Question Number 133658 by liberty last updated on 23/Feb/21 Commented by mr W last updated on 23/Feb/21 $${i}\:{get}\:{headache}\:{when}\:{reading}\:{such} \\ $$$${colorful}\:{text},\:{not}\:{to}\:{mention}\:{to}\:{find} \\ $$$$\left.{the}\:{correct}\:{solution}\::\right) \\ $$ Commented…
Question Number 133653 by greg_ed last updated on 23/Feb/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{everybody}}\:! \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\pi}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{irrational}}\:\boldsymbol{\mathrm{number}}\:??? \\ $$ Answered by Dwaipayan Shikari last updated on 23/Feb/21 $$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{9}}−\frac{\mathrm{1}}{\mathrm{11}}+…=\frac{\pi}{\mathrm{4}} \\ $$$${As}\:{It}\:{is}\:{an}\:{Infinte}\:{series}\:{so}\:{it}\:{can}\:{never}\:{be}\:{rational}…
Question Number 68116 by aliesam last updated on 05/Sep/19 $$\int\frac{{dx}}{{sin}\mathrm{2}{x}−{sec}\left({x}\right)} \\ $$ Commented by MJS last updated on 06/Sep/19 $$\mathrm{look}\:\mathrm{at}\:\mathrm{question}\:\mathrm{68141} \\ $$ Answered by MJS…
Question Number 68113 by Joel122 last updated on 05/Sep/19 $$\mathrm{Solve} \\ $$$${y}.{y}''\:=\:\mathrm{3}\left({y}'\right)^{\mathrm{2}} \\ $$ Answered by Smail last updated on 05/Sep/19 $$\Leftrightarrow\frac{{y}''}{{y}'}=\mathrm{3}\frac{{y}'}{{y}} \\ $$$${ln}\mid{y}'\mid=\mathrm{3}{ln}\mid{y}\mid+{c} \\…
Question Number 68110 by TawaTawa last updated on 05/Sep/19 Commented by kaivan.ahmadi last updated on 07/Sep/19 $$\left(\frac{{y}}{\mathrm{2}}\right)^{\mathrm{2}} =\mathrm{1}−\left(\frac{{x}}{\mathrm{3}}\right)^{\mathrm{2}} \Rightarrow{y}=\pm\mathrm{2}\sqrt{\mathrm{1}−\left(\frac{{x}}{\mathrm{3}}\right)^{\mathrm{2}} } \\ $$$${equation}\:{of}\:{BC}: \\ $$$${m}={tg}\mathrm{30}=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\…
Question Number 2575 by prakash jain last updated on 22/Nov/15 $${a}_{\mathrm{1}} =\mathrm{0} \\ $$$${a}_{{n}} =\mathrm{27}×{a}_{{n}−\mathrm{1}} +\left({n}−\mathrm{1}\right) \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{m}} {\sum}}{a}_{{k}} =? \\ $$ Commented by…
Question Number 133641 by mohammad17 last updated on 23/Feb/21 $${what}\:{is}\:{the}\:{mean}\:{of}\:{Ei}\left({x}\right)\:{and}\:{what}\:{is} \\ $$$${the}\:{folmulla}\:{of}\:{Ei}\left({x}\right)? \\ $$ Answered by Dwaipayan Shikari last updated on 23/Feb/21 $${Ei}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \frac{{e}^{{x}}…
Question Number 133642 by liberty last updated on 23/Feb/21 Commented by liberty last updated on 23/Feb/21 $$\mathrm{dear}\:\mathrm{Mr}\:\mathrm{W},\:\mathrm{Mr}\:\mathrm{Edwin}\:\mathrm{and}\:\mathrm{all}\:\mathrm{master} \\ $$ Answered by bobhans last updated on…
Question Number 68100 by ~ À ® @ 237 ~ last updated on 04/Sep/19 $${Find}\:\:{K}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}−{t}+{t}^{\mathrm{2}} \right)}{{t}}\:{dt}\:\:\:\:\: \\ $$ Commented by mind is power…
Question Number 2564 by Rasheed Soomro last updated on 22/Nov/15 $${A}=\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}\\{\mathrm{2}}&{\mathrm{5}}\end{bmatrix},{B}=\begin{bmatrix}{\mathrm{3}}&{−\mathrm{1}}\\{\mathrm{4}}&{+\mathrm{2}}\end{bmatrix} \\ $$$${determine}\:{A}^{{B}} \\ $$ Answered by Yozzi last updated on 22/Nov/15 $$\mid{A}\mid=\mathrm{5}−\mathrm{4}=\mathrm{1}\neq\mathrm{0}\:\Rightarrow{A}\:{is}\:{non}−{singular}. \\ $$$${A}^{{B}}…