Question Number 2358 by 123456 last updated on 18/Nov/15 $${a}_{{n}+\mathrm{1}} =−\frac{{a}_{{n}} \left(\mid{a}_{{n}} \mid+\mathrm{1}\right)}{\mid{a}_{{n}} \mid},{a}_{\mathrm{1}} =\mathrm{1} \\ $$$${b}_{{n}+\mathrm{1}} ={b}_{{n}} +{a}_{{n}+\mathrm{1}} ,{b}_{\mathrm{1}} ={a}_{\mathrm{1}} \\ $$$${b}_{\mathrm{10}} =? \\…
Question Number 133394 by Dwaipayan Shikari last updated on 21/Feb/21 Commented by Dwaipayan Shikari last updated on 21/Feb/21 $${Three}\:{indentical}\:{point}\:{charges}\:,\:{each}\:{of}\:{mass}\:\boldsymbol{{m}}\:{and}\:{charge} \\ $$$$\boldsymbol{{Q}}\:,{hanging}\:{from}\:{three}\:{strings}\:.{Find}\:{the}\:{value}\:{of}\:\boldsymbol{{Q}}\:{in}\:{terms} \\ $$$${of}\:\boldsymbol{{m}},\boldsymbol{{L}}\:{and}\:\boldsymbol{\theta}\:\left({They}\:{are}\:{in}\:{equilibrium}\right) \\ $$…
Question Number 133381 by Dwaipayan Shikari last updated on 21/Feb/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }\left(\frac{\mathrm{1}}{\mathrm{2}.\mathrm{1}!}\right)+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}\right)+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}\right)+…=\frac{\pi}{\mathrm{2}}{log}\left(\mathrm{2}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 2289 by 123456 last updated on 14/Nov/15 $$\mathrm{suppose}\:\mathrm{that}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R},\:\mathrm{lets}\:{f}\in\mathrm{C}^{\mathrm{2}} \\ $$$$\mathrm{and}\:\mathrm{suppose}\:\mathrm{that}\:\exists\alpha\in\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left(\alpha\right)+{f}\left(\mathrm{1}−\alpha\right)=\mathrm{1} \\ $$$$\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that} \\ $$$$\exists\xi\in\left[\mathrm{0},\mathrm{1}\right],{f}\left(\xi\right)=\xi \\ $$ Commented by Rasheed Soomro last…
Question Number 67820 by angezbcn last updated on 31/Aug/19 $${x}^{\mathrm{3}} −{x}^{\mathrm{2}} −\mathrm{6}{x} \\ $$ Commented by mr W last updated on 01/Sep/19 $$={x}\left({x}^{\mathrm{2}} −{x}−\mathrm{6}\right) \\…
Question Number 133344 by Dwaipayan Shikari last updated on 21/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left(\frac{{n}}{\pi}\right)}{{n}^{\mathrm{4}} }=−\frac{\mathrm{1}}{\mathrm{48}\pi^{\mathrm{4}} }+\frac{\mathrm{1}}{\mathrm{12}}\left(\mathrm{1}−\frac{\mathrm{1}}{\pi^{\mathrm{2}} }\right)+\frac{\pi^{\mathrm{4}} }{\mathrm{90}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 133346 by bramlexs22 last updated on 21/Feb/21 $$\:\mathrm{Find}\:\mathrm{modulus}\:\mathrm{and}\:\mathrm{argumen}\:\mathrm{of}\: \\ $$$$\:\mathrm{z}\:=\:\frac{\left(\mathrm{1}−{i}\right)^{\mathrm{4}} \left(\sqrt{\mathrm{3}}+{i}\right)^{\mathrm{7}} }{\left(\mathrm{1}+{i}\sqrt{\mathrm{2}}\right)^{\mathrm{8}} \left(−\mathrm{1}−{i}\sqrt{\mathrm{3}}\right)^{\mathrm{12}} } \\ $$ Answered by mathmax by abdo last updated…
Question Number 133321 by 777316 last updated on 21/Feb/21 $${Find}\:{x}\:: \\ $$$${sin}\left(\mathrm{3}{x}\right)−{sin}\left(\mathrm{2}{x}\right)−\mathrm{2}{sin}\left({x}\right)\:=\:\sqrt{\mathrm{3}}{cos}\left({x}\right) \\ $$ Commented by bramlexs22 last updated on 21/Feb/21 $$\mathrm{x}=\frac{\mathrm{2}\pi}{\mathrm{3}} \\ $$$$\mathrm{sin}\:\left(\mathrm{3}×\frac{\mathrm{2}\pi}{\mathrm{3}}\right)−\mathrm{sin}\:\left(\mathrm{2}×\frac{\mathrm{2}\pi}{\mathrm{3}}\right)−\mathrm{2sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)= \\…
Question Number 2234 by madscientist last updated on 10/Nov/15 $${in}\:{quantum}\:{physics}\:{is}\:{this}\:{a}\:{true}\: \\ $$$${statement}?\:{h}={h}\:{bar} \\ $$$$\frac{{d}}{{dt}}\langle\psi\left({t}\right)\mid\psi\left({t}\right)\rangle=\mathrm{0} \\ $$$$\frac{{d}}{{dt}}\langle\psi\left({t}\right)\mid\psi\left({t}\right)=\int\psi^{\ast} \left({t}\right)\psi\left({t}\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\int\frac{{d}\psi^{\ast} }{{dt}}\psi{dx}+\int\psi^{\ast} {H}\psi{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=−\frac{\mathrm{1}}{{ih}}\int\left({H}\psi\right)^{\ast} \psi{dx}+\frac{\mathrm{1}}{{ih}}\int\psi^{\ast} {H}\psi{dx}…
Question Number 67745 by Enock last updated on 31/Aug/19 $${solve}\:{the}\:{system}\:{of}\:{equations\begin{cases}{\mathrm{3}\mid{x}−\mathrm{5}\mid+\mathrm{4}={y}}\\{\mid{y}−\mathrm{3}\mid=\mathrm{4}{x}−\mathrm{12}}\end{cases}} \\ $$ Answered by Rasheed.Sindhi last updated on 31/Aug/19 $$\begin{cases}{\mathrm{3}\mid{x}−\mathrm{5}\mid+\mathrm{4}={y}\Rightarrow{y}\geqslant\mathrm{4}}\\{\mid{y}−\mathrm{3}\mid=\mathrm{4}{x}−\mathrm{12}\Rightarrow\mathrm{4}{x}−\mathrm{12}\geqslant\mathrm{1}\Rightarrow{x}\geqslant\frac{\mathrm{13}}{\mathrm{4}}}\end{cases} \\ $$$$\left(\mathrm{i}\right)\rightarrow\left(\mathrm{ii}\right): \\ $$$$\Rightarrow\mid\:\left(\mathrm{3}\mid{x}−\mathrm{5}\mid+\mathrm{4}\right)−\mathrm{3}\:\mid=\mathrm{4}{x}−\mathrm{12} \\…