Question Number 7022 by Master Moon last updated on 06/Aug/16 $$\mathrm{Prove}\:\mathrm{that}\:\sqrt{\frac{\mathrm{2a}}{\mathrm{a}+\mathrm{b}}}\:+\:\sqrt{\frac{\mathrm{2b}}{\mathrm{b}+\mathrm{c}}}\:+\:\sqrt{\frac{\mathrm{2c}}{\mathrm{c}+\mathrm{a}}}\:\leqslant\:\mathrm{3} \\ $$$$\:{where}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7013 by Master Moon last updated on 06/Aug/16 Commented by Yozzis last updated on 06/Aug/16 $$\left(\mathrm{1}−{x}\right)^{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}\left(−\mathrm{1}\right)^{{k}} {x}^{{k}} =\mathrm{1}+\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}\left(−\mathrm{1}\right)^{{k}}…
Question Number 138077 by mohammad17 last updated on 09/Apr/21 $$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left(\sqrt[{\mathrm{3}}]{{cotx}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{cotx}}}\right)^{\mathrm{2}} {dx} \\ $$ Answered by Dwaipayan Shikari last updated on 09/Apr/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 138068 by Ñï= last updated on 09/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{x}^{\mathrm{2}{n}} \zeta\left(\mathrm{2}{n}\right)=\frac{\mathrm{1}}{\mathrm{2}}−\frac{\pi{x}}{\mathrm{2}}\mathrm{cot}\:\pi{x} \\ $$ Answered by Dwaipayan Shikari last updated on 09/Apr/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 138061 by sahnaz last updated on 09/Apr/21 $$\mathrm{x}^{\mathrm{x}+\mathrm{4}} =\mathrm{32}\:\:\:\:\mathrm{x}=? \\ $$ Answered by MJS_new last updated on 10/Apr/21 $${x}\approx\mathrm{1}.\mathrm{81486813} \\ $$ Terms of…
Question Number 138060 by mathocean1 last updated on 09/Apr/21 $${We}\:{throw}\:\mathrm{2}\:{times}\:{a}\:{cubic}\:{dice}\:.\:{Its} \\ $$$${faces}\:{are}\:{numeroted}\:\mathrm{0},\:\mathrm{0},\:−\mathrm{1},\:\mathrm{1},\mathrm{1},\mathrm{1}. \\ $$$${We}\:{note}\:{a}\:{the}\:{result}\:{of}\:{the}\:{face}\:{throw} \\ $$$${and}\:{b}\:{the}\:{result}\:{of}\:{second}\:{one}.\: \\ $$$$\left.\mathrm{1}\right){Calculate}\:{the}\:{probabilities}\:{to}\:{have}\: \\ $$$${a}\:{and}\:{b}\:{which}\:{verify}\:: \\ $$$$\bullet{a}=−\mathrm{1}\:{and}\:{b}=\mathrm{0} \\ $$$$\bullet{a}=\mathrm{1}\:{and}\:{b}=\mathrm{0} \\…
Question Number 6987 by sarathon last updated on 04/Aug/16 $${why}\:\:{e}^{{ln}\frac{\mathrm{1}}{\mathrm{3}}} \:{to}\:{be}\:\frac{\mathrm{1}}{\mathrm{3}}??? \\ $$$$ \\ $$$$ \\ $$ Commented by FilupSmith last updated on 04/Aug/16 $${a}^{\mathrm{log}_{{a}}…
Question Number 72507 by otchereabdullai@gmail.com last updated on 29/Oct/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 6946 by 314159 last updated on 03/Aug/16 $${Find}\:{all}\:{continuous}\:{functions}\:{f}\left({x}\right)\:{such}\: \\ $$$${that}\:{f}\left(\mathrm{2}{x}+\mathrm{1}\right)={f}\left({x}\right)\:{for}\:{all}\:{real}\:{x}. \\ $$ Commented by Yozzii last updated on 04/Aug/16 $${f}\left(\mathrm{1}\right)={f}\left(\mathrm{0}\right) \\ $$$${f}'\left({x}\right)=\mathrm{2}{f}'\left(\mathrm{2}{x}+\mathrm{1}\right) \\…
Question Number 72458 by naka3546 last updated on 29/Oct/19 Terms of Service Privacy Policy Contact: info@tinkutara.com