Question Number 70021 by naka3546 last updated on 30/Sep/19 $$\sqrt[{\mathrm{3}}]{\sqrt{\sqrt{\mathrm{12345689654321233}\:+\:\mathrm{5333334096}\:\sqrt{\mathrm{12345679}}}}\:−\:\sqrt{\sqrt{\mathrm{12345689654321233}\:−\:\mathrm{5333334096}\:\sqrt{\mathrm{12345679}}}}}\:\:=\:\:… \\ $$ Commented by MJS last updated on 30/Sep/19 $$\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve} \\ $$$$\sqrt{{a}+{b}\sqrt{{c}}}={p}+{q}\sqrt{{c}}\:\Leftrightarrow\:{a}={p}^{\mathrm{2}} +{cq}^{\mathrm{2}} \wedge{b}=\mathrm{2}{pq} \\…
Question Number 135544 by 0731619177 last updated on 13/Mar/21 Answered by Olaf last updated on 13/Mar/21 $${f}\left({x}\right)\:=\:\mathrm{sin}{x}+\mathrm{cos}{x}\:=\:\sqrt{\mathrm{2}}\mathrm{cos}\left(\frac{\pi}{\mathrm{4}}−{x}\right) \\ $$$${x}\in\left[\mathrm{0},\frac{\pi}{\mathrm{4}}\right]\:\Rightarrow\:{f}\left({x}\right)\in\left[\mathrm{1},\sqrt{\mathrm{2}}\right] \\ $$$$\Rightarrow\:\forall{x}\in\left[\mathrm{0},\frac{\pi}{\mathrm{4}}\right]\:\lfloor{f}\left({x}\right)\rfloor\:=\:\mathrm{1} \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{cos}\left(\mathrm{2}{x}\right)×\mathrm{2}^{\mathrm{1}}…
Question Number 135543 by 0731619177 last updated on 13/Mar/21 Answered by Olaf last updated on 13/Mar/21 $$\Omega\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{cos}\left(\mathrm{2}{x}\right)\mathrm{tan}\left(\frac{{x}}{\mathrm{2}}\right){dx} \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} {x}}\mathrm{tan}\left(\frac{{x}}{\mathrm{2}}\right){dx}…
Question Number 135540 by mohammad17 last updated on 13/Mar/21 Answered by Olaf last updated on 13/Mar/21 $$\left.\mathrm{Q1a}\right) \\ $$$$\mathrm{1}/\:\:\:\mathrm{S}_{{n}} \:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left[\frac{\mathrm{1}}{\mathrm{5}^{{k}} }−\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)}\right] \\ $$$$\mathrm{S}_{{n}}…
Question Number 135539 by mohammad17 last updated on 13/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 70003 by Maclaurin Stickker last updated on 29/Sep/19 $${Let}\:{f}\left({x}\right)=\mathrm{3}^{{x}−\mathrm{1}} ,\:{g}\left({x}\right)=\mathrm{3}^{{x}} \:{and}\:{h}\left({x}\right)=\mathrm{4} \\ $$$${determine}\:{the}\:{values}\:{of}\:\boldsymbol{{x}}\:{for}\:{which}: \\ $$$${f}\left({x}\right)+{g}\left({x}\right)\geqslant{h}\left({x}\right). \\ $$$$ \\ $$ Commented by Abdo msup.…
Question Number 69979 by Maclaurin Stickker last updated on 29/Sep/19 $${Using}\:{the}\:{definition}\:{calculate}\:{the} \\ $$$${derivative}\:{at}\:{point}\:{x}=\mathrm{2} \\ $$$${f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} \\ $$$$ \\ $$ Commented by kaivan.ahmadi last updated on…
Question Number 135507 by 0731619177 last updated on 13/Mar/21 Answered by Rasheed.Sindhi last updated on 15/Mar/21 $$\left({x}+{y}\right)\left(\mathrm{81}+{xy}\right)\:−\:\mathrm{9}\left({x}+{y}\right)^{\mathrm{2}} =\mathrm{210} \\ $$$$\left({x}+{y}\right)\left(\mathrm{81}+{xy}−\mathrm{9}\left({x}+{y}\right)\right)=\mathrm{210} \\ $$$$ \\ $$$${Let}\:{x}+{y}={n}\:{where}\:{n}\in\mathbb{Z}\:\wedge\:{n}\:\mid\:\mathrm{210} \\…
Question Number 135498 by aurpeyz last updated on 13/Mar/21 $$ \\ $$$$\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{\mathrm{25}−{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by john_santu last updated on 13/Mar/21 $$\mathscr{F}\:=\:\int\:\frac{{dx}}{{x}^{\mathrm{3}} \:\sqrt{\mathrm{25}{x}^{−\mathrm{2}}…
Question Number 4418 by Syaka last updated on 23/Jan/16 $${What}\:{the}\:{exact}\:{value}\:{of}\:: \\ $$$${sin}\:\mathrm{10}°\:\left(\mathrm{2}{cos}\:\mathrm{10}°\:+\:\mathrm{1}\right)\left(\mathrm{2}{cos}\:\mathrm{10}°\:−\:\mathrm{1}\right)\:=\:….? \\ $$$$ \\ $$ Answered by Yozzii last updated on 24/Jan/16 $${sin}\mathrm{10}°\left(\mathrm{2}{cos}\mathrm{10}°+\mathrm{1}\right)\left(\mathrm{2}{cos}\mathrm{10}°−\mathrm{1}\right) \\…