Question Number 107831 by mathdave last updated on 12/Aug/20 Answered by hgrocks last updated on 12/Aug/20 Commented by mathdave last updated on 12/Aug/20 $${correct}\:{man}\:{thanks} \\…
Question Number 42289 by mondodotto@gmail.com last updated on 22/Aug/18 $$\boldsymbol{\mathrm{log}}\left(\boldsymbol{{x}}+\boldsymbol{{y}}\right)=\mathrm{1} \\ $$$$\boldsymbol{\mathrm{log}}_{\mathrm{2}} \boldsymbol{{x}}+\boldsymbol{\mathrm{log}}_{\mathrm{4}} \boldsymbol{{y}}^{\mathrm{2}} =\mathrm{4} \\ $$ Commented by math khazana by abdo last updated…
Question Number 107818 by mathdave last updated on 12/Aug/20 Commented by hgrocks last updated on 12/Aug/20 $$\mathrm{No}\:\mathrm{It}\:\mathrm{is}\:\mathrm{not}\:\mathrm{correct}\: \\ $$$$\mathrm{For}\:\mathrm{e}.\mathrm{g}.\:\mathrm{put}\:\mathrm{x}\:=\:\mathrm{2} \\ $$$$ \\ $$$$\mathrm{L}.\mathrm{H}.\mathrm{S}.\:=\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{3}\right) \\…
Question Number 107812 by I want to learn more last updated on 12/Aug/20 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\:\:\mathrm{x}^{\mathrm{2}} \:\:−\:\:\mathrm{x}\:\:−\:\:\mathrm{1}\:\:\:=\:\:\mathrm{0}\:\:\:\mathrm{are}\:\:\:\alpha\:\:\mathrm{and}\:\:\beta, \\ $$$$\mathrm{provided}\:\mathrm{that}\:\:\:\:\:\:\mathrm{x}_{\mathrm{n}} \:\:=\:\:\alpha^{\mathrm{n}} \:\:+\:\:\beta^{\mathrm{n}} \:\:.\:\:\:\mathrm{Find}\:\:\:\:\mathrm{x}_{\mathrm{16}} . \\ $$ Answered by…
Question Number 173350 by Muktarr last updated on 10/Jul/22 Answered by aleks041103 last updated on 10/Jul/22 $${r}.{m}.{s}.\:=\:{root}\:{mean}\:{square} \\ $$$${RMS}\left({f}\left({x}\right)\right)=\sqrt{\langle{f}^{\:\mathrm{2}} \left({x}\right)\rangle}=\sqrt{\frac{\mathrm{1}}{{T}}\underset{{x}_{\mathrm{0}} } {\overset{{x}_{\mathrm{0}} +{T}} {\int}}{f}^{\:\mathrm{2}} \left({x}\right)\:{dx}}…
Question Number 107766 by mohammad17 last updated on 12/Aug/20 Answered by bobhans last updated on 12/Aug/20 $$\:\:\:\:\:\:\:\:\frac{\mathcal{B}\mathrm{obhans}}{\Pi} \\ $$$$\:\:\mathrm{y}\:=\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{4}}{\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{6}}\:=\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{6}+\mathrm{5x}−\mathrm{10}}{\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{6}} \\ $$$$\:\mathrm{y}\:=\:\frac{\mathrm{x}^{\mathrm{2}}…
Question Number 173296 by DAVONG last updated on 09/Jul/22 $$\mathrm{I}=\int\frac{\left(\mathrm{cosx}−\mathrm{sinx}\right)\left(\mathrm{1}+\mathrm{sin2x}\right)}{\left(\mathrm{sinx}+\mathrm{cosx}\right)}\mathrm{dx}=\: \\ $$ Answered by Jamshidbek last updated on 09/Jul/22 $$\int\frac{\left(\mathrm{cosx}−\mathrm{sinx}\right)\left(\mathrm{sinx}+\mathrm{cosx}\right)^{\mathrm{2}} }{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}=\int\left(\mathrm{cosx}−\mathrm{sinx}\right)\left(\mathrm{cosx}+\mathrm{sinx}\right)\mathrm{dx}= \\ $$$$=\int\mathrm{cos}^{\mathrm{2}} \mathrm{x}−\mathrm{sin}^{\mathrm{2}} \mathrm{xdx}=\int\mathrm{cos2xdx}=\frac{\mathrm{sin2x}}{\mathrm{2}}+\mathrm{C}…
Question Number 173293 by pete last updated on 09/Jul/22 $$\mathrm{A}\:\mathrm{particle}\:\boldsymbol{\mathrm{P}}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{at}\:\mathrm{time}\:\boldsymbol{{t}}\:\mathrm{seconds},\:\mathrm{its}\:\mathrm{velocity},\:\boldsymbol{\mathrm{v}}=\left(\mathrm{2t}\boldsymbol{{i}}−\boldsymbol{{t}}^{\mathrm{3}} \right)\mathrm{ms}^{−\mathrm{1}} . \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find},\:\mathrm{when}\:{t}=\mathrm{2},\:\mathrm{the}\:\mathrm{magnitudeof}\:\mathrm{the}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{velocity}\:\mathrm{of}\:\boldsymbol{\mathrm{P}}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{acceleration}\:\mathrm{of}\:\boldsymbol{\mathrm{P}}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Given}\:\mathrm{that}\:\boldsymbol{\mathrm{P}}\:\mathrm{is}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\mathrm{with}\:\mathrm{position}\: \\ $$$$\mathrm{vector}\:\left(\mathrm{3i}+\mathrm{2j}\right)\:\mathrm{when}\:\mathrm{t}=\mathrm{1},\:\mathrm{find}\:\mathrm{the}\:\mathrm{position} \\…
Question Number 107746 by mathdave last updated on 12/Aug/20 Answered by Aziztisffola last updated on 12/Aug/20 $$\mathrm{300000}\:\mathrm{L}=\mathrm{300}\:\mathrm{m}^{\mathrm{3}} \\ $$$$\mathrm{7}.\mathrm{5}×\mathrm{4}.\mathrm{2}×\mathrm{1}.\mathrm{2}=\mathrm{37}.\mathrm{8}\:\mathrm{m}^{\mathrm{3}} \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{not}\:\mathrm{transfer}\:\mathrm{all}\:\mathrm{300}\:\mathrm{m}^{\mathrm{3}\:} \mathrm{in}\:\mathrm{tank} \\ $$$$\mathrm{of}\:\mathrm{37}.\mathrm{8}\:\mathrm{m}^{\mathrm{3}} \\…
Question Number 107737 by mathdave last updated on 12/Aug/20 Answered by hgrocks last updated on 12/Aug/20 $$\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)\:=\:\:\frac{\mathrm{1}}{\mathrm{2}}.\left(\left(\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)\:+\right.\right. \\ $$$$\left.\mathrm{l}\left.\mathrm{n}\left(\mathrm{1}−\mathrm{x}\right)\right)^{\mathrm{2}} \:−\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{x}\right)\:−\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}−\mathrm{x}\right)\right) \\ $$$$ \\…