Question Number 201357 by sonukgindia last updated on 05/Dec/23 Commented by mahdipoor last updated on 05/Dec/23 $$\left(\mathrm{1}−\mathrm{4}{i}\right){z}=\mathrm{4}{ni}\Rightarrow{z}=\frac{\mathrm{4}{ni}}{\mathrm{1}−\mathrm{4}{i}}=\frac{\mathrm{4}{n}\left(\mathrm{4}+{i}\right)}{\mathrm{17}} \\ $$$${im}\left({z}\right)=\frac{\mathrm{4}{n}}{\mathrm{17}}=\mathrm{164}\Rightarrow{n}=\mathrm{17}×\mathrm{41}=\mathrm{697} \\ $$$${z}=\mathrm{656}+\mathrm{164}{i} \\ $$ Terms of…
Question Number 201352 by cortano12 last updated on 05/Dec/23 $$\:\:\:\mathrm{2023}^{\mathrm{2023}} \:=\:…\:\left(\mathrm{mod}\:\mathrm{13}\right) \\ $$ Answered by Rasheed.Sindhi last updated on 05/Dec/23 $$\:\:\:\mathrm{2023}^{\mathrm{2023}} \:\equiv\:…\:\left(\mathrm{mod}\:\mathrm{13}\right) \\ $$$$\mathrm{2023}^{\mathrm{2023}} \\…
Question Number 201353 by sonukgindia last updated on 05/Dec/23 Commented by mr W last updated on 05/Dec/23 $${do}\:{you}\:{have}\:{the}\:{answer}? \\ $$ Answered by mr W last…
Question Number 201355 by MrGHK last updated on 05/Dec/23 Answered by witcher3 last updated on 05/Dec/23 $$=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{xy}\right)\mathrm{y}}{\left(\mathrm{xy}+\mathrm{1}\right)\left(\mathrm{y}+\mathrm{1}\right)}\mathrm{dxdy}\:\mathrm{can}\:\mathrm{be}\:\mathrm{solved}\: \\ $$ Terms…
Question Number 201348 by sonukgindia last updated on 05/Dec/23 Answered by aleks041103 last updated on 05/Dec/23 $${I}=\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} {ln}\left({sin}\left({x}\right)\right){dx} \\ $$$${u}=\pi/\mathrm{2}−{x}\Rightarrow{du}=−{dx} \\ $$$$\Rightarrow{I}=\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} {ln}\left({cos}\left({u}\right)\right){du}…
Question Number 201349 by sonukgindia last updated on 05/Dec/23 Answered by Sutrisno last updated on 05/Dec/23 $${misal}\:: \\ $$$${A}\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{ln}\left({cosx}\right)\:{dx} \\ $$$${B}\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{ln}\left({sinx}\right)\:{dx}…
Question Number 201350 by sonukgindia last updated on 05/Dec/23 Answered by Calculusboy last updated on 05/Dec/23 $$\boldsymbol{{Solution}}:\:\boldsymbol{{let}}\:\boldsymbol{{y}}=\frac{\boldsymbol{\pi}}{\mathrm{4}}−\boldsymbol{{x}}\:\:\:\boldsymbol{{dy}}=−\boldsymbol{{dx}} \\ $$$$\boldsymbol{{when}}\:\boldsymbol{{x}}=\frac{\boldsymbol{\pi}}{\mathrm{4}}\:\:\boldsymbol{{y}}=\mathrm{0}\:\:\boldsymbol{{and}}\:\boldsymbol{{when}}\:\boldsymbol{{x}}=\mathrm{0}\:\boldsymbol{{y}}=\frac{\boldsymbol{\pi}}{\mathrm{4}} \\ $$$$\boldsymbol{{I}}=\int_{\frac{\boldsymbol{\pi}}{\mathrm{4}}} ^{\mathrm{0}} \boldsymbol{{In}}\left[\mathrm{1}+\boldsymbol{{tan}}\left(\frac{\boldsymbol{\pi}}{\mathrm{4}}−\boldsymbol{{y}}\right)\right]−\boldsymbol{{dy}}\:\:\:\:\left(\boldsymbol{{change}}\:\boldsymbol{{of}}\:\boldsymbol{{variable}}\right) \\ $$$$\boldsymbol{{I}}=\int_{\mathrm{0}}…
Question Number 201351 by sonukgindia last updated on 05/Dec/23 Answered by Sutrisno last updated on 05/Dec/23 $$=\int_{\mathrm{0}} ^{\pi} \frac{{x}}{\mathrm{1}+{sinx}}.\frac{\mathrm{1}−{sinx}}{\mathrm{1}−{sinx}}{dx} \\ $$$$=\int_{\mathrm{0}} ^{\pi} \frac{{x}−{xsinx}}{\mathrm{1}−{sin}^{\mathrm{2}} {x}}{dx} \\…
Question Number 201408 by Ari last updated on 05/Dec/23 Answered by mr W last updated on 05/Dec/23 $$=\frac{\mathrm{1}×\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }×\frac{\mathrm{2}×\mathrm{4}}{\mathrm{3}^{\mathrm{2}} }×\frac{\mathrm{3}×\mathrm{5}}{\mathrm{4}^{\mathrm{2}} }×…×\frac{\mathrm{98}×\mathrm{100}}{\mathrm{99}^{\mathrm{2}} } \\ $$$$=\frac{\mathrm{1}×\cancel{\mathrm{3}}}{\mathrm{2}^{\cancel{\mathrm{2}}} }×\frac{\cancel{\mathrm{2}}×\cancel{\mathrm{4}}}{\cancel{\mathrm{3}^{\mathrm{2}}…
Question Number 201346 by sonukgindia last updated on 05/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com