Question Number 22347 by Tinkutara last updated on 16/Oct/17 $$\mathrm{Total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mid\mathrm{cot}\:{x}\mid\:= \\ $$$$\mathrm{cot}\:{x}\:+\:\frac{\mathrm{1}}{\mathrm{sin}\:{x}},\:{x}\:\in\:\left[\mathrm{0},\:\mathrm{3}\pi\right]\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 22345 by ibraheem160 last updated on 16/Oct/17 $$\mathrm{6}^{\mathrm{x}+\mathrm{2}} =\mathrm{2}\left(\mathrm{3}^{\mathrm{x}} \right),\:\mathrm{find}\:\mathrm{x}? \\ $$ Commented by JI Siam last updated on 21/Dec/17 $$\mathrm{Here}\:\mathrm{6}^{\mathrm{x}+\mathrm{1}} =\mathrm{3}^{\mathrm{x}−\mathrm{1}} \:\mathrm{so},\mathrm{likely}\:\mathrm{x}\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{normal}\:\mathrm{number}.…
Question Number 87881 by Rio Michael last updated on 06/Apr/20 $$\:\int_{−\infty} ^{\:+\infty} \frac{\mathrm{1}}{{x}}\:{dx}\:=\: \\ $$ Commented by mathmax by abdo last updated on 06/Apr/20 $${the}\:{function}\:{x}\rightarrow\frac{\mathrm{1}}{{x}}\:{is}\:{odd}\:\Rightarrow\int_{−\infty}…
Question Number 87878 by Cmr 237 last updated on 06/Apr/20 $${posons}\: \\ $$$$\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{3}}\right)^{\boldsymbol{{n}}} =\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} +\boldsymbol{\mathrm{b}}_{\boldsymbol{\mathrm{n}}} \sqrt{\mathrm{3}} \\ $$$$\boldsymbol{\mathrm{montre}}\:\boldsymbol{\mathrm{que}}\:\boldsymbol{\mathrm{pgcd}}\left(\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} ;\boldsymbol{{b}}_{\boldsymbol{{n}}} \right)=\mathrm{1} \\ $$ Answered by mind…
Question Number 153412 by mathdanisur last updated on 07/Sep/21 $$\mathrm{If}\:\:\:\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d}\in\left(\mathrm{0};\infty\right)\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{a}^{\mathrm{3}} }{\mathrm{bc}}\:+\:\frac{\mathrm{b}^{\mathrm{3}} }{\mathrm{cd}}\:+\:\frac{\mathrm{c}^{\mathrm{3}} }{\mathrm{da}}\:+\:\frac{\mathrm{d}^{\mathrm{3}} }{\mathrm{ab}}\:\geqslant\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:+\:\mathrm{d} \\ $$ Answered by puissant last updated on 07/Sep/21…
Question Number 87876 by M±th+et£s last updated on 06/Apr/20 $${prove}\:{that} \\ $$$$\Gamma\left({z}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} \:{x}^{{z}−\mathrm{1}} \:{dx},{Re}\left({z}\right)>\mathrm{0} \\ $$ Commented by Joel578 last updated on 07/Apr/20…
Question Number 87877 by Cmr 237 last updated on 06/Apr/20 $${posons}\: \\ $$$$\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{3}}\right)^{\boldsymbol{{n}}} =\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} +\boldsymbol{\mathrm{b}}_{\boldsymbol{\mathrm{n}}} \sqrt{\mathrm{3}} \\ $$$$\boldsymbol{\mathrm{montre}}\:\boldsymbol{\mathrm{que}}\:\boldsymbol{\mathrm{pgcd}}\left(\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} ;\boldsymbol{{b}}_{\boldsymbol{{n}}} \right)=\mathrm{1} \\ $$ Terms of Service…
Question Number 153409 by SOMEDAVONG last updated on 07/Sep/21 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{S}=\mathrm{4}\pi\mathrm{r}^{\mathrm{2}} \\ $$ Answered by puissant last updated on 07/Sep/21 $${S}\:{is}\:{derivate}\:{of}\:{V}.\:\:{now},\: \\ $$$${V}=\frac{\mathrm{4}}{\mathrm{3}}\pi{R}^{\mathrm{3}} . \\ $$$$\frac{\partial}{\partial{R}}{V}=\:{S}\:\Rightarrow\:{S}=\frac{\mathrm{4}}{\mathrm{3}}×\mathrm{3}\pi{R}^{\mathrm{2}}…
Question Number 153405 by rexford last updated on 07/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 87870 by Prithwish Sen 1 last updated on 06/Apr/20 $$\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{amd}}\:\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{imtegers}}. \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{many}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{solitions}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{eqiation}}\:\boldsymbol{\mathrm{has}} \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{10}\boldsymbol{\mathrm{y}}^{\mathrm{2}} \:=\:\pm\mathrm{1} \\ $$ Terms of Service Privacy Policy…