Question Number 4437 by Rasheed Soomro last updated on 25/Jan/16 $$\mathrm{An}\:\boldsymbol{\mathrm{ellipse}}\:\mathrm{having}\:\boldsymbol{\mathrm{semi}}-\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axis}}\: \\ $$$$\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\boldsymbol{\mathrm{semi}}-\boldsymbol{\mathrm{minor}}\:\boldsymbol{\mathrm{axis}}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{b}} \\ $$$$\mathrm{and}\:\mathrm{a}\:\boldsymbol{\mathrm{circle}}\:\mathrm{having}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{r}}\:\mathrm{have}\:\mathrm{equal} \\ $$$$\boldsymbol{\mathrm{area}}. \\ $$$$\mathrm{Express}\:\boldsymbol{\mathrm{r}}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}. \\ $$$$ \\ $$ Answered by…
Question Number 135507 by 0731619177 last updated on 13/Mar/21 Answered by Rasheed.Sindhi last updated on 15/Mar/21 $$\left({x}+{y}\right)\left(\mathrm{81}+{xy}\right)\:−\:\mathrm{9}\left({x}+{y}\right)^{\mathrm{2}} =\mathrm{210} \\ $$$$\left({x}+{y}\right)\left(\mathrm{81}+{xy}−\mathrm{9}\left({x}+{y}\right)\right)=\mathrm{210} \\ $$$$ \\ $$$${Let}\:{x}+{y}={n}\:{where}\:{n}\in\mathbb{Z}\:\wedge\:{n}\:\mid\:\mathrm{210} \\…
Question Number 69966 by necxxx last updated on 29/Sep/19 Commented by necxxx last updated on 29/Sep/19 $${please}\:{help} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 4430 by alib last updated on 24/Jan/16 $$\left\{\left({x}−{y}\right)\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)=\mathrm{3}{a}^{\mathrm{2}} \right. \\ $$$$\left({x}+{y}\right)\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)=\mathrm{15}{a}^{\mathrm{2}} \\ $$$$ \\ $$$${Solve}\:{the}\:{system}\:{of}\:{equation} \\ $$$$ \\ $$…
Question Number 4429 by alib last updated on 24/Jan/16 $$\left({sin}\:{x}\:+\sqrt{\mathrm{3}}\:{cos}\:{x}\right)\:{sin}\:\mathrm{3}{x}\:=\:\mathrm{2} \\ $$ Answered by Yozzii last updated on 24/Jan/16 $${sinx}+\sqrt{\mathrm{3}}{cosx}=\sqrt{\mathrm{1}+\mathrm{3}}{sin}\left({x}+\pi/\mathrm{3}\right) \\ $$$$=\mathrm{2}{sin}\left({x}+\frac{\pi}{\mathrm{3}}\right) \\ $$$$\left({sinx}+\sqrt{\mathrm{3}}{cosx}\right){sin}\mathrm{3}{x}=\mathrm{2}………\left(\Upsilon\right) \\…
Question Number 135497 by EDWIN88 last updated on 13/Mar/21 $$\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}+\frac{\pi}{\mathrm{4}}\right)\:=\:\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}−\frac{\pi}{\mathrm{4}}\right)+\:\sqrt{\mathrm{7}}\:\mathrm{cos}\:\mathrm{x} \\ $$ Answered by john_santu last updated on 13/Mar/21 $$\Leftrightarrow\:\mathrm{sin}\:^{\mathrm{2}} \left({x}+\frac{\pi}{\mathrm{4}}\right)−\mathrm{sin}\:^{\mathrm{2}} \left({x}−\frac{\pi}{\mathrm{4}}\right)=\sqrt{\mathrm{7}}\:\mathrm{cos}\:{x} \\…
Question Number 135498 by aurpeyz last updated on 13/Mar/21 $$ \\ $$$$\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{\mathrm{25}−{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by john_santu last updated on 13/Mar/21 $$\mathscr{F}\:=\:\int\:\frac{{dx}}{{x}^{\mathrm{3}} \:\sqrt{\mathrm{25}{x}^{−\mathrm{2}}…
Question Number 135493 by EDWIN88 last updated on 13/Mar/21 $$\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} −{x}−\mathrm{2}}\:=\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$ Answered by john_santu last updated on 13/Mar/21 $$\left(\mathrm{1}\right)\begin{cases}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}\geqslant\mathrm{0}}\\{{x}^{\mathrm{2}} −{x}−\mathrm{2}\geqslant\mathrm{0}}\\{{x}^{\mathrm{2}}…
Question Number 4423 by Rasheed Soomro last updated on 24/Jan/16 $$\mathrm{Determine}\:\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{such}\:\mathrm{that}\:\forall\:\mathrm{t}\in\mathbb{Z} \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{8x}+\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{has}\:\mathrm{integer}-\mathrm{solution}. \\ $$ Commented by Yozzii last updated on 24/Jan/16 $${Try}\:{f}\left({t}\right)={c};\:{c}\:{is}\:{a}\:{real}\:{constant}. \\…
Question Number 135495 by greg_ed last updated on 13/Mar/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{guyz}}\:! \\ $$$$\boldsymbol{\mathrm{let}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{try}}\:\boldsymbol{\mathrm{this}}\::\:\boldsymbol{\mathrm{I}}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\boldsymbol{{sin}}^{\mathrm{2}} \boldsymbol{{x}}}{\boldsymbol{{cos}}^{\mathrm{3}} \boldsymbol{{x}}}\boldsymbol{{dx}}. \\ $$ Answered by mathmax by abdo last updated…