Question Number 16589 by ajfour last updated on 24/Jun/17 $$\:\:\:\mathrm{x}^{\mathrm{2}} −\mid\mathrm{3x}+\mathrm{2}\mid+\mathrm{x}\:\geqslant\:\mathrm{0} \\ $$$$\:\mathrm{find}\:\mathrm{range}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{agreeing} \\ $$$$\mathrm{with}\:\mathrm{above}\:\mathrm{inequality}. \\ $$ Answered by mrW1 last updated on 24/Jun/17 $$\mathrm{if}\:\mathrm{3x}+\mathrm{2}\geqslant\mathrm{0}\:\mathrm{or}\:\mathrm{x}\geqslant−\frac{\mathrm{2}}{\mathrm{3}}\:\left(\approx−\mathrm{0}.\mathrm{67}\right)…
Question Number 147640 by mathdanisur last updated on 22/Jul/21 $$\mathrm{8}{sin}\left({x}\right)\:=\:\frac{\sqrt{\mathrm{3}}}{{cos}\left({x}\right)}\:+\:\frac{\mathrm{1}}{{sin}\left({x}\right)}\:\:\Rightarrow\:{x}=? \\ $$ Answered by gsk2684 last updated on 25/Jul/21 $$\mathrm{8}\:\mathrm{sin}\:^{\mathrm{2}} {x}\:\mathrm{cos}\:{x}\:=\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x} \\ $$$$\mathrm{4}\:\mathrm{sin}\:\mathrm{2}{x}\:\mathrm{sin}\:{x}\:=\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x} \\ $$$$\mathrm{2}\left(\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{x}\:\mathrm{sin}\:{x}\:\right)=\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}…
Question Number 147621 by mathdanisur last updated on 22/Jul/21 $${Find}\:{the}\:{general}\:{solution}\:{for}: \\ $$$$\frac{{dy}}{{dx}}\:=\:\left(\mathrm{3}{x}\:+\:\mathrm{2}{y}\:+\:\mathrm{1}\right)^{\mathrm{2}} \\ $$ Answered by gsk2684 last updated on 22/Jul/21 $${put}\:{u}=\mathrm{3}{x}+\mathrm{2}{y}+\mathrm{1}\Rightarrow\frac{{du}}{{dx}}=\mathrm{3}+\mathrm{2}\frac{{dy}}{{dx}} \\ $$$$\frac{{du}}{{dx}}=\mathrm{3}+\mathrm{2}{u}^{\mathrm{2}} \\…
Question Number 147626 by mathdanisur last updated on 22/Jul/21 $$\underset{\:\mathrm{0}} {\overset{\:\mathrm{3}} {\int}}\:\frac{{dx}}{\mathrm{2}\:+\:{cosx}}\:=\:? \\ $$ Answered by mathmax by abdo last updated on 22/Jul/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\mathrm{3}}…
Question Number 82082 by TawaTawa last updated on 18/Feb/20 $$\mathrm{Evaluate}:\:\:\:\:\:\:\left(\frac{\sqrt{\mathrm{30}\:+\:\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}}{\:\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}\right)^{\mathrm{1}/\mathrm{4}} \\ $$ Commented by MJS last updated on 18/Feb/20 $$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{expand}\:\mathrm{or}\:\mathrm{factorise}\:\sqrt{\mathrm{30}+\sqrt{\mathrm{8}}+\sqrt{\mathrm{5}}}\: \\ $$$$\Rightarrow\:\mathrm{we}\:\mathrm{can}\:\mathrm{only}\:\mathrm{use}\:\mathrm{a}\:\mathrm{calculator} \\ $$ Commented…
Question Number 16542 by gourav~ last updated on 23/Jun/17 $${if}\:\frac{{a}}{\mid{Z}_{\mathrm{2}} −{Z}_{\mathrm{3}} \mid}=\frac{{b}}{\mid{Z}_{\mathrm{3}} −{Z}_{\mathrm{1}} \mid}=\frac{{c}}{\mid{Z}_{\mathrm{1}} −{Z}_{\mathrm{2}} \mid}\:\:{Then}.. \\ $$$${find}..\:\frac{{a}^{\mathrm{2}} }{{Z}_{\mathrm{2}} −{Z}_{\mathrm{3}} }\:+\:\frac{{b}^{\mathrm{2}} }{{Z}_{\mathrm{3}} −{Z}_{\mathrm{1}} }\:+\:\frac{{c}^{\mathrm{2}} }{{Z}_{\mathrm{1}}…
Question Number 147611 by mathdanisur last updated on 22/Jul/21 $$\left(\mathrm{111}\right)_{\mathrm{10}} \:=\:\left({x}\right)_{\mathrm{5}} \\ $$$$\Rightarrow\:{x}\:=\:? \\ $$ Answered by bobhans last updated on 22/Jul/21 $$\left(\mathrm{111}\right)_{\mathrm{10}} =\:\mathrm{1}×\mathrm{10}^{\mathrm{2}} +\mathrm{1}×\mathrm{10}^{\mathrm{1}}…
Question Number 16540 by gourav~ last updated on 23/Jun/17 $${if}\:\mid{Z}\mid=\mathrm{1}\:{Then}\:\frac{\mathrm{1}+{Z}}{\mathrm{1}+\bar {{Z}}}\:\:{is}\:{equal}\:{to}… \\ $$$$\left.{a}\right)\:{Z}\:\: \\ $$$$\left.{b}\right)\:\:\bar {{Z}} \\ $$$$\left.{c}\right)\:{Z}+\bar {{Z}} \\ $$$$\left.{d}\right)\:{N}.{O}.{T} \\ $$ Answered by…
Question Number 82071 by jagoll last updated on 18/Feb/20 $${x}\neq\:{y}\:\neq{z}\:\neq\:\mathrm{0} \\ $$$${xy}\:+\:{xz}\:+\:{yz}\:=\:\mathrm{0} \\ $$$${prove}\:{that}\:\frac{{x}+{y}}{{z}}+\frac{{x}+{z}}{{y}}+\frac{{y}+{z}}{{x}}\:=\:−\mathrm{3} \\ $$$$ \\ $$ Answered by TANMAY PANACEA last updated on…
Question Number 82073 by TawaTawa last updated on 18/Feb/20 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\mathrm{j}_{\mathrm{3}/\mathrm{2}} \left(\mathrm{x}\right)\:\:=\:\:\frac{\sqrt{\mathrm{2}}}{\pi\mathrm{x}}\:\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\:−\:\mathrm{cos}\:\mathrm{x}\right) \\ $$ Commented by jagoll last updated on 18/Feb/20 $${what}\:{is}\:{j}_{\frac{\mathrm{3}}{\mathrm{2}}} ? \\ $$ Commented…