Question Number 21549 by x² – y²@gmail.com last updated on 27/Sep/17 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression}\: \\ $$$$\mathrm{3}\left(\mathrm{sin}\:\theta−\mathrm{cos}\:\theta\right)^{\mathrm{4}} +\mathrm{6}\left(\mathrm{sin}\:\theta+\mathrm{cos}\:\theta\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\mathrm{4}\left(\mathrm{sin}^{\mathrm{6}} \theta+\mathrm{cos}^{\mathrm{6}} \theta\right)\:\:\mathrm{is} \\ $$ Answered by Tikufly last…
Question Number 21519 by ram1234 last updated on 26/Sep/17 $$\mathrm{If}\:\mathrm{th}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} +\mathrm{2}{ax}+{b}=\mathrm{0} \\ $$$$\mathrm{are}\:\mathrm{real}\:\mathrm{and}\:\mathrm{disinct}\:\mathrm{and}\:\mathrm{they}\:\mathrm{differ}\:\mathrm{by} \\ $$$$\mathrm{at}\:\mathrm{most}\:\mathrm{2}{m},\:\mathrm{then}\:\:{b}\:\mathrm{lies}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$ Answered by mrW1 last updated on 26/Sep/17 $$\mathrm{x}^{\mathrm{2}}…
Question Number 87034 by Zainal Arifin last updated on 02/Apr/20 $$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{running}\:\mathrm{along}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{square}\:\mathrm{park}.\:\mathrm{The}\:\mathrm{corners}\:\mathrm{of}\:\mathrm{the}\:\mathrm{park} \\ $$$$\mathrm{are}\:\mathrm{facing}\:\mathrm{north},\:\mathrm{south},\:\mathrm{east}\:\mathrm{and}\:\mathrm{west} \\ $$$$\mathrm{and}\:\mathrm{are}\:\mathrm{named}\:\mathrm{N},\:\mathrm{S},\:\mathrm{E},\:\mathrm{W}\:\:\mathrm{respectively}. \\ $$$$\mathrm{They}\:\mathrm{start}\:\mathrm{at}\:\mathrm{E}\:\mathrm{and}\:\mathrm{run}\:\mathrm{towards}\:\mathrm{S}.\:\mathrm{If} \\ $$$$\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{A}\:\mathrm{is}\:\mathrm{6}\:\mathrm{tines}\:\mathrm{that}\:\mathrm{of}\:\mathrm{B},\:\mathrm{where} \\ $$$$\mathrm{do}\:\mathrm{they}\:\mathrm{meet}\:\mathrm{for}\:\mathrm{the}\:\mathrm{27}^{\mathrm{th}} \:\mathrm{time}? \\…
Question Number 87033 by Zainal Arifin last updated on 02/Apr/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}^{\mathrm{3}} +\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:\:\:,\:\:\:\mathrm{when} \\ $$$$\:\:\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{5} \\ $$ Answered by redmiiuser last updated on 02/Apr/20 $$\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}}…
Question Number 21467 by nawroozdawry last updated on 24/Sep/17 $$\underset{\:\mathrm{1}} {\overset{{e}} {\int}}\:\:\mathrm{log}\:{x}\:{dx}\:= \\ $$ Answered by $@ty@m last updated on 24/Sep/17 $${I}=\int\mathrm{log}{x}.\mathrm{1}{dx}\: \\ $$$$=\mathrm{log}{x}\int\mathrm{1}{dx}−\int\frac{\mathrm{1}}{{x}}.{xdx} \\…
Question Number 21398 by math1967 last updated on 23/Sep/17 $$\underset{\:\mathrm{0}} {\overset{\infty} {\int}}\:\:\:\frac{\mathrm{1}}{\mathrm{1}+{e}^{{x}} }\:{dx}\:= \\ $$ Answered by sma3l2996 last updated on 23/Sep/17 $${e}^{{x}} ={t}\Rightarrow{dx}=\frac{{dt}}{{t}} \\…
Question Number 86897 by ram roop sharma last updated on 01/Apr/20 $$\mathrm{If}\:\int\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}\:{dx} \\ $$$$\:\:\:\:\:\:\:\:=\:\:{A}\:\mathrm{tan}^{−\mathrm{1}} {x}+{B}\:\mathrm{tan}^{−\mathrm{1}} \frac{{x}}{\mathrm{2}}+{C},\:\mathrm{then} \\ $$ Commented by Tony Lin last…
Question Number 21174 by akinyeni last updated on 15/Sep/17 $$\mathrm{The}\:\mathrm{factors}\:\mathrm{of}\:\begin{vmatrix}{{x}}&{{a}}&{{b}}\\{{a}}&{{x}}&{{b}}\\{{a}}&{{b}}&{{x}}\end{vmatrix}\mathrm{are} \\ $$ Answered by $@ty@m last updated on 15/Sep/17 $$=\begin{vmatrix}{{x}}&{{a}}&{{b}}\\{\mathrm{0}}&{{x}−{b}}&{{b}−{x}}\\{{a}}&{{b}}&{{x}}\end{vmatrix},{by}\:{R}_{\mathrm{2}} \rightarrow{R}_{\mathrm{2}} −{R}_{\mathrm{3}} \\ $$$$=\left({x}−{b}\right)\begin{vmatrix}{{x}}&{{a}}&{{b}}\\{\mathrm{0}}&{\mathrm{1}}&{−\mathrm{1}}\\{{a}}&{{b}}&{{x}}\end{vmatrix} \\…
Question Number 86663 by ram roop sharma last updated on 30/Mar/20 $$\mathrm{The}\:\mathrm{matrix}\:{A}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\begin{bmatrix}{\mathrm{1}}&{\mathrm{3}}\\{\mathrm{0}}&{\mathrm{1}}\end{bmatrix}{A}\:=\:\begin{bmatrix}{\mathrm{1}}&{\:\:\:\:\mathrm{1}}\\{\mathrm{0}}&{−\mathrm{1}}\end{bmatrix}\:\mathrm{is} \\ $$ Commented by Prithwish Sen 1 last updated on 30/Mar/20…
Question Number 21083 by chernoaguero@gmail.com last updated on 12/Sep/17 $$\mathrm{4}^{\mathrm{sin}^{\mathrm{2}} {x}} +\:\mathrm{4}^{\mathrm{cos}^{\mathrm{2}} {x}} \:= \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com