Question Number 164457 by mathls last updated on 17/Jan/22 $$\frac{\mathrm{20}}{\mathrm{10}}=\mathrm{2}\frac{\mathrm{0}}{\mathrm{10}}=>\frac{\mathrm{20}}{\mathrm{10}}=\mathrm{0}\:\:\:\:\:{why}? \\ $$ Answered by mahdipoor last updated on 17/Jan/22 $$\frac{\mathrm{20}}{\mathrm{10}}=\mathrm{2}\frac{\mathrm{0}}{\mathrm{10}}=\mathrm{2}+\frac{\mathrm{0}}{\mathrm{10}}\:\left({not}\:\mathrm{2}×\frac{\mathrm{0}}{\mathrm{10}}\right) \\ $$ Terms of Service…
Question Number 164451 by Zaynal last updated on 17/Jan/22 $$\boldsymbol{\mathrm{How}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{true}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{false}}??; \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{Prove}}\:\boldsymbol{{the}}: \\ $$$$\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{\mathrm{p}}+\boldsymbol{\mathrm{p}}^{\mathrm{2}} +\boldsymbol{\mathrm{p}}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{{q}}+\boldsymbol{{q}}^{\mathrm{2}} +\boldsymbol{{q}}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{{r}}+\boldsymbol{{r}}^{\mathrm{2}} +\boldsymbol{{r}}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{{s}}+\boldsymbol{{s}}^{\mathrm{2}} +\boldsymbol{{s}}^{\mathrm{3}\:} }\:\geqslant\:\mathrm{1} \\…
Question Number 98914 by shaxzod last updated on 17/Jun/20 $$\mathrm{2}{x}+\mathrm{3}{y}=\mathrm{5} \\ $$$$\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \underset{{min}} {\right)}=? \\ $$ Commented by john santu last updated on 17/Jun/20…
Question Number 164445 by mathlove last updated on 17/Jan/22 Commented by mr W last updated on 17/Jan/22 $${i}\:{don}'{t}\:{think}\:{there}\:{is}\:{a}\:{nice}\:{solution}. \\ $$$${one}\:{can}\:{only}\:{approximate}. \\ $$$${x}=\mathrm{2}−{t} \\ $$$${y}=\mathrm{2}+{t} \\…
Question Number 164434 by mathlove last updated on 17/Jan/22 Answered by TheSupreme last updated on 17/Jan/22 $$\mathrm{2}{f}\left({sin}\left({x}\right)\right)−{f}\left({cos}\left({x}\right)\right)=\mathrm{3}{x} \\ $$$$\mathrm{2}{f}\left({cos}\left({x}\right)\right)−{f}\left({sin}\left({x}\right)\right)=\mathrm{3}\left(\frac{\pi}{\mathrm{2}}−{x}\right) \\ $$$$\mathrm{3}{f}\left({sin}\left({x}\right)\right)=\mathrm{6}{x}−\mathrm{3}\left(\frac{\pi}{\mathrm{2}}−{x}\right) \\ $$$${f}\left({sin}\left({x}\right)\right)=\mathrm{9}{x}−\frac{\mathrm{3}}{\mathrm{2}}\pi \\ $$$${f}\left({t}\right)=\mathrm{9}{arcsin}\left({x}\right)−\frac{\mathrm{3}}{\mathrm{2}}\pi+\mathrm{2}{k}\pi…
Question Number 164429 by malwan last updated on 17/Jan/22 $${If}\:{C}\left(\mathrm{2}{x}\:,\:{x}\right)\:=\:\mathrm{70} \\ $$$${prove}\:{that}\:{x}\:=\:\mathrm{4} \\ $$ Answered by alephzero last updated on 17/Jan/22 $${C}_{{x}} ^{\mathrm{2}{x}} \:=\:\mathrm{70} \\…
Question Number 164425 by Zaynal last updated on 17/Jan/22 $$\mathrm{What}\:\mathrm{it}'\mathrm{s}\:?? \\ $$$$\mathrm{5}×\mathrm{55}×\mathrm{555}×\mathrm{5555}×\mathrm{55555}………….\infty= \\ $$ Answered by alephzero last updated on 17/Jan/22 $$\mathrm{Let}\:{a}_{{n}} \:=\:\underset{{n}-\mathrm{times}} {\underbrace{\mathrm{5555}…\mathrm{5555}}} \\…
Question Number 164417 by HongKing last updated on 16/Jan/22 Answered by Rasheed.Sindhi last updated on 17/Jan/22 $${y}=\mathrm{4}{x}−\mathrm{3} \\ $$$$\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{6}{y}+\mathrm{9}}\:+\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{2}{y}+\mathrm{2}}\: \\ $$$$=\sqrt{{x}^{\mathrm{2}}…
Question Number 164416 by HongKing last updated on 16/Jan/22 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}<\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{3}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\left(\mathrm{1}\:+\:\frac{\mathrm{b}}{\mathrm{a}}\right)^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{b}}^{\mathrm{2}} }} \centerdot\:\left(\mathrm{1}\:+\:\frac{\mathrm{c}}{\mathrm{b}}\right)^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{c}}^{\mathrm{2}} }} \centerdot\:\left(\mathrm{1}\:+\:\frac{\mathrm{a}}{\mathrm{c}}\right)^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{2}} }} \geqslant\:\mathrm{8} \\ $$ Terms of Service Privacy Policy…
Question Number 164418 by HongKing last updated on 16/Jan/22 Commented by Kamel last updated on 16/Jan/22 Commented by Kamel last updated on 16/Jan/22 $${With}\:{differential}\:{equation}. \\…