Question Number 134981 by oooooooo last updated on 09/Mar/21 $$\left(\mathrm{a}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{b}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{c}}+\mathrm{1}\right)=\mathrm{2}\boldsymbol{\mathrm{abc}}\: \\ $$$$\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}}\:\varepsilon\:\mathrm{N} \\ $$ Answered by MJS_new last updated on 10/Mar/21 $$\mathrm{let}\:{a}\leqslant{b}\leqslant{c} \\ $$$$\left(\mathrm{1}\right)\:{c}=\left({a}+\mathrm{1}\right)\left({b}+\mathrm{1}\right) \\…
Question Number 134977 by 0731619177 last updated on 09/Mar/21 Answered by Ñï= last updated on 09/Mar/21 $${tanhx}=\frac{{x}}{\mathrm{1}+\frac{{x}^{\mathrm{2}} }{\mathrm{3}+\frac{{x}^{\mathrm{2}} }{\mathrm{5}+\frac{{x}^{\mathrm{2}} }{\mathrm{7}+…}}}} \\ $$$$\int_{{a}} ^{{b}} {tanhxdx}={ln}\left(\mathrm{cosh}\:{x}\right)\mid_{{a}} ^{{b}}…
Question Number 69436 by azizullah last updated on 23/Sep/19 Answered by $@ty@m123 last updated on 23/Sep/19 $$\left({x}+\mathrm{4}\right)=\mathrm{2}\left({x}−\mathrm{6}\right) \\ $$$${x}=\mathrm{16} \\ $$ Commented by azizullah last…
Question Number 3900 by Filup last updated on 24/Dec/15 $$\mathrm{I}\:\mathrm{asked}\:\mathrm{this}\:\mathrm{question}\:\mathrm{a}\:\mathrm{while}\:\mathrm{ago}, \\ $$$$\mathrm{but}\:\mathrm{I}\:\mathrm{forgot}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}: \\ $$$$ \\ $$$${S}=\int_{\mathrm{0}} ^{\:{n}} \lfloor{x}\rfloor{dx} \\ $$ Answered by Yozzii last updated…
Question Number 69433 by azizullah last updated on 23/Sep/19 Answered by Kunal12588 last updated on 23/Sep/19 $$\mathrm{630}−\mathrm{7}{x}=\mathrm{3}{x} \\ $$$$\Rightarrow{x}=\mathrm{63} \\ $$ Commented by azizullah last…
Question Number 69431 by azizullah last updated on 23/Sep/19 Answered by Kunal12588 last updated on 23/Sep/19 $$\mathrm{120}={x}+{y}…\left(\mathrm{1}\right) \\ $$$${let}\:{x}>{y} \\ $$$$\mathrm{3}{y}=\mathrm{2}{x}…\left(\mathrm{2}\right) \\ $$$${from}\:\left(\mathrm{1}\right) \\ $$$$\mathrm{240}=\mathrm{2}{x}+\mathrm{2}{y}…
Question Number 3894 by Filup last updated on 24/Dec/15 $$\mathrm{I}\:\mathrm{have}\:{n}\:\mathrm{six}\:\mathrm{sided}\:\mathrm{dice}. \\ $$$$\mathrm{I}\:\mathrm{roll}\:\mathrm{them}\:\mathrm{all}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{proability} \\ $$$$\mathrm{that}\:{k}\:\mathrm{of}\:\mathrm{them}\:\mathrm{share}\:\mathrm{the}\:\mathrm{same}\:\mathrm{value}? \\ $$ Commented by Filup last updated on 24/Dec/15 $$\mathrm{Whoops}.\:\mathrm{That}\:\mathrm{was}\:\mathrm{my}\:\mathrm{mistake}! \\…
Question Number 69429 by Learner-123 last updated on 23/Sep/19 Commented by Learner-123 last updated on 23/Sep/19 $${v}_{{a}} =\:\mathrm{162}{km}/{h}\:\left(\nwarrow\right) \\ $$$${v}_{{b}} =\mathrm{144}{km}/{h}\:\left(\searrow\right) \\ $$ Commented by…
Question Number 134960 by bobhans last updated on 09/Mar/21 $$\mathrm{Number}\:\mathrm{theory} \\ $$A palindrome is a number that reads the same backwards as forwards, as 3141413.…
Question Number 134962 by 0731619177 last updated on 09/Mar/21 Answered by Olaf last updated on 09/Mar/21 $$\forall{x}\in\mathbb{R}^{\ast} ,\:\mathrm{arctan}{x}+\mathrm{arctan}\frac{\mathrm{1}}{{x}}\:=\:\frac{\pi}{\mathrm{2}} \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\infty} \frac{{x}\mathrm{arctan}{x}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\…