Question Number 70974 by Tinku Tara last updated on 10/Oct/19 $$\boldsymbol{\mathrm{Password}}\:\boldsymbol{\mathrm{reset}}\:\boldsymbol{\mathrm{changes}} \\ $$$$\mathrm{In}\:\mathrm{case}\:\mathrm{you}\:\mathrm{forget}\:\mathrm{any}\:\mathrm{password}\:\mathrm{set} \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{simple}\:\mathrm{reset}\:\mathrm{by}\:\mathrm{going}\:\mathrm{to} \\ $$$$\mathrm{set}/\mathrm{update}\:\mathrm{password}. \\ $$$$ \\ $$$$\mathrm{Leave}\:\mathrm{old}\:\mathrm{password}\:\mathrm{field}\:\mathrm{blank}. \\ $$$$ \\ $$$$\mathrm{This}\:\mathrm{will}\:\mathrm{work}\:\mathrm{only}\:\mathrm{if}\:\mathrm{you}\:\mathrm{are}\:\mathrm{trying}…
Question Number 136514 by mohammad17 last updated on 22/Mar/21 $${if}\:{z}=\frac{\mathrm{1}−{i}\sqrt{\mathrm{3}}}{\mathrm{2}}\:\:{find}\:{arg}\left(−{z}\right) \\ $$ Answered by mr W last updated on 22/Mar/21 $$−{z}=−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{i} \\ $$$${arg}\left(−{z}\right)=\frac{\mathrm{2}\pi}{\mathrm{3}}=\mathrm{120}° \\ $$…
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Question Number 136466 by aurpeyz last updated on 22/Mar/21 $$\int\frac{\mathrm{4}{dx}}{\mathrm{3}−\mathrm{5}{sin}\:{x}} \\ $$ Answered by mathmax by abdo last updated on 22/Mar/21 $$\Phi=\int\:\:\frac{\mathrm{4dx}}{\mathrm{3}−\mathrm{5sinx}}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{tan}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)=\mathrm{t}\:\Rightarrow \\ $$$$\Phi=\int\:\:\frac{\mathrm{4}}{\left(\mathrm{3}−\mathrm{5}\frac{\mathrm{2t}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\right)}\frac{\mathrm{2dt}}{\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}}…
Question Number 136463 by Plutonic last updated on 22/Mar/21 $${Evaluate}\:\mathrm{4}\sqrt{\mathrm{3}\:}\left(\frac{\mathrm{3}}{\:\sqrt{\mathrm{3}}}+\sqrt{\mathrm{3}}\right) \\ $$ Answered by aurpeyz last updated on 22/Mar/21 $${multiply}\:{through}\:{by}\:\mathrm{4}\sqrt{\mathrm{3}} \\ $$$$\mathrm{12}+\mathrm{12}=\mathrm{24} \\ $$ Terms…
Question Number 136458 by aurpeyz last updated on 22/Mar/21 $$\int\sqrt{\mathrm{1}−\mathrm{4}{x}^{\mathrm{2}} }{dx} \\ $$ Answered by mathmax by abdo last updated on 22/Mar/21 $$\mathrm{I}=\int\sqrt{\mathrm{1}−\mathrm{4x}^{\mathrm{2}} }\mathrm{dx}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{chamgement}\:\mathrm{2x}=\mathrm{sin}\theta\:\Rightarrow \\…
Question Number 70917 by Kunal12588 last updated on 09/Oct/19 $$\int\sqrt{{tan}^{\mathrm{2}} {x}+\mathrm{3}}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 09/Oct/19 $$\left.\sqrt{\mathrm{3}}{t}={tanx}\:\Rightarrow{x}={arctan}\left({t}\sqrt{\mathrm{3}}\right)\right)\:\Rightarrow \\ $$$$\int\sqrt{\mathrm{3}+{tan}^{\mathrm{2}}…
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Question Number 5380 by 314159 last updated on 12/May/16 $${Suppose}\:{that}\:{a},{b},{c}>\mathrm{0}.{Prove}\:{that}\: \\ $$$$\frac{\mathrm{1}}{{a}\left(\mathrm{1}+{b}\right)}+\frac{\mathrm{1}}{{b}\left(\mathrm{1}+{c}\right)}+\frac{\mathrm{1}}{{c}\left(\mathrm{1}+{a}\right)}\:\geqslant\frac{\mathrm{3}}{\mathrm{1}+{abc}}. \\ $$ Commented by Rasheed Soomro last updated on 14/May/16 $$\mathrm{LHS}=\frac{{bc}\left(\mathrm{1}+{c}\right)\left(\mathrm{1}+{a}\right)+{ac}\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{a}\right)+{ab}\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{c}\right)}{{a}\mathrm{bc}\left(\mathrm{1}+\mathrm{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+\mathrm{c}\right)} \\ $$$$=\frac{{ab}\left(\mathrm{1}+{c}+{b}+{bc}\right)+{bc}\left(\mathrm{1}+{a}+{c}+{ca}\right)+{ca}\left(\mathrm{1}+{a}+{b}+{ab}\right)}{{a}\mathrm{bc}\left(\mathrm{1}+\mathrm{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+\mathrm{c}\right)}…
Question Number 70915 by Mr. K last updated on 09/Oct/19 Commented by Mr. K last updated on 09/Oct/19 $${The}\:{circles}\:{have}\:{the}\:{same}\:{radius}.\: \\ $$$${The}\:{triangle}\:{is}\:{equilateral}\:{side} \\ $$$$\mathrm{28}\left(\mathrm{1}+\sqrt{\mathrm{3}}\right).\:{Determine}\:{the}\:{radius} \\ $$$${of}\:{the}\:{circumferences}.…