Question Number 216900 by MathematicalUser2357 last updated on 24/Feb/25 Commented by MathematicalUser2357 last updated on 24/Feb/25 Is this right? (Part 2) - Complex number to the power of complex number Sorry for solving too complicated. But I was trying to solve clearly. Added more equivalent solution step from the last solution step and graph. The red one is the fixed one. Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 216861 by badiane last updated on 23/Feb/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 216859 by ajfour last updated on 23/Feb/25 Commented by ajfour last updated on 23/Feb/25 $${Radius}\:{of}\:{inner}\:{disc}\:{is}\:{R}.\:{As}\:{it}\:{rolls}\:{up} \\ $$$${the}\:{outer}\:{circular}\:{track}\:{of}\:{radius}\:\mathrm{2}{R},\:{find} \\ $$$${equation}\:{of}\:{trajectory}\:{of}\:{a}\:{point}\:\boldsymbol{{P}}\:{on}\:{the} \\ $$$${wheel}\:{until}\:{it}\:{comes}\:{into}\:{contact}\:{with} \\ $$$${the}\:{outer}\:{track}.…
Question Number 216886 by Engr_Jidda last updated on 23/Feb/25 $${Evaluate}\:\frac{\underset{{k}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\int_{\mathrm{0}} ^{{k}} \left(\mathrm{4}{u}+\mathrm{1}\right){du}\right)}{\mathrm{5}^{\mathrm{2}} \underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left(\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{2}}{{m}^{\mathrm{2}} +\mathrm{2}{m}}\right)^{{n}−\mathrm{1}} }\int_{{sin}^{−\mathrm{1}} \left(\frac{−\sqrt{\mathrm{2}}}{\mathrm{2}}\right)} ^{\frac{\pi}{\mathrm{2}}{cos}\frac{\pi}{\mathrm{2}}} \left(\frac{\mathrm{1}−{sec}\theta{sin}\theta}{\frac{{tan}\theta+{cot}\theta}{\varrho^{\theta} −\varrho^{\pi{i}}…
Question Number 216887 by zetamaths last updated on 23/Feb/25 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}{cos}\left(\frac{{x}}{\mathrm{2}^{{k}} }\right)={Pn}\left({x}\right) \\ $$$${evaluate}\:{Pn}\left({x}\right)\:\:{and}\:\:{P}_{{n}} \left({x}^{\mathrm{2}} +\mathrm{1}\right) \\ $$$$ \\ $$$$ \\ $$ Terms of…
Question Number 216855 by BaliramKumar last updated on 23/Feb/25 Answered by AntonCWX08 last updated on 23/Feb/25 Commented by AntonCWX08 last updated on 23/Feb/25 $${s}=\frac{\mathrm{51}+\mathrm{36}+\mathrm{75}}{\mathrm{2}}=\mathrm{81} \\…
Question Number 216875 by ArshadS last updated on 23/Feb/25 $$\mathrm{Let}\:\:\mathrm{p}\:\:\mathrm{be}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{3}.\:\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{p}^{\mathrm{2}} −\:\mathrm{1}\:\: \\ $$$$\mathrm{is}\:\:\mathrm{always}\:\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{24}. \\ $$ Answered by maths2 last updated on 23/Feb/25 $$\left({p}−\mathrm{1}\right)\left({p}+\mathrm{1}\right) \\ $$$$\mathrm{3}\mid\left({p}−\mathrm{1}\right)\left({p}+\mathrm{1}\right);{since}\:{p}\equiv\mathrm{1},\mathrm{2}\left[\mathrm{3}\right]…
Question Number 216830 by MrGaster last updated on 22/Feb/25 $$\mathrm{Prove}:\forall{x}\in\mathbb{R},\mid\mathrm{cos}\:{x}\mid+\mid\mathrm{cos}\:\mathrm{2}{x}\mid+\ldots+\mid\mathrm{cos}\:{nx}\mid\geq\frac{{n}−\mathrm{1}}{\mathrm{2}}\left({n}\in\mathbb{Z}_{>\mathrm{0}} \right)\:\: \\ $$ Commented by MathematicalUser2357 last updated on 25/Feb/25 $$\mathrm{Or}\:\mathrm{you}\:\mathrm{could}\:\mathrm{do}\:\left\{{n}\mid{n}\in\mathbb{Z}\wedge{n}>\mathrm{0}\right\}\:\left(\mathrm{or}\:\left\{{n}\mid{n}\in\mathbb{N}\right\}\right) \\ $$ Answered by…
Question Number 216841 by hardmath last updated on 22/Feb/25 $$\mathrm{Prove}\:\mathrm{that}:\:\:\:\:\:\delta\left(\mathrm{n}\right)\:=\:\underset{\frac{\boldsymbol{\mathrm{d}}}{\boldsymbol{\mathrm{n}}}} {\sum}\:\boldsymbol{\varphi}\left(\mathrm{d}\right)\:\boldsymbol{\tau}\left(\frac{\mathrm{n}}{\mathrm{d}}\right) \\ $$$$\boldsymbol{\delta}\left(\mathrm{n}\right)\:=\:\underset{\frac{\boldsymbol{\mathrm{d}}}{\boldsymbol{\mathrm{n}}}} {\sum}\:\mathrm{d}\:\:\:,\:\:\:\boldsymbol{\tau}\left(\mathrm{n}\right)\:=\:\underset{\frac{\boldsymbol{\mathrm{d}}}{\boldsymbol{\mathrm{n}}}} {\sum}\:{l}\:\:\:\mathrm{and}\:\:\:\varphi-\mathrm{Eyler}.\mathrm{f} \\ $$ Answered by MrGaster last updated on 23/Feb/25 $$\mathrm{Let}\:{f}\left({n}\right)=\underset{{d}\mid{n}}…
Question Number 216842 by ArshadS last updated on 22/Feb/25 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{integers}\:\:\mathrm{x},\:\mathrm{y}\:\:\mathrm{that}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\:\mathrm{system}\:\: \\ $$$$\mathrm{xy}\:+\:\mathrm{x}\:+\:\mathrm{y}=\mathrm{71}\: \\ $$$$\mathrm{x}^{\mathrm{2}} \mathrm{y}\:+\:\mathrm{xy}^{\mathrm{2}} =\mathrm{880} \\ $$ Answered by Frix last updated…