Question Number 153079 by mathdanisur last updated on 04/Sep/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\sqrt{\mathrm{1}-\boldsymbol{{z}}}\:=\:\mathrm{2}\boldsymbol{{z}}^{\mathrm{2}} \:-\:\mathrm{1}\:+\:\mathrm{2}\boldsymbol{{z}}\:\sqrt{\mathrm{1}-\boldsymbol{{z}}^{\mathrm{2}} } \\ $$ Commented by MJS_new last updated on 04/Sep/21 $$\mathrm{I}\:\mathrm{get}\:{z}=\mathrm{sin}\:\frac{\pi}{\mathrm{5}}\:=\frac{\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{4}} \\…
Question Number 87540 by Power last updated on 04/Apr/20 Commented by abdomathmax last updated on 05/Apr/20 $${let}\:\:{I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} }\:{changement}\:{x}\:={sh}\left({t}\right)\:{give} \\ $$$${I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ch}\left({t}\right)\:{dt}}{\left({sh}\left({t}\right)+{cht}\right)^{\mathrm{2}}…
Question Number 87538 by Power last updated on 04/Apr/20 Commented by mathmax by abdo last updated on 04/Apr/20 $${I}\:=\int_{−\mathrm{1}} ^{\mathrm{1}} \:{f}^{−\mathrm{1}} \left({x}\right){dx}\:\:\:{changement}\:{f}^{−\mathrm{1}} \left({x}\right)={t}\:{give}\:{x}\:={f}\left({t}\right)\Rightarrow \\ $$$${dx}\:={f}^{'}…
Question Number 87536 by M±th+et£s last updated on 04/Apr/20 $${solve}\: \\ $$$$\mid\mathrm{2}{x}−\mathrm{1}\mid=\mathrm{3}\lfloor{x}\rfloor+\mathrm{2}\left\{{x}\right\} \\ $$$$ \\ $$ Answered by mr W last updated on 05/Apr/20 $${x}={n}+\delta…
Question Number 22001 by vk loyal last updated on 09/Oct/17 $${if}\:\begin{vmatrix}{{z}−\frac{{z}}{\mathrm{4}}}\\{}\end{vmatrix}=\mathrm{2}\:{then}\:{value}\:{of}\:\begin{vmatrix}{{z}}\\{}\end{vmatrix} \\ $$ Answered by ajfour last updated on 09/Oct/17 $$\mid{z}−\frac{{z}}{\mathrm{4}}\mid=\frac{\mathrm{3}}{\mathrm{4}}\mid{z}\mid=\mathrm{2} \\ $$$$\Rightarrow\:\mid{z}\mid=\frac{\mathrm{8}}{\mathrm{3}}\:. \\ $$…
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Question Number 87534 by mathmax by abdo last updated on 04/Apr/20 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{arctan}\left({sinx}\right)}{{sinx}}{dx} \\ $$ Commented by mathmax by abdo last updated on 06/Apr/20…
Question Number 87535 by mathmax by abdo last updated on 04/Apr/20 $${let}\:{U}_{{n}} =\left\{{z}\in{C}\:/{z}^{{n}} =\mathrm{1}\right\} \\ $$$${calculate}\:\sum_{{k}=\mathrm{0}\:{and}\:{z}\in{U}_{{n}} } ^{{p}−\mathrm{1}} \:{z}^{{k}} \\ $$ Terms of Service Privacy…
Question Number 87532 by niroj last updated on 04/Apr/20 $$\:\left(\mathrm{1}\right).\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{general}}\:\boldsymbol{\mathrm{solution}}: \\ $$$$\:\:\:\boldsymbol{\mathrm{y}}=\:\boldsymbol{\mathrm{px}}\:+\boldsymbol{\mathrm{p}}^{\boldsymbol{\mathrm{n}}} \\ $$$$\:\left(\mathrm{2}\right).\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)^{\mathrm{2}} \:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:+\:\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}=\:\left(\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{3}\right)\left(\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{4}\right). \\ $$$$\:\: \\ $$ Commented by…
Question Number 153070 by bobhans last updated on 04/Sep/21 $$\:\:\:{Find}\:{the}\:{solution}\:{set}\:{of}\:{inequality} \\ $$$$\:\:\:\:\:\:\:\sqrt{\mathrm{3}{x}+\mathrm{4}}\:\geqslant\:{x}−\mathrm{2}\: \\ $$ Answered by Rasheed.Sindhi last updated on 04/Sep/21 $$\:\:\:\:\:\:\:\sqrt{\mathrm{3}{x}+\mathrm{4}}\:\geqslant\:{x}−\mathrm{2}\: \\ $$$$\:\:\:\:\:\:\:\left(\:\sqrt{\mathrm{3}{x}+\mathrm{4}}\:\geqslant\:{x}−\mathrm{2}\:\right)^{\mathrm{2}} \\…