Question Number 70885 by naka3546 last updated on 09/Oct/19 $$\sqrt[{\mathrm{3}}]{\mathrm{2}}\:\:=\:{a}\:+\:\frac{\mathrm{1}}{{b}\:+\:\frac{\mathrm{1}}{{c}\:+\:\frac{\mathrm{1}}{{d}\:+\:\ldots}}} \\ $$$${a},\:{b},\:{c},\:{d}\:\:\in\:\mathbb{Z}^{+} \\ $$$${What}'{s}\:\:{b}\:\:? \\ $$ Answered by MJS last updated on 09/Oct/19 $$\mathrm{the}\:\mathrm{continued}\:\mathrm{fraction}\:\mathrm{of}\:\sqrt[{\mathrm{3}}]{\mathrm{2}}\:\mathrm{is}\:\mathrm{non}+\mathrm{periodic} \\…
Question Number 136417 by I want to learn more last updated on 21/Mar/21 Answered by EDWIN88 last updated on 22/Mar/21 $$\mathrm{even}\:\mathrm{number}\:=\:\left\{\mathrm{2},\mathrm{4}\right\}\:,\:\mathrm{odd}\:\mathrm{number}=\left\{\mathrm{1},\mathrm{3},\mathrm{5}\right\} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}\:\mathrm{on}\:\mathrm{two}\:\mathrm{balls} \\ $$$$\mathrm{have}\:\mathrm{probabability}\:=\:\frac{\mathrm{1}+\mathrm{3}}{\mathrm{C}_{\mathrm{2}}…
Question Number 5343 by sanusihammed last updated on 09/May/16 $$\left[\frac{\mathrm{1}−{x}^{−\mathrm{1}} −\mathrm{6}{x}^{−\mathrm{2}} }{\mathrm{1}−\mathrm{5}{x}^{−\mathrm{1}} −\mathrm{24}{x}^{−\mathrm{2}} }\right]^{{x}} \\ $$$$ \\ $$$${Limit}\:{x}\:\rightarrow\:\infty \\ $$$$ \\ $$$${please}\:{help}. \\ $$ Commented…
Question Number 136415 by ajfour last updated on 21/Mar/21 Commented by ajfour last updated on 21/Mar/21 $${Find}\:{maximum}\:{area}\:{of} \\ $$$$\bigtriangleup{APQ}\:\:{in}\:{terms}\:{of}\:{a},{b},{c},{h}. \\ $$ Answered by mr W…
Question Number 70876 by Fakhar last updated on 09/Oct/19 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{The}\:\mathrm{necessary}\:\mathrm{and}\:\mathrm{sufficient}\:\mathrm{condition} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{be}\:\mathrm{plane}\:\left(\mathrm{curve}\right)\:\mathrm{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{r}}',\boldsymbol{\mathrm{r}}'',\boldsymbol{\mathrm{r}}'''\right]=\mathrm{0}. \\ $$$$\:\mathrm{OR}\:\:\:\: \\ $$$$\mathrm{A}\:\mathrm{curve}\:\mathrm{is}\:\mathrm{plane}\:\mathrm{curve}\:\mathrm{iff}\:\tau=\mathrm{0}. \\ $$ Terms of Service…
Question Number 5341 by FilupSmith last updated on 09/May/16 $$\mathrm{Three}\:\mathrm{circles}\:\mathrm{with}\:\mathrm{radius}\:{r} \\ $$$$\mathrm{The}\:\mathrm{circles}\:\mathrm{have}\:\mathrm{equations}: \\ $$$${c}_{\mathrm{1}} :\:\:\:\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$${c}_{\mathrm{2}} :\:\:\:\:\:\left({x}−{r}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$${c}_{\mathrm{3}} :\:\:\:\:\:{x}^{\mathrm{2}}…
Question Number 70874 by Mr. K last updated on 09/Oct/19 $${If}\:\mathrm{4}−\mathrm{2}\sqrt{\mathrm{5}}\:{and}\:\mathrm{4}+\mathrm{2}\sqrt{\mathrm{5}\:}\:{are}\:{solutions} \\ $$$${of}\:{x}^{\mathrm{2}} +\left(\mathrm{5}{a}−{b}\right){x}+\left(\mathrm{3}{b}−{a}\right)=\mathrm{0} \\ $$$${whete}\:{a}\:{and}\:{b}\:{are}\:{real}\:{numbers},\: \\ $$$${determine}\:{the}\:{product}\:{of}\:\boldsymbol{{ab}}. \\ $$ Answered by tw000001 last updated…
Question Number 136408 by nimnim last updated on 21/Mar/21 $$\:\:\:\:\:\:{S}=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{3}{k}^{\mathrm{2}} }{\mathrm{2}{k}^{\mathrm{3}} +\mathrm{2}}\:\:=? \\ $$$$\:\:\:\:\:\:\:\:\:=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{3}{k}^{\mathrm{2}} }{{k}^{\mathrm{3}} +\mathrm{1}}\right)=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left[\frac{\mathrm{1}}{{k}+\mathrm{1}}+\frac{\mathrm{2}{k}−\mathrm{1}}{{k}^{\mathrm{2}} −{k}+\mathrm{1}}\right] \\ $$$$\:\:\:\:\:\:\:\:\:{I}\:{dont}\:{know}\:{how}\:{to}\:{continue}…{Please}\:{Help}.…
Question Number 5338 by FilupSmith last updated on 09/May/16 Commented by FilupSmith last updated on 09/May/16 $$\mathrm{I}\:\mathrm{have}\:{n}\:\mathrm{lines}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{interior}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{semi}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{radius}\:{r}.\:\mathrm{All}\:\mathrm{lines}\:\mathrm{are} \\ $$$$\mathrm{of}\:\mathrm{length}\:{a}. \\ $$$$ \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{lines}\:\mathrm{is}\:\mathrm{less}\:\mathrm{than}…
Question Number 70872 by Abdo msup. last updated on 09/Oct/19 $${calculate}\:\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}} } \:\:\:{e}^{−{x}−{y}} \:{ln}\left(\mathrm{2}{x}+{y}\right){dxdy} \\ $$ Commented by Abdo msup. last updated on 11/Oct/19 $${let}\:{I}=\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}}…