Question Number 164511 by HongKing last updated on 18/Jan/22 $$\mathrm{sin}\centerdot\left(\pi\:\mathrm{sin}\:\mathrm{x}\right)\:-\:\mathrm{cos}\centerdot\left(\pi\:\mathrm{sin}\:\mathrm{x}\right)\:=\:\mathrm{1} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$ Answered by mindispower last updated on 18/Jan/22 $${sin}\left({a}\right)−{cos}\left({a}\right)=\sqrt{\mathrm{2}}{sin}\left({a}−\frac{\pi}{\mathrm{4}}\right) \\ $$$$\Leftrightarrow\:{withea}=\pi{sin}\left({x}\right) \\…
Question Number 164496 by HongKing last updated on 18/Jan/22 $$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{xy}\:=\:\mathrm{11}}\\{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{xy}\:=\:\mathrm{24}}\end{cases}\:\:\Rightarrow\:\mid\mathrm{x}+\mathrm{y}\mid=? \\ $$ Answered by Rasheed.Sindhi last updated on 18/Jan/22 $$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{xy}\:=\:\mathrm{11}}\\{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{xy}\:=\:\mathrm{14}}\end{cases}\:\:\Rightarrow\:\mid\mathrm{x}+\mathrm{y}\mid=? \\…
Question Number 164497 by mnjuly1970 last updated on 18/Jan/22 Answered by cortano1 last updated on 18/Jan/22 Commented by mnjuly1970 last updated on 18/Jan/22 $${thanks}\:{alot}\:{sir}\:{cortano} \\…
Question Number 164466 by Zaynal last updated on 17/Jan/22 Commented by Zaynal last updated on 17/Jan/22 $$\left(\mathrm{xy}\right)^{\mathrm{2}} \:+\left({yz}\right)^{\mathrm{2}} +\left(\boldsymbol{{zx}}\right)^{\mathrm{2}} =\mathrm{1} \\ $$ Terms of Service…
Question Number 98925 by ajfour last updated on 17/Jun/20 $${If}\:{the}\:{curve}\:{shown}\:{below}\:{has}\:{the}\: \\ $$$${equation},\:\:{y}=\left({x}−{p}\right)\left({x}^{\mathrm{3}} −{bx}−{c}\right) \\ $$$${then}\:{find}\:\:{q}/{p}\:\:{in}\:{terms}\:{of}\:{b}\:{and}\:{c}. \\ $$ Commented by ajfour last updated on 17/Jun/20 Answered…
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…