Question Number 5351 by sanusihammed last updated on 10/May/16 $${A}\:{cylindrical}\:{iron}\:{rod}\:\mathrm{8}{cm}\:{and}\:\mathrm{6}{cm}\:{in}\:{diameter}\:{stands}\:{in}\:{a} \\ $$$${cylindrical}\:{tin}\:{of}\:\mathrm{12}{cm}\:{in}\:{diameter}.\:{Water}\:{is}\:{poured}\:{into}\:{the} \\ $$$${tin}\:{until}\:{it}\:{depth}\:{is}\:\mathrm{8}{cm}.\:{How}\:{far}\:{would}\:{the}\:{level}\:{drop}\:{when}\:{the}\: \\ $$$${rod}\:{is}\:{removed}\:? \\ $$ Commented by Yozzii last updated on 11/May/16…
Question Number 136420 by Dwaipayan Shikari last updated on 21/Mar/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left(\mathrm{2}{n}+\mathrm{1}\right)\theta}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{\theta}{\mathrm{2}}{log}\left(\mathrm{2}\right)+{sin}\theta\frac{{log}\left({sin}\theta\right)}{\mathrm{4}}\:_{\mathrm{2}} {F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\frac{\mathrm{3}}{\mathrm{2}};{sin}^{\mathrm{2}} \theta\right)+\frac{{sin}\theta}{\mathrm{16}}\:_{\mathrm{2}} {F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\frac{\mathrm{3}}{\mathrm{2}};\frac{\mathrm{3}}{\mathrm{2}};{sin}^{\mathrm{2}} \theta\right) \\ $$$${Prove}\:{or}\:{disprove}\:\:\:\:\:\mathrm{0}<\theta<\pi \\ $$ Answered…
Question Number 70887 by naka3546 last updated on 09/Oct/19 Commented by ajfour last updated on 09/Oct/19 Commented by ajfour last updated on 09/Oct/19 $${s}\mathrm{sin}\:\alpha={r}\mathrm{sin}\:\gamma \\…
Question Number 5350 by sanusihammed last updated on 09/May/16 $${Suppose}\:{the}\:{radius}\:{of}\:{the}\:{earth}\:{is}\:\mathrm{6400}{km}.\:{the}\:{acceleration}\: \\ $$$${of}\:{a}\:{person}\:{at}\:{latitude}\:\mathrm{60}°\:{due}\:{to}\:{the}\:{earth}\:{rotation}\:{is}\:? \\ $$$$ \\ $$$$\left({a}\right)\:\mathrm{0}.\mathrm{034}{m}/{s}^{\mathrm{2}} \\ $$$$\left({b}\right)\:\mathrm{232}.\mathrm{7}{m}/{s}^{\mathrm{2}} \\ $$$$\left({c}\right)\:\mathrm{0}.\mathrm{0169}{m}/{s}^{\mathrm{2}} \\ $$$$\left({d}\right)\:\mathrm{465}.\mathrm{4}{m}/{s}^{\mathrm{2}} \\ $$$$ \\…
Question Number 70885 by naka3546 last updated on 09/Oct/19 $$\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}}…