Question Number 79417 by mr W last updated on 25/Jan/20 $${For}\:{x},{y}\in\mathbb{R}\:{find}\:{the}\:{minimum}\:{and} \\ $$$${maximum}\:{of}\:\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{4}{y} \\ $$$${if}\:{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} −{xy}−\mathrm{5}{x}−\mathrm{7}{y}−\mathrm{30}=\mathrm{0}. \\ $$ Commented by john santu last…
Question Number 144947 by mathdanisur last updated on 30/Jun/21 $$\underset{{k}=\mathrm{1}} {\overset{\mathrm{12}} {\prod}}\mathrm{2}\centerdot{sin}\left(\frac{\pi{k}}{\mathrm{24}}\right)\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 01/Jul/21 $$\mathrm{sin2}\theta\:=\:\mathrm{2cos}\theta\mathrm{sin}\theta \\ $$$$\mathrm{2cos}\theta\:=\:\frac{\mathrm{sin2}\theta}{\mathrm{sin}\theta} \\…
Question Number 144936 by mathdanisur last updated on 30/Jun/21 Answered by mindispower last updated on 30/Jun/21 $${sec}^{\mathrm{4}} \left({x}\right)+{csc}^{\mathrm{4}} \left({x}\right)\geqslant\frac{\mathrm{2}}{{cos}^{\mathrm{2}} \left({x}\right){sin}^{\mathrm{2}} \left({x}\right)}=\frac{\mathrm{8}}{\left({sin}\left(\mathrm{2}{x}\right)\right)^{\mathrm{2}} } \\ $$$$\geqslant\mathrm{8} \\…
Question Number 144922 by mathdanisur last updated on 30/Jun/21 $${if}\:\:{z}^{\mathrm{2}} \:-\:\mathrm{16}\sqrt{{z}}\:=\:\mathrm{12} \\ $$$${find}\:\:{z}\:-\:\mathrm{2}\sqrt{{z}}\:=\:? \\ $$ Answered by liberty last updated on 30/Jun/21 $$\:\mathrm{x}^{\mathrm{4}} −\mathrm{16x}−\mathrm{12}=\mathrm{0} \\…
Question Number 144917 by mathdanisur last updated on 30/Jun/21 $${if}\:\:{x};{y}>\mathrm{0}\:\:{then}: \\ $$$$\mathrm{10}\:\centerdot\:\sqrt{\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{\mathrm{2}}}\:+\:\frac{\mathrm{8}{xy}}{{x}+{y}}\:\geqslant\:\mathrm{7}{x}+\mathrm{7}{y} \\ $$ Answered by justtry last updated on 30/Jun/21 $${remember}\:: \\…
Question Number 144901 by loveineq last updated on 30/Jun/21 $$\mathrm{Let}\:{a},{b}\:>\:\mathrm{0}\:\mathrm{and}\:{a}+{b}+\mathrm{1}\:=\:\mathrm{3}{ab}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}}{{a}^{\mathrm{2}} +\mathrm{1}}+\frac{{b}}{{b}^{\mathrm{2}} +\mathrm{1}}\:\leqslant\:\mathrm{1}\:\leqslant\:\frac{{a}^{\mathrm{3}} }{{a}^{\mathrm{2}} +\mathrm{1}}+\frac{{b}^{\mathrm{3}} }{{b}^{\mathrm{2}} +\mathrm{1}} \\ $$$$ \\ $$$$\mathrm{Let}\:{a},{b}\:>\:\mathrm{0},\:{n}\:\in\:\mathbb{Z}^{+} \:\mathrm{and}\:{a}+{b}+\mathrm{1}\:=\:\mathrm{3}{ab}.\:\mathrm{Prove}\:\mathrm{or}\:\mathrm{disprove} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{{n}−\mathrm{1}}…
Question Number 144897 by physicstutes last updated on 30/Jun/21 $$\underset{\mathrm{0}} {\overset{\frac{\left[{x}\right]}{\mathrm{3}}} {\int}}\frac{\mathrm{8}^{{x}} }{\mathrm{2}^{\left[\mathrm{3}{x}\right]} }\:{dx}=\:???\:\mathrm{where}\:\left[.\right]\:\mathrm{is}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{function}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 144888 by imjagoll last updated on 30/Jun/21 Commented by imjagoll last updated on 30/Jun/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{area}. \\ $$ Answered by nimnim last updated on…
Question Number 144887 by imjagoll last updated on 30/Jun/21 Answered by nimnim last updated on 30/Jun/21 $$=\sqrt{\left(\sqrt{\mathrm{125}+\mathrm{44}}\right)\left(\mathrm{9}\right)+\mathrm{4}}=\sqrt{\left(\sqrt{\mathrm{169}}\right)\left(\mathrm{9}\right)+\mathrm{4}} \\ $$$$=\sqrt{\mathrm{13}\left(\mathrm{9}\right)+\mathrm{4}}=\sqrt{\mathrm{117}+\mathrm{4}}=\sqrt{\mathrm{121}}=\mathrm{11} \\ $$$$\: \\ $$ Terms of…
Question Number 144877 by imjagoll last updated on 30/Jun/21 $$\:\:\mathrm{u}+\sqrt{\mathrm{u}}+\sqrt[{\mathrm{3}}]{\mathrm{u}}+\sqrt[{\mathrm{4}}]{\mathrm{u}}+\sqrt[{\mathrm{5}}]{\mathrm{u}}+…\:+\infty=? \\ $$$$ \\ $$ Answered by MJS_new last updated on 30/Jun/21 $$\forall{u}>\mathrm{0}:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{u}^{\mathrm{1}/{n}} \:=+\infty…