Question Number 63108 by ajfour last updated on 29/Jun/19 Commented by ajfour last updated on 29/Jun/19 $${Find}\:{x}_{{A}} \:{in}\:{terms}\:{of}\:{a},{b},{s}\:. \\ $$$$\:\:\:\:\:{s}_{{min}} \leqslant{s}\leqslant{s}_{{max}} \:. \\ $$$${a},{b}\:{are}\:{parameters}\:{of}\:{ellipse} \\…
Question Number 128643 by liberty last updated on 09/Jan/21 $$\:\mathrm{If}\:\mathrm{tan}\:\mathrm{x}+\mathrm{sec}\:\mathrm{x}\:=\:\mathrm{b}\:\mathrm{then}\:\mathrm{cos}\:\mathrm{x}\:=? \\ $$ Commented by john_santu last updated on 09/Jan/21 $$\:\mathrm{tan}\:\mathrm{x}\:=\:\mathrm{b}−\mathrm{sec}\:\mathrm{x}\: \\ $$$$\mathrm{squaring}\:\Rightarrow\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}=\mathrm{b}^{\mathrm{2}} −\mathrm{2bsec}\:\mathrm{x}+\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}…
Question Number 128641 by john_santu last updated on 09/Jan/21 $$\:\mathrm{Given}\:\begin{cases}{\mathrm{A}+\mathrm{B}=\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{2}}}\\{\mathrm{A}−\mathrm{B}=\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{3}}}\end{cases} \\ $$$$\:\mathrm{then}\:\mathrm{tan}\:\mathrm{A}\:=? \\ $$ Answered by liberty last updated on 09/Jan/21 $$\:\left(\mathrm{1}\right)+\left(\mathrm{2}\right)\:\Rightarrow\:\mathrm{2A}\:=\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\mathrm{tan}\:\mathrm{2A}\:=\:\frac{\mathrm{1}/\mathrm{2}+\mathrm{1}/\mathrm{3}}{\mathrm{1}−\left(\mathrm{1}/\mathrm{2}\right)×\left(\mathrm{1}/\mathrm{3}\right)}\:=\:\mathrm{1} \\…
Question Number 63103 by aseer imad last updated on 29/Jun/19 Commented by aseer imad last updated on 29/Jun/19 how to do this...Tia. Commented by Hope last updated on…
Question Number 128636 by john_santu last updated on 09/Jan/21 $$\mathrm{Solve}\:\mathrm{diopthantine}\:\mathrm{equation}\: \\ $$$$\:\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}\:=\:\frac{\mathrm{2}}{\mathrm{17}}. \\ $$ Answered by liberty last updated on 09/Jan/21 $$\Rightarrow\:\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}=\frac{\mathrm{2}}{\mathrm{17}}\:;\:\mathrm{2ab}\:=\:\mathrm{17}\left(\mathrm{a}+\mathrm{b}\right) \\ $$$$\mathrm{consider}\:\left(\mathrm{2a}−\mathrm{17}\right)\left(\mathrm{2b}−\mathrm{17}\right)=\mathrm{4ab}−\mathrm{34}\left(\mathrm{a}+\mathrm{b}\right)+\mathrm{17}^{\mathrm{2}} \\…
Question Number 63101 by mathmax by abdo last updated on 29/Jun/19 $${calculate}\:\:{S}\:=\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}\:+\frac{\mathrm{1}}{\mathrm{5}×\mathrm{6}}\:+….. \\ $$ Commented by mathmax by abdo last updated on 29/Jun/19 $${let}\:{try}\:{another}\:{way}\:{we}\:{have}\:\frac{{d}}{{dx}}{ln}\left(\mathrm{1}+{x}\right)\:=\frac{\mathrm{1}}{\mathrm{1}+{x}}\:=\sum_{{n}=\mathrm{0}} ^{\infty}…
Question Number 128634 by liberty last updated on 09/Jan/21 $$\theta\:=\:\int\:\left(\mathrm{1}+\mathrm{4x}^{\mathrm{4}} \right)\mathrm{e}^{\mathrm{x}^{\mathrm{4}} } \:\mathrm{dx}\: \\ $$ Answered by john_santu last updated on 09/Jan/21 $$\theta=\int\:\mathrm{e}^{\mathrm{x}^{\mathrm{4}} } \:\mathrm{dx}\:+\:\int\:\mathrm{4x}^{\mathrm{4}}…
Question Number 128632 by shaker last updated on 09/Jan/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128633 by Lordose last updated on 09/Jan/21 $$\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{x}^{\mathrm{2n}} \mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on 09/Jan/21 $$\mathrm{let}\:\mathrm{try}\:\mathrm{another}\:\mathrm{way}\:\:\mathrm{x}=\frac{\mathrm{t}}{\mathrm{3}}\:\Rightarrow…
Question Number 63095 by aliesam last updated on 28/Jun/19 Answered by MJS last updated on 29/Jun/19 $$\sqrt[{\mathrm{3}}]{\mathrm{4}{x}^{\mathrm{4}} −\mathrm{40}{x}^{\mathrm{2}} +\mathrm{100}}−\sqrt[{\mathrm{3}}]{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{10}}=\mathrm{20}−\mathrm{2}{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} ={s} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{4}{s}^{\mathrm{2}}…