Question Number 25823 by ajfour last updated on 15/Dec/17 $${z}_{\mathrm{1}} =\mathrm{4}−\mathrm{3}{i} \\ $$$${z}_{\mathrm{2}} =\mathrm{9}+\mathrm{2}{i} \\ $$$${Find}\:\:\left({a}\right)\:{z}_{\mathrm{1}} {oz}_{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left({b}\right)\:{z}_{\mathrm{1}} ×{z}_{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({c}\right)\:{angle}\:{between}\:{z}_{\mathrm{1}} {and}\:{z}_{\mathrm{2}} . \\…
Question Number 156880 by MathSh last updated on 16/Oct/21 $$\boldsymbol{\Omega}\:=\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{0}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\frac{\mathrm{1}}{\boldsymbol{\pi}^{\boldsymbol{\mathrm{n}}} }\:\centerdot\:\left(\frac{\pi}{\mathrm{e}}\right)^{\boldsymbol{\mathrm{k}}} =\:? \\ $$ Answered by Mathspace last updated on 16/Oct/21…
Question Number 156881 by MathSh last updated on 16/Oct/21 $$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{log}\left(\mathrm{1}\:-\:\mathrm{x}\right)\:\mathrm{log}\left(\mathrm{1}\:-\:\mathrm{y}\right)}{\mathrm{1}\:-\:\mathrm{xy}}\:\mathrm{dxdy}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 156867 by cortano last updated on 16/Oct/21 Answered by qaz last updated on 16/Oct/21 $$\frac{\mathrm{1}}{\mathrm{a}+\mathrm{b}}+\frac{\mathrm{9}}{\mathrm{c}}+\frac{\mathrm{16}}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\geqslant\frac{\left(\mathrm{1}+\mathrm{3}+\mathrm{4}\right)^{\mathrm{2}} }{\mathrm{2}\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)}=\mathrm{8} \\ $$$$\mathrm{Min}=\mathrm{8}\:\mathrm{holds}\:\mathrm{only}\:\mathrm{when}\:\frac{\mathrm{1}}{\mathrm{a}+\mathrm{b}}=\frac{\mathrm{3}}{\mathrm{c}}=\frac{\mathrm{4}}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\:\:\mathrm{ie}.\mathrm{a}+\mathrm{b}=\mathrm{1}\:\:\:\mathrm{c}=\mathrm{3} \\ $$ Commented by cortano…
Question Number 25787 by ibraheem160 last updated on 14/Dec/17 $$\mathrm{2}^{{x}} ={x}^{\mathrm{2}\:} ,{hence}\:{x}=\mathrm{2}\:.\:{prove} \\ $$ Commented by mrW1 last updated on 14/Dec/17 $${It}'{s}\:{not}\:{true},\:{Sir}. \\ $$$${If}\:\mathrm{2}^{{x}} ={x}^{\mathrm{2}}…
Question Number 156836 by MathSh last updated on 16/Oct/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 156834 by MathSh last updated on 16/Oct/21 Answered by MJS_new last updated on 16/Oct/21 $${x}=\mathrm{2} \\ $$ Commented by MathSh last updated on…
Question Number 91277 by john santu last updated on 29/Apr/20 $${p}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+…+\frac{\mathrm{1}}{\mathrm{2003}}−\frac{\mathrm{1}}{\mathrm{2004}} \\ $$$${q}=\frac{\mathrm{1}}{\mathrm{1003}}+\frac{\mathrm{1}}{\mathrm{1004}}+…+\frac{\mathrm{1}}{\mathrm{2004}} \\ $$$${p}^{\mathrm{2}} +{q}^{\mathrm{2}} \:=\: \\ $$ Answered by naka3546 last updated on…
Question Number 156809 by MathSh last updated on 15/Oct/21 $$\mathrm{Solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:=\:\sqrt{\mathrm{40x}^{\mathrm{2}} \:+\:\mathrm{32x}\:-\:\mathrm{16}} \\ $$ Commented by MathSh last updated on 15/Oct/21 $$\mathrm{Yes}\:\mathrm{dear}\:\boldsymbol{\mathrm{S}}\mathrm{er} \\…