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Author: Tinku Tara

2x-1-1-3-x-1-1-3-1-

Question Number 68768 by aliesam last updated on 15/Sep/19 $$\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{1}}\:+\sqrt[{\mathrm{3}}]{{x}−\mathrm{1}}\:=\:\mathrm{1} \\ $$ Commented by kaivan.ahmadi last updated on 15/Sep/19 $${t}={x}−\mathrm{1}\Rightarrow{x}={t}+\mathrm{1}\Rightarrow \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{2}{t}+\mathrm{1}}+\sqrt[{\mathrm{3}}]{{t}}=\mathrm{1}\Rightarrow\sqrt[{\mathrm{3}}]{\mathrm{2}{t}+\mathrm{1}}=\mathrm{1}−\sqrt[{\mathrm{3}}]{{t}}\Rightarrow \\ $$$$\mathrm{2}{t}+\mathrm{1}=\mathrm{1}−\mathrm{3}\sqrt[{\mathrm{3}}]{{t}}+\mathrm{3}\sqrt[{\mathrm{3}}]{{t}^{\mathrm{2}} }−{t}\Rightarrow\mathrm{3}{t}=\mathrm{3}\sqrt[{\mathrm{3}}]{{t}}\left(\sqrt[{\mathrm{3}}]{{t}}−\mathrm{1}\right)\Rightarrow…

0-x-2-1-x-2-4-dx-

Question Number 134301 by bramlexs22 last updated on 02/Mar/21 $$\Omega\:=\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{4}} }\:{dx} \\ $$ Answered by EDWIN88 last updated on 02/Mar/21 $$\mathrm{replace}\:\mathrm{x}\:\mathrm{by}\:\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{yields}\:…

F-0-16-arctan-x-1-x-2-dx-

Question Number 134303 by bramlexs22 last updated on 02/Mar/21 $$\mathcal{F}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{16}\:\mathrm{arctan}\:\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$ Answered by Ñï= last updated on 02/Mar/21 $$\mathcal{F}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{16}\:\mathrm{arctan}\:\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}}…

Question-134297

Question Number 134297 by mathlove last updated on 02/Mar/21 Answered by Ñï= last updated on 02/Mar/21 $$\frac{{d}}{{dx}}{ln}\left({x}^{{x}} +\mathrm{2}^{{x}^{{x}} } \right)=\frac{\mathrm{1}}{{x}^{{x}} +\mathrm{2}^{{x}^{{x}} } }\left[{x}^{{x}} \left({lnx}+\mathrm{1}\right)+\left({ln}\mathrm{2}\right)\mathrm{2}^{{x}^{{x}} }…

Question-134296

Question Number 134296 by EDWIN88 last updated on 02/Mar/21 Answered by bramlexs22 last updated on 02/Mar/21 $$\mathrm{total}\:\mathrm{three}\:\mathrm{digit}\:\mathrm{numbers}\:=\:\mathrm{4}×\mathrm{5}^{\mathrm{2}} =\mathrm{100} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{has}\:\mathrm{identical}\:\mathrm{digit}? \\ $$$$\left[\:\mathrm{111},\:\mathrm{333},\:\mathrm{555},\:\mathrm{999}\:\right]\:=\:\mathrm{4}\:\mathrm{numbers} \\ $$$$\mathrm{the}\:\mathrm{p}\left(\mathrm{A}\right)=\:\frac{\mathrm{4}}{\mathrm{100}}\:=\:\frac{\mathrm{1}}{\mathrm{25}} \\…

Two-arcs-having-their-centers-on-a-circle-are-cutting-each-other-at-a-single-point-inside-the-circle-and-thus-dividing-the-circle-in-four-regions-If-the-arcs-cut-each-other-in-a-b-amp-c-d-ratio

Question Number 68761 by Rasheed.Sindhi last updated on 15/Sep/19 $$\mathrm{Two}\:\boldsymbol{\mathrm{arcs}}\:\mathrm{having}\:\mathrm{their}\:\mathrm{centers}\:\mathrm{on}\:\mathrm{a} \\ $$$$\boldsymbol{\mathrm{circle}}\:\mathrm{are}\:\mathrm{cutting}\:\mathrm{each}\:\mathrm{other}\:\mathrm{at}\:\mathrm{a}\: \\ $$$$\mathrm{single}\:\mathrm{point}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{and}\:\mathrm{thus} \\ $$$$\:\mathrm{dividing}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{in}\:\mathrm{four}\:\mathrm{regions}. \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{arcs}\:\mathrm{cut}\:\mathrm{each}\:\mathrm{other}\:\mathrm{in}\:\boldsymbol{\mathrm{a}}:\boldsymbol{\mathrm{b}}\:\&\:\boldsymbol{\mathrm{c}}:\boldsymbol{\mathrm{d}}\: \\ $$$$\mathrm{ratios}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{between}\:\mathrm{four} \\ $$$$\mathrm{regions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{when}\:\mathrm{the}\:\mathrm{circle} \\…