Question Number 181439 by mnjuly1970 last updated on 25/Nov/22 Answered by mr W last updated on 25/Nov/22 Commented by mr W last updated on 25/Nov/22…
Question Number 181394 by yaojun2t last updated on 24/Nov/22 Answered by FelipeLz last updated on 25/Nov/22 $${p}:\:{parabola} \\ $$$${d}:\:{directrix} \\ $$$${r}:\:{line}\:{passing}\:{through}\:{F} \\ $$$${s}:\:{line}\:{passing}\:{through}\:{O} \\ $$$$\begin{cases}{{F}\:=\:\left({f},\:\mathrm{0}\right)}\\{{O}\:=\:\left(\mathrm{0},\:\mathrm{0}\right)\:}\end{cases}\rightarrow\:{d}:\:{x}\:=\:−{f}…
Question Number 50299 by OTCHRRE ABDULLAI last updated on 15/Dec/18 $${please}\:{help}\:{me}\:{solve}\:{these}\:{two} \\ $$$${questions}\: \\ $$$$\mathrm{1}.\:{A}\:{magician}\:{cuts}\:{a}\:{rope}\:{into}\:{two}\: \\ $$$$\:\:{parts}\:{at}\:{a}\:{point}\:{selected}\:{at}\: \\ $$$${random}.\:{what}\:{is}\:{the}\:{probability}\:{that} \\ $$$${the}\:{length}\:{of}\:\:{the}\:{longer}\:\:{rope}\:{is}\:{at}\:{least}\: \\ $$$$\mathrm{8}\:{times}\:{the}\:{length}\:{of}\:{the}\:{shorter}\: \\ $$$${rope}.…
Question Number 50274 by Tawa1 last updated on 15/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 15/Dec/18 $$\left.\mathrm{10}\right)\int_{{a}} ^{{b}} \frac{{Q}}{\mathrm{2}\pi\epsilon_{\mathrm{0}} \epsilon_{{r}} {r}}{dr} \\ $$$$=\frac{{Q}}{\mathrm{2}\pi\epsilon_{\mathrm{0}} \epsilon_{{r}} }{ln}\left(\frac{{b}}{{a}}\right)…
Question Number 50275 by Tawa1 last updated on 15/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 15/Dec/18 $$\bigtriangleup{S}=\int_{{T}_{\mathrm{1}} } ^{{T}_{\mathrm{2}} } {C}_{{v}} \frac{{dT}}{{T}}−{R}\int_{{V}_{\mathrm{1}} } ^{{V}_{\mathrm{2}} }…
Question Number 181331 by Mastermind last updated on 24/Nov/22 $$\mathrm{Solve}: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{e}^{\mathrm{x}} \left(\mathrm{sinx}\right)\left(\mathrm{y}+\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{2}\right)=−\mathrm{1} \\ $$$$ \\ $$$$. \\ $$ Answered by FelipeLz last updated on…
Question Number 181330 by Mastermind last updated on 24/Nov/22 $$\mathrm{Solve}: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{2x}\left(\mathrm{y}+\mathrm{1}\right)=\mathrm{0},\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{2} \\ $$ Answered by FelipeLz last updated on 24/Nov/22 $$\frac{{dy}}{{dx}}+\mathrm{2}{x}\left({y}+\mathrm{1}\right)\:=\:\mathrm{0} \\ $$$$\frac{{dy}}{{dx}}+\mathrm{2}{xy}\:=\:−\mathrm{2}{x} \\…
Question Number 50257 by Raj Singh last updated on 15/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 15/Dec/18 $${a}+{d}=\mathrm{8} \\ $$$${a}+{b}=\mathrm{13} \\ $$$${b}−{c}=\mathrm{6} \\ $$$${c}+{d}=\mathrm{8} \\…
Question Number 115732 by gab last updated on 28/Sep/20 Commented by Dwaipayan Shikari last updated on 28/Sep/20 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} }{\mathrm{2n}^{\mathrm{2}} }\mathrm{e}^{\pi\mathrm{in}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{e}^{\mathrm{i}\pi} }{\mathrm{1}^{\mathrm{2}}…
Question Number 181245 by Mastermind last updated on 23/Nov/22 $$\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)\left(\mathrm{x}^{\frac{\mathrm{4}}{\mathrm{3}}} +\mathrm{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} \left(\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\right) \\ $$$$ \\ $$$$\mathrm{prove}\:\mathrm{LHS}=\mathrm{RHS} \\ $$ Commented by Socracious last…