\ $$ Commented by Yozzii last updated…
Question Number 5313 by qw last updated on 06/May/16 $$\mathrm{tan}^{−\mathrm{1}} \sqrt{\frac{{a}\left({a}+{b}+{c}\right)}{{bc}}}\:+\:\mathrm{tan}^{−\mathrm{1}} \sqrt{\frac{{b}\left({a}+{b}+{c}\right)}{{ca}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\:\mathrm{tan}^{−\mathrm{1}} \sqrt{\frac{{c}\left({a}+{b}+{c}\right)}{{ab}}}\:\:= \\ $$ Commented by Yozzii last updated on 07/May/16 $${Let}\:{j}={tan}\left({tan}^{−\mathrm{1}}…
Question Number 5206 by ´[ last updated on 30/Apr/16 $$\mathrm{If}\:\alpha,\:\beta\:\in\:{R},\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0},\:{k}\:\in\:{R}\:\mathrm{lies}\:\mathrm{between}\:\alpha\:\mathrm{and} \\ $$$$\beta,\:\mathrm{if} \\ $$ Commented by prakash jain last updated on 30/Apr/16…
Question Number 5109 by shaikreshma last updated on 13/Apr/16 $$\mathrm{If}\:\:{k}\:\mathrm{is}\:\mathrm{a}\:\mathrm{scalar}\:\mathrm{and}\:{A}\:\mathrm{is}\:\mathrm{an}\:{n}×{n}\:\mathrm{square} \\ $$$$\mathrm{matrix}.\:\mathrm{Then}\:\mid{kA}\mid= \\ $$ Commented by prakash jain last updated on 13/Apr/16 $$={k}^{{n}} \mid{A}\mid \\…
Question Number 5018 by lec123 last updated on 02/Apr/16 $$\mathrm{If}\:\left({a}−{b}\right)^{\mathrm{2}} +\left({b}−{c}\right)^{\mathrm{2}} +\left({c}−{a}\right)^{\mathrm{2}} =\mathrm{0},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{equal}. \\ $$ Commented by Rasheed Soomro last updated on 03/Apr/16…
Question Number 4891 by Rasheed Soomro last updated on 19/Mar/16 $$\mathrm{A}\:\mathrm{train}\:\mathrm{150}\:\mathrm{metres}\:\mathrm{long}\:\mathrm{completely} \\ $$$$\mathrm{passes}\:\mathrm{a}\:\mathrm{boy}\:\mathrm{walking}\:\mathrm{in}\:\mathrm{the}\:\mathrm{opposite} \\ $$$$\mathrm{direction}\:\mathrm{at}\:\mathrm{6}\:\mathrm{kmph}\:\mathrm{in}\:\mathrm{9}\:\mathrm{seconds}\:\mathrm{and} \\ $$$$\mathrm{a}\:\mathrm{car}\:\:\mathrm{travelling}\:\:\mathrm{in}\:\mathrm{the}\:\:\mathrm{opposite}\: \\ $$$$\mathrm{direction}\:\mathrm{in}\:\mathrm{6}\:\mathrm{sec}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{car}. \\ $$ Commented by…
Question Number 4882 by Rishabh Jain last updated on 19/Mar/16 $$\mathrm{Roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{9}{x}^{\mathrm{2}} −\mathrm{18}\mid{x}\mid+\mathrm{5}=\mathrm{0} \\ $$$$\mathrm{belonging}\:\mathrm{to}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{definition} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)=\mathrm{log}\:\left({x}^{\mathrm{2}} −{x}−\mathrm{2}\right)\:\mathrm{is}/ \\ $$$$\mathrm{are} \\ $$ Answered by Yozzii last…
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…