Question Number 70920 by TawaTawa last updated on 09/Oct/19 $$\mathrm{i}\:!\:\:=\:\:? \\ $$ Commented by prakash jain last updated on 10/Oct/19 $${i}!=\Gamma\left(\mathrm{1}+{i}\right) \\ $$$$\mathrm{where}\:{i}=\sqrt{−\mathrm{1}} \\ $$…
Question Number 5385 by sanusihammed last updated on 12/May/16 $${Find}\:{the}\:{value}\:{of}\:{x}\:{if}\: \\ $$$$ \\ $$$$\sqrt{{x}^{{x}^{\mathrm{6}} } }\:=\:\:\mathrm{729} \\ $$ Answered by prakash jain last updated on…
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 $$\mathrm{I}=\int\sqrt{\mathrm{1}−\mathrm{4x}^{\mathrm{2}} }\mathrm{dx}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{chamgement}\:\mathrm{2x}=\mathrm{sin}\theta\:\Rightarrow \\…
Question Number 5381 by Rasheed Soomro last updated on 12/May/16 Commented by Rasheed Soomro last updated on 15/May/16 $$\bigtriangleup\mathrm{ABC}\sim\bigtriangleup\mathrm{EFD} \\ $$ Terms of Service Privacy…
Question Number 70917 by Kunal12588 last updated on 09/Oct/19 $$\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 \\ $$$$\int\sqrt{\mathrm{3}+{tan}^{\mathrm{2}}…
Question Number 5380 by 314159 last updated on 12/May/16 $${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 $$\mathrm{LHS}=\frac{{bc}\left(\mathrm{1}+{c}\right)\left(\mathrm{1}+{a}\right)+{ac}\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{a}\right)+{ab}\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{c}\right)}{{a}\mathrm{bc}\left(\mathrm{1}+\mathrm{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+\mathrm{c}\right)} \\ $$$$=\frac{{ab}\left(\mathrm{1}+{c}+{b}+{bc}\right)+{bc}\left(\mathrm{1}+{a}+{c}+{ca}\right)+{ca}\left(\mathrm{1}+{a}+{b}+{ab}\right)}{{a}\mathrm{bc}\left(\mathrm{1}+\mathrm{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+\mathrm{c}\right)}…
Question Number 136449 by mathdave last updated on 22/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 70914 by 20190927 last updated on 09/Oct/19 $$\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}.…