Question Number 98770 by bemath last updated on 16/Jun/20 Commented by bemath last updated on 16/Jun/20 $$\mathrm{the}\:\mathrm{choice}\:\mathrm{answer}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{12}\:\:\:\:\:\:\left(\mathrm{b}\right)\mathrm{13}\:\:\:\:\:\left(\mathrm{c}\right)\mathrm{14} \\ $$$$\left(\mathrm{d}\right)\mathrm{15}\:\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{16} \\ $$ Commented by…
Question Number 164299 by mr W last updated on 15/Jan/22 $${if}\:\underset{{n}\:{times}} {{f}\left({f}\left({f}\left(…{f}\left({x}\right)…\right)\right)\right)}=\mathrm{2}{x}+\mathrm{1},\: \\ $$$${find}\:{f}\left(\mathrm{1}\right)=? \\ $$ Answered by ajfour last updated on 16/Jan/22 $${y}_{\mathrm{1}} ={ax}+{b}…
Question Number 98761 by bemath last updated on 16/Jun/20 $$\sqrt{\mathrm{x}+\sqrt{\mathrm{x}}\:}\:−\sqrt{\mathrm{x}−\sqrt{\mathrm{x}}}\:=\:\mathrm{m}\sqrt{\frac{\mathrm{x}}{\mathrm{x}+\sqrt{\mathrm{x}}}} \\ $$$$\mathrm{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{parameter} \\ $$ Commented by MJS last updated on 16/Jun/20 $$\mathrm{if}\:{x}\in\mathbb{R} \\ $$$$\Rightarrow\:{x}>\mathrm{0}\wedge{x}−\sqrt{{x}}\geqslant\mathrm{0}\:\Rightarrow\:{x}\geqslant\mathrm{1} \\…
Question Number 164290 by HongKing last updated on 15/Jan/22 Answered by Kamel last updated on 16/Jan/22 $$ \\ $$$$\left.\Omega\left.\left({n}\right)=\int_{\mathrm{0}} ^{\pi} {cot}\left(\frac{{x}}{\mathrm{2}}\right){Arctan}\left(\frac{{nsin}\left({x}\right)}{\mathrm{1}+{ncos}\left({x}\right)}\right){dx};\:{u}=\frac{{n}−\mathrm{1}}{{n}+\mathrm{1}},\:{n}\in\right]−\mathrm{1};\mathrm{1}\right]. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{1}}{{t}\left(\mathrm{1}+{t}^{\mathrm{2}}…
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Question Number 164269 by Zaynal last updated on 15/Jan/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{Solve}}\:\boldsymbol{{the}}\:\boldsymbol{{inequality}}; \\ $$$$\:\:\left(\boldsymbol{{x}}+\mathrm{3}\right)\left[\left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{2}} −\boldsymbol{{x}}\left(\boldsymbol{{x}}+\frac{\mathrm{3}}{\mathrm{4}}\right)\right]+\mathrm{6}+\frac{\mathrm{7}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{29}\boldsymbol{{x}}}{\mathrm{4}}>\mathrm{0} \\ $$$$\left\{\boldsymbol{{Z}}.\boldsymbol{{A}}\right\} \\ $$ Answered by manxsolar last updated on 15/Jan/22…
Question Number 33200 by pieroo last updated on 12/Apr/18 $$\mathrm{Solve}\:\mathrm{2}^{\mathrm{3n}+\mathrm{2}} \:−\mathrm{7}×\mathrm{2}^{\mathrm{2n}+\mathrm{2}} \:−\mathrm{31}×\mathrm{2}^{\mathrm{n}} \:−\mathrm{8}=\mathrm{0},\:\mathrm{n}\in\boldsymbol{\mathrm{R}}. \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{some}\:\mathrm{help}\:\mathrm{with}\:\mathrm{this} \\ $$ Answered by MJS last updated on 12/Apr/18 $$\mathrm{2}^{\mathrm{3}{n}+\mathrm{2}}…
Question Number 33193 by SammyKT last updated on 12/Apr/18 $$\mathrm{Q}.\:\:\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} −\mathrm{3}{x}−\mathrm{1}=\mathrm{0}, \\ $$$$\:\:\:\:\:\:\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{other}\:\mathrm{roots}\:\mathrm{are} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{2}−\alpha^{\mathrm{2}} \:\mathrm{and}\:\alpha^{\mathrm{2}} −\alpha−\mathrm{2}. \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Please}\:\mathrm{help}. \\ $$ Answered by…
Question Number 33186 by NECx last updated on 12/Apr/18 $${Find}\:{the}\:{exact}\:{value}\:{of}\:{sin}\theta\:{if} \\ $$$${cos}\theta=\frac{\mathrm{1}}{\mathrm{57}}\:{and}\:\theta\:{is}\:{obtuse} \\ $$ Answered by MJS last updated on 12/Apr/18 $$\mathrm{cos}^{\mathrm{2}} \theta+\mathrm{sin}^{\mathrm{2}} \theta=\mathrm{1} \\…