Question Number 29049 by NECx last updated on 03/Feb/18 $${Prove}\:{that} \\ $$$$\:\:\:\:\:{e}^{{i}\pi} +\mathrm{1}=\mathrm{0} \\ $$ Answered by Penguin last updated on 03/Feb/18 $${e}^{{i}\theta} =\mathrm{cos}\left(\theta\right)+{i}\mathrm{sin}\left(\theta\right) \\…
Question Number 160123 by mr W last updated on 24/Nov/21 $${if}\:{we}\:{write}\:{all}\:{natural}\:{numbers} \\ $$$${together}\:{like}\:{this} \\ $$$$\mathrm{1234567891011121314151617}…, \\ $$$${what}\:{is}\:{the}\:\mathrm{1000}{th}\:{digit}? \\ $$ Answered by nikif99 last updated on…
Question Number 160064 by HongKing last updated on 24/Nov/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{positive}\:\mathrm{integer}\:\:\boldsymbol{\mathrm{n}}\:\:\mathrm{for} \\ $$$$\mathrm{which}\:\:\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{5}^{\boldsymbol{\mathrm{n}}} \:-\:\boldsymbol{\mathrm{n}}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{1000} \\ $$ Commented by Rasheed.Sindhi last updated on 24/Nov/21 $$\mathrm{For}\:\mathrm{n}=\mathrm{1000},\:\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{5}^{\boldsymbol{\mathrm{n}}}…
Question Number 160063 by HongKing last updated on 24/Nov/21 $$\mathrm{Find}: \\ $$$$\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}!}\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\left(\left(\mathrm{1}\:-\:\mathrm{x}\right)^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{cos}\boldsymbol{\mathrm{nx}}\right)\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 160062 by HongKing last updated on 24/Nov/21 $$\mathrm{Find}: \\ $$$$\Omega\:=\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{n}^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}+\mathrm{1}}} }{\mathrm{2}}\right)\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 94522 by Abdulrahman last updated on 19/May/20 $$\mathrm{if}\:\:\mathrm{sinA}+\mathrm{sinB}=\mathrm{n}\:\mathrm{and}\:\mathrm{cosA}+\mathrm{cosB}=\mathrm{m} \\ $$$$\mathrm{then}\:\:\mathrm{sin}\left(\mathrm{A}+\mathrm{B}\right)=? \\ $$$$\mathrm{a}:\:\frac{\mathrm{3mn}}{\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\:\:\:\:\mathrm{b}:\frac{\mathrm{2mn}}{\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\:\:\mathrm{c}:\frac{\mathrm{mn}}{\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\:\:\mathrm{d}:\frac{\mathrm{2mn}}{\mathrm{m}+\mathrm{n}} \\ $$$$\mathrm{with}\:\mathrm{steps}? \\ $$ Answered…
Question Number 94521 by Abdulrahman last updated on 19/May/20 $$\mathrm{if}\:\mathrm{a}^{\mathrm{10}} +\mathrm{a}^{\mathrm{5}} +\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{a}^{\mathrm{2005}} +\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2005}} }=? \\ $$$$\mathrm{a}:\:\mathrm{a}^{\mathrm{10}} +\mathrm{a}^{\mathrm{11}} \:\:\:\:\mathrm{b}:\mathrm{a}^{\mathrm{10}} +\mathrm{a}^{\mathrm{5}} \:\:\:\mathrm{c}:\mathrm{3}\left(\mathrm{a}^{\mathrm{10}} +\mathrm{a}^{\mathrm{5}} \right)\:\:\mathrm{d}:\mathrm{0} \\…
Question Number 160058 by Rasheed.Sindhi last updated on 24/Nov/21 $${Find}\:{n}\:{so}\:{that}\:\frac{{a}^{{n}+\mathrm{1}} +{b}^{{n}+\mathrm{1}} }{{a}^{{n}} +{b}^{{n}} }\:{may}\:{be} \\ $$$${the}\:{arithmetic}\:{mean}\:{between}\:{a} \\ $$$${and}\:{b}. \\ $$ Commented by Tinku Tara last…
Question Number 160048 by HongKing last updated on 23/Nov/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{x}\:\mathrm{sin}^{-\mathrm{1}} \:\mathrm{x}}{\mathrm{1}\:+\:\mathrm{sin}^{-\mathrm{1}} \:\mathrm{x}}\:\mathrm{dx}\:<\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 160045 by HongKing last updated on 23/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com