Question Number 145772 by mathdanisur last updated on 07/Jul/21 $${a};{b};{c}>\mathrm{0}\:;\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{2}\:{prove}: \\ $$$$\left({a}^{\mathrm{6}} +{b}^{\mathrm{6}} +{c}^{\mathrm{6}} \right)^{\mathrm{3}} \:\geqslant\:\left({a}^{\mathrm{5}} +{b}^{\mathrm{5}} +{c}^{\mathrm{5}} \right)^{\mathrm{4}} \\ $$ Terms…
Question Number 145774 by Engr_Jidda last updated on 08/Jul/21 $${find}\:{the}\:{area}\:{bounded}\:{by}\:{y}=\mathrm{2}{x},\:{y}=\frac{{x}}{\mathrm{2}}\:{and}?{xy}=\mathrm{2} \\ $$ Answered by ArielVyny last updated on 08/Jul/21 $$\forall{x}\in\mathbb{R}\:\mathrm{2}{x}\geqslant\frac{{x}}{\mathrm{2}}\:\:{A}=\int\left(\mathrm{2}{x}−\frac{{x}}{\mathrm{2}}\right){dx}=\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} \\ $$$${A}={x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}{x}^{\mathrm{2}} =\frac{\mathrm{3}}{\mathrm{4}}{x}^{\mathrm{2}}…
Question Number 145769 by Engr_Jidda last updated on 07/Jul/21 $${find}\:{x}\:{if}\:\:\mathrm{2}^{{x}} +\mathrm{2}^{\mathrm{3}{x}} =\mathrm{16} \\ $$ Commented by 7770 last updated on 08/Jul/21 $$\mathrm{2}^{\boldsymbol{{x}}} +\mathrm{2}^{\mathrm{3}\boldsymbol{{x}}} =\mathrm{16} \\…
Question Number 145768 by mathdanisur last updated on 07/Jul/21 $${x};{y};{z};{t}\in\mathbb{Z}^{+} \\ $$$$\begin{cases}{{xy}\:+\:{zt}\:=\:\mathrm{38}}\\{{xz}\:+\:{yt}\:=\:\mathrm{34}}\\{{xt}\:+\:{yz}\:=\:\mathrm{43}}\end{cases}\:\:\Rightarrow\:{x}+{y}+{z}+{t}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 145763 by gsk2684 last updated on 07/Jul/21 $${if}\:{z}=\left(\frac{\mathrm{3}+{i}\:\mathrm{sin}\:\theta}{\mathrm{4}−{i}\:\mathrm{cos}\:\theta}\right){is}\:{purely}\:{real}\:{and}\: \\ $$$$\frac{\Pi}{\mathrm{2}}<\theta<\Pi\:{then}\:{find}\:{arg}\left(\mathrm{sin}\:\theta\:+{i}\:\mathrm{cos}\:\theta\right)? \\ $$ Answered by mathmax by abdo last updated on 08/Jul/21 $$\mathrm{z}\:\mathrm{real}\:\Rightarrow\mathrm{z}=\overset{−} {\mathrm{z}}\:\Rightarrow\frac{\mathrm{3}+\mathrm{isin}\theta}{\mathrm{4}−\mathrm{icos}\theta}=\frac{\mathrm{3}−\mathrm{isin}\theta}{\mathrm{4}+\mathrm{icos}\theta}\:\Rightarrow…
Question Number 145759 by mathdanisur last updated on 07/Jul/21 Commented by mr W last updated on 07/Jul/21 $$\sqrt{{ab}}\leqslant\frac{{a}+{b}}{\mathrm{2}}={x} \\ $$$$\Rightarrow{ab}\leqslant{x}^{\mathrm{2}} ={maximum} \\ $$ Commented by…
Question Number 80219 by Power last updated on 01/Feb/20 Answered by som(math1967) last updated on 01/Feb/20 $${let}\frac{\pi}{\mathrm{7}}=\theta\: \\ $$$$\therefore{cos}\mathrm{2}\theta+{cos}\mathrm{4}\theta+{cos}\mathrm{6}\theta \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}{sin}\theta}\left(\mathrm{2}{cos}\mathrm{2}\theta{sin}\theta+\mathrm{2}{sin}\theta{cos}\mathrm{4}\theta\right. \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\mathrm{2}{sin}\theta{cos}\mathrm{6}\theta\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}{sin}\theta}\left({sin}\mathrm{3}\theta−{sin}\theta+{sin}\mathrm{5}\theta−{sin}\mathrm{3}\theta\right.…
Question Number 145755 by loveineq last updated on 07/Jul/21 $$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{abc}\:=\:\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{8}\left({a}^{\mathrm{2}} +\mathrm{1}\right)\left({b}^{\mathrm{2}} +\mathrm{1}\right)\left({c}^{\mathrm{2}} +\mathrm{1}\right)}{\left({a}+\mathrm{1}\right)\left({b}+\mathrm{1}\right)\left({c}+\mathrm{1}\right)}\:\leqslant\:\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com