Question Number 194634 by York12 last updated on 12/Jul/23 $${a}_{\mathrm{1}} ,{a}_{\mathrm{2}} ,{a}_{\mathrm{3}} ,….,{a}_{{n}} >\mathrm{0}\:{such}\:{that}\:{a}_{{i}} \in\left[\mathrm{0},{i}\right]\: \\ $$$$\forall\:{i}\in\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},…,{n}\right\}\:{prove}\:{that} \\ $$$$\mathrm{2}^{{n}} .{a}_{\mathrm{1}} \left({a}_{\mathrm{1}} +{a}_{\mathrm{2}} \right)…\left({a}_{\mathrm{1}} +{a}_{\mathrm{2}} +…+{a}_{{n}}…
Question Number 194662 by SANOGO last updated on 12/Jul/23 $$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \sqrt{\mathrm{4}{sin}^{\mathrm{2}} {t}+{cos}^{\mathrm{2}} {t}}\:\:{dt} \\ $$ Commented by Frix last updated on 12/Jul/23 $$\mathrm{Same}\:\mathrm{as}\:\mathrm{before}: \\…
Question Number 194619 by Shrinava last updated on 11/Jul/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}: \\ $$$$−\mathrm{3x}^{\mathrm{3}} \:+\:\mathrm{8x}^{\mathrm{2}} \:−\:\mathrm{6x}\:−\:\mathrm{7}\:=\:\mathrm{0} \\ $$ Answered by Frix last updated on 11/Jul/23…
Question Number 194613 by cortano12 last updated on 11/Jul/23 $$\:\:\:\:\:\:\cancel{\underline{ }} \\ $$ Answered by MM42 last updated on 11/Jul/23 $$\frac{\mathrm{1}}{{log}_{{x}} \mathrm{4}{x}}+\frac{\mathrm{1}}{{log}_{{x}} \frac{{x}}{\mathrm{2}}}=\mathrm{2} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}{log}_{{x}}…
Question Number 194612 by Abdullahrussell last updated on 11/Jul/23 Commented by TheHoneyCat last updated on 15/Jul/23 $$\left.\mathrm{1}\right)\:\mathrm{Let}\:\alpha=\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}=\mathrm{45} \\ $$$$\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{digits}\:\mathrm{in}\:\mathrm{basis}\:\mathrm{10}. \\ $$$$\mathrm{Let}\:{S}_{\mathrm{1}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{first}\:\mathrm{sum},\:{S}_{\mathrm{1},\mathrm{0}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all} \\ $$$$\mathrm{unit}\:\mathrm{digits},\:{S}_{\mathrm{1},\mathrm{1}}…
Question Number 194624 by BaliramKumar last updated on 11/Jul/23 Commented by BaliramKumar last updated on 11/Jul/23 $$\mathrm{Please}\:\mathrm{Help}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{only}\:\mathrm{answer}\:\mathrm{no}\:\mathrm{solution} \\ $$$$\mathrm{BF}=? \\ $$$$\mathrm{FH}=? \\ $$$$\mathrm{HJ}=? \\ $$$$\mathrm{JC}=?…
Question Number 194610 by justenspi last updated on 11/Jul/23 $${where}\:{can}\:{I}\:{learn}\:{about}\:{multiple}\:{sigma}\:{notaions} \\ $$$${of}\:{dependent}\:{and}\:{independent}\:{variables} \\ $$$$ \\ $$$${something}\:{like}\:{this} \\ $$$$\underset{\mathrm{1}\leqslant{i}} {\sum}\underset{<{j}} {\sum}\underset{<{k}\leqslant\mathrm{1}} {\sum}\left({i}+{j}+{k}\right)=\lambda \\ $$$${find}\:\lambda \\ $$$${I}\:{want}\:{to}\:{know}\:{what}\:{to}\:{study}…
Question Number 194591 by horsebrand11 last updated on 11/Jul/23 $$\:\:\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\:\underset{\mathrm{2x}^{\mathrm{2}} } {\overset{\mathrm{8}} {\int}}\:\:\underset{−\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}−\mathrm{x}^{\mathrm{2}} }} {\overset{\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}−\mathrm{x}^{\mathrm{2}} }} {\int}}\:\left(\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{3z}^{\mathrm{2}} }\:\right)\mathrm{dzdydx} \\ $$ Terms of…
Question Number 194586 by Shrinava last updated on 10/Jul/23 $$\mathrm{abc}\:=\:\mathrm{e}^{\mathrm{3}} \:+\:\mathrm{d}^{\mathrm{3}} \:+\:\mathrm{f}^{\mathrm{3}} \\ $$$$\mathrm{edf}\:=\:\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{c}^{\mathrm{3}} \\ $$$$\mathrm{find}:\:\mathrm{abc}\:\:\mathrm{and}\:\:\mathrm{edf}\: \\ $$ Commented by Shrinava last updated…
Question Number 194579 by MM42 last updated on 10/Jul/23 $${if}\:\:\:\:{u}_{{n}} =\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left[\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{{n}} −\left(\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{{n}} \right] \\ $$$$\:{then}\:\:\:{u}_{{n}+\mathrm{1}} ={u}_{{n}} +{u}_{{n}−\mathrm{1}} \:\:\:?\:\:\:\:\:;\:\:\:{n}=\mathrm{0},\mathrm{1},\mathrm{2},.. \\ $$ Answered by Frix last updated…