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. \\ $$$$\left.\mathrm{l}\left.\mathrm{n}\left(\mathrm{1}−\mathrm{x}\right)\right)^{\mathrm{2}} \:−\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{x}\right)\:−\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}−\mathrm{x}\right)\right) \\ $$$$ \\…
Question Number 107728 by mathdave last updated on 12/Aug/20 Answered by john santu last updated on 12/Aug/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\frac{\clubsuit\mathcal{JS}\clubsuit}{\ldots} \\ $$$${let}\:{f}\left({x}\right)={x}^{\mathrm{2020}} +{ax}^{\mathrm{2}} +{bx}+{c}\: \\ $$$$\left(\mathrm{1}\right){f}\left(\mathrm{2}\right)=\:\mathrm{2}^{\mathrm{2020}} +\mathrm{4}{a}+\mathrm{2}{b}+{c}\:=\:\mathrm{0}…
Question Number 107729 by M±th+et+s last updated on 12/Aug/20 $$\left.\mathrm{1}\right)\:{solve}\:{the}\:{D}.{E}\:\:\:: \\ $$$$\frac{{dy}}{{dx}}−{y}\:{tan}\left({x}\right)=−{y}^{\mathrm{2}} {sec}\left({x}\right)\: \\ $$$$ \\ $$$$\left.\mathrm{2}\right){find}\:{x} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{25}} {\prod}}\left({x}+\frac{{x}}{\mathrm{3}^{{k}} }\right)=\mathrm{1} \\ $$$$ \\…
Question Number 107718 by mohammad17 last updated on 12/Aug/20 Answered by Aziztisffola last updated on 12/Aug/20 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\overset{−} {\mathrm{z}}_{\mathrm{n}} =\overline {\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{z}_{\mathrm{n}} }=\:\overset{−}…
Question Number 42182 by mondodotto@gmail.com last updated on 19/Aug/18 $$\boldsymbol{\mathrm{integrate}}\:\:\int\boldsymbol{\mathrm{e}}^{\boldsymbol{{x}}^{\mathrm{2}} } \boldsymbol{{x}}^{\mathrm{2}} \:\boldsymbol{{dx}} \\ $$ Commented by mondodotto@gmail.com last updated on 19/Aug/18 $$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{help}}\:\boldsymbol{\mathrm{this}} \\ $$…
Question Number 42170 by lucha116 last updated on 19/Aug/18 $$\left(\mathrm{2}{tanx}−\mathrm{5}\right){tanx}+\left(\mathrm{2}{cotx}−\mathrm{5}\right){cotx}−\mathrm{8}=\mathrm{0} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 19/Aug/18 $$\left(\mathrm{2}{a}−\mathrm{5}\right){a}+\left(\frac{\mathrm{2}}{{a}}−\mathrm{5}\right)\frac{\mathrm{1}}{{a}}−\mathrm{8}=\mathrm{0} \\ $$$$\left(\mathrm{2}{a}^{\mathrm{2}} −\mathrm{5}{a}\right)+\left(\frac{\mathrm{2}−\mathrm{5}{a}}{{a}}\right)\frac{\mathrm{1}}{{a}}−\mathrm{8}=\mathrm{0} \\ $$$$\mathrm{2}{a}^{\mathrm{2}}…
Question Number 42169 by lucha116 last updated on 19/Aug/18 $${solve} \\ $$$$\mathrm{2}{sin}\mathrm{3}{x}\left({sinx}+\sqrt{\mathrm{3}}{cosx}\right)+\mathrm{1}+\mathrm{2}{cos}\mathrm{2}{x}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com