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Question Number 70914 by 20190927 last updated on 09/Oct/19 $$\mathrm{1}+\left(\mathrm{z}+\mathrm{2i}\right)+\left(\mathrm{z}+\mathrm{2i}\right)^{\mathrm{2}} +\left(\mathrm{z}+\mathrm{2i}\right)^{\mathrm{3}} +\left(\mathrm{z}+\mathrm{2i}\right)^{\mathrm{4}} =\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{z}\:,\:\mathrm{z}\in\mathrm{C} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 136448 by adhigenz last updated on 22/Mar/21 $$\mathrm{Mr}.\mathrm{A}\:\mathrm{wants}\:\mathrm{to}\:\mathrm{deliver}\:\mathrm{7}\:\mathrm{letters}\:\mathrm{to}\:\mathrm{his}\:\mathrm{7}\:\mathrm{friends}\:\mathrm{so}\:\mathrm{that}\:\mathrm{each}\:\mathrm{gets}\:\mathrm{1}\:\mathrm{letter}. \\ $$$$\mathrm{All}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{written}\:\mathrm{of}\:\mathrm{the}\:\mathrm{addresses}\:\mathrm{of}\:\mathrm{his}\:\mathrm{7}\:\mathrm{friends}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probbility}\:\mathrm{that}, \\ $$$$\mathrm{3}\:\mathrm{of}\:\mathrm{his}\:\mathrm{friends}\:\mathrm{receive}\:\mathrm{the}\:\mathrm{correct}\:\mathrm{letters}\:\mathrm{and}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{4}\:\mathrm{receive}\:\mathrm{the}\:\mathrm{wrong}\:\mathrm{ones}. \\ $$ Answered by mr W last updated on 22/Mar/21 $${p}=\frac{{P}_{\mathrm{3}}…
Question Number 70915 by Mr. K last updated on 09/Oct/19 Commented by Mr. K last updated on 09/Oct/19 $${The}\:{circles}\:{have}\:{the}\:{same}\:{radius}.\: \\ $$$${The}\:{triangle}\:{is}\:{equilateral}\:{side} \\ $$$$\mathrm{28}\left(\mathrm{1}+\sqrt{\mathrm{3}}\right).\:{Determine}\:{the}\:{radius} \\ $$$${of}\:{the}\:{circumferences}.…
Question Number 70913 by TawaTawa last updated on 09/Oct/19 Commented by mathmax by abdo last updated on 10/Oct/19 $${we}\:{have}\:\frac{{z}^{\mathrm{2017}} −\mathrm{1}}{{z}−\mathrm{1}}\:=\prod_{{k}=\mathrm{1}} ^{\mathrm{2016}} \left({z}−{e}^{\frac{{i}\mathrm{2}{k}\pi}{\mathrm{2017}}} \right) \\ $$$${z}=−\mathrm{1}\:\Rightarrow\mathrm{1}\:=\prod_{{k}=\mathrm{1}}…
Question Number 136445 by aupo14 last updated on 22/Mar/21 Answered by liberty last updated on 22/Mar/21 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\:{x}} \:\frac{{t}−\mathrm{3}}{{t}^{\mathrm{2}} +\mathrm{7}}\:{dt}\: \\ $$$${f}\:'\left({x}\right)=\:\frac{{x}−\mathrm{3}}{{x}^{\mathrm{2}} +\mathrm{7}}\:=\:\mathrm{0}\Rightarrow{x}=\mathrm{3} \\ $$$${f}\:''\left({x}\right)\mid_{{x}=\mathrm{3}}…
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Question Number 70909 by rajesh4661kumar@gmail.com last updated on 09/Oct/19 Commented by rajesh4661kumar@gmail.com last updated on 10/Oct/19 $$\mathrm{28} \\ $$ Commented by Abdo msup. last updated…
Question Number 136440 by liberty last updated on 22/Mar/21 $$\:\int\:\frac{{dx}}{\mathrm{sin}\:^{\mathrm{6}} {x}}\:? \\ $$ Answered by rs4089 last updated on 22/Mar/21 $$\int{cosec}^{\mathrm{6}} {x}.{dx} \\ $$$$\int\left(\mathrm{1}+{cot}^{\mathrm{2}} {x}\right)^{\mathrm{2}}…