Question Number 194691 by CrispyXYZ last updated on 13/Jul/23 $${a},\:{b},\:{c}\geqslant\mathrm{0},\:{a}+{b}+{c}=\mathrm{2}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{3}{a}+\mathrm{8}{ab}+\mathrm{16}{abc}\leqslant\mathrm{12}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 194654 by sonukgindia last updated on 12/Jul/23 Answered by MM42 last updated on 12/Jul/23 $$\left(\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\right)^{{tanx}} \right)^{{tanx}+\mathrm{2}} ={u} \\ $$$$\Rightarrow{u}+\frac{\mathrm{1}}{{u}}=\mathrm{6}\Rightarrow{u}^{\mathrm{2}} −\mathrm{6}{u}+\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow{u}=\mathrm{3}\pm\mathrm{2}\sqrt{\mathrm{2}} \\…
Question Number 194649 by SANOGO last updated on 12/Jul/23 $${calcul}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \sqrt{\mathrm{4}{sin}^{\mathrm{2}} {t}+{cos}^{\mathrm{2}} {t}\:}{dt} \\ $$ Commented by Frix last updated on 12/Jul/23…
Question Number 194648 by universe last updated on 12/Jul/23 Commented by Frix last updated on 12/Jul/23 $$\frac{\mathrm{7}}{\mathrm{8}} \\ $$ Commented by universe last updated on…
Question Number 194640 by cortano12 last updated on 12/Jul/23 $$\:\:\:\:\underbrace{ } \\ $$ Answered by horsebrand11 last updated on 12/Jul/23 $$\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}}\:=\:\mathrm{y} \\ $$$$\:\underset{\mathrm{y}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}}{\mathrm{y}\:\mathrm{sin}\:\mathrm{3y}}\:=\underset{\mathrm{y}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}}…
Question Number 194642 by horsebrand11 last updated on 12/Jul/23 $$\:\mathrm{If}\:\mathrm{A}=\begin{pmatrix}{\mathrm{a}\:\:\:\:\mathrm{b}\:\:\:\:\:\:\mathrm{c}}\\{\mathrm{b}\:\:\:\:\mathrm{c}\:\:\:\:\:\:\mathrm{a}}\\{\mathrm{c}\:\:\:\:\:\mathrm{a}\:\:\:\:\:\:\mathrm{b}}\end{pmatrix}\:\mathrm{and}\:\mathrm{a},\mathrm{b},\mathrm{c}\:>\mathrm{0} \\ $$$$\:\:\mathrm{such}\:\mathrm{that}\:\mathrm{abc}=\mathrm{1}\:\mathrm{and}\:\mathrm{A}^{\mathrm{T}} .\mathrm{A}=\mathrm{I} \\ $$$$\:\mathrm{find}\:\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} −\mathrm{3abc}\:. \\ $$ Answered by som(math1967) last updated…
Question Number 194637 by manxsol last updated on 12/Jul/23 $$ \\ $$$${x}+{y}=\mathrm{1} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}^{\mathrm{11}} +{y}^{\mathrm{11}} =? \\ $$$$ \\ $$$$ \\…
Question Number 194636 by universe last updated on 12/Jul/23 Commented by TheHoneyCat last updated on 14/Jul/23 what is "gif"? Commented by Tinku Tara last updated on 14/Jul/23…
Question Number 194638 by Erico last updated on 12/Jul/23 $$\mathrm{Prove}\:\mathrm{that}\:\forall{n}\in\mathrm{IN}^{\ast} \:\:\:\:\: \\ $$$$\:\:\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}^{{n}} −\mathrm{1}} {\sum}}\:\frac{\mathrm{1}}{{sin}^{\mathrm{2}} \left(\frac{{k}\pi}{\mathrm{2}^{{n}+\mathrm{1}} }\right)}=\:\frac{\mathrm{2}^{\mathrm{2}{n}+\mathrm{1}} −\mathrm{2}}{\mathrm{3}} \\ $$$$\mathrm{Give}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{n}\:\:\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}^{{n}} −\mathrm{1}} {\sum}}\:\frac{\mathrm{1}}{{sin}^{\mathrm{4}} \left(\frac{{k}\pi}{\mathrm{2}^{{n}+\mathrm{1}}…