Question Number 86246 by Rio Michael last updated on 27/Mar/20 $$\int\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{4}} }}\:{dx}\:=\:? \\ $$ Answered by TANMAY PANACEA. last updated on 27/Mar/20 $$\int\frac{\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 151780 by Tawa11 last updated on 23/Aug/21 Answered by puissant last updated on 23/Aug/21 $${Q}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{arctanx}}{{x}}{dx} \\ $$$${arctanx}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \frac{{x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{2}{n}+\mathrm{1}}…
Question Number 86247 by M±th+et£s last updated on 27/Mar/20 $$\int_{\mathrm{0}} ^{\mathrm{8}} \int_{\mathrm{0}} ^{{x}^{\frac{\mathrm{2}}{\mathrm{3}}} } \:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{1}}\:{dy}\:{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 86244 by TawaTawa1 last updated on 27/Mar/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151782 by gloriousman last updated on 23/Aug/21 $$ \\ $$$$\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c}\geqslant\mathrm{0}\:\mathrm{and}\:\frac{\mathrm{x}−\mathrm{1}}{\mathrm{4}}=\frac{\mathrm{y}−\mathrm{3}}{\mathrm{2}}=\frac{\mathrm{z}+\mathrm{2}}{\mathrm{3}}, \\ $$$$\mathrm{min}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{z}^{\mathrm{2}} \right)=? \\ $$$$ \\ $$ Answered by liberty last…
Question Number 151777 by Olaf_Thorendsen last updated on 22/Aug/21 $$\mathrm{Le}\:\mathrm{dernier}\:\mathrm{jour}\:\mathrm{d}'\mathrm{un}\:\mathrm{certain}\:\mathrm{mois}\:\mathrm{au}\: \\ $$$$\mathrm{cours}\:\mathrm{de}\:\mathrm{la}\:\mathrm{premiere}\:\mathrm{guerre}\:\mathrm{mondiale}, \\ $$$$\mathrm{une}\:\mathrm{bombe}\:\mathrm{tombe}\:\mathrm{sur}\:\mathrm{la}\:\mathrm{tombe}\:\mathrm{d}'\mathrm{un} \\ $$$$\mathrm{hallebardier}. \\ $$$$ \\ $$$$\mathrm{Sachant}\:\mathrm{que}\:\mathrm{1}.\mathrm{872}.\mathrm{269}\:\mathrm{est}\:\mathrm{le}\:\mathrm{produit} \\ $$$$\mathrm{de}\:: \\ $$$$ \\…
Question Number 86242 by niroj last updated on 27/Mar/20 $$\:\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{C}}\mathrm{F}+\boldsymbol{\mathrm{P}}\mathrm{I}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }+\mathrm{3}\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}+\mathrm{2}\boldsymbol{\mathrm{y}}=\:\boldsymbol{\mathrm{e}}^{\mathrm{2}\boldsymbol{\mathrm{x}}} \:\boldsymbol{\mathrm{sinx}}\:. \\ $$$$\: \\ $$$$ \\ $$ Answered by TANMAY PANACEA.…
Question Number 86240 by Rio Michael last updated on 27/Mar/20 $$\mathrm{use}\:\mathrm{the}\:\mathrm{Chinese}\:\mathrm{Remainder}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{find} \\ $$$$\:\:{x}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:{x}\:\equiv\:\mathrm{2}\left(\mathrm{mod}\:\mathrm{3}\right) \\ $$$$\mathrm{2}{x}\:\equiv\:\mathrm{3}\left(\mathrm{mod}\:\mathrm{5}\right) \\ $$$$\:\mathrm{3}{x}\equiv\:\mathrm{4}\left(\:\mathrm{mod}\:\mathrm{7}\right) \\ $$ Answered by mr W…
Question Number 20705 by mondodotto@gmail.com last updated on 01/Sep/17 Answered by dioph last updated on 01/Sep/17 $$\mathrm{40}\:=\:\frac{\Sigma{x}_{{i}} −\left(\mathrm{43}+\mathrm{35}\right)+\left(\mathrm{34}+\mathrm{53}\right)}{\mathrm{200}} \\ $$$$\mathrm{8000}\:=\:\Sigma{x}_{{i}} \:−\:\mathrm{78}\:+\:\mathrm{87} \\ $$$$\Sigma{x}_{{i}} \:=\:\mathrm{7991} \\…
Question Number 20704 by tammi last updated on 01/Sep/17 $$\mathrm{4cos}\:\theta\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{3}}+\theta\right)\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{3}}+\theta\right)=\mathrm{cos}\:\mathrm{3}\theta \\ $$ Commented by myintkhaing last updated on 01/Sep/17 $$\mathrm{L}.\mathrm{H}.\mathrm{S}=\mathrm{2cos}\theta\left[\mathrm{cos}\left(\mathrm{2}\pi+\theta\right)+\mathrm{cos}\frac{\mathrm{2}\pi}{\mathrm{3}}\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2cos}\theta\left[\mathrm{cos2}\theta−\mathrm{cos}\frac{\pi}{\mathrm{3}}\right]=\mathrm{2cos}\theta\left[\mathrm{2cos}^{\mathrm{2}} \theta−\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{4cos}^{\mathrm{3}}…