Question Number 87533 by mr W last updated on 04/Apr/20 Commented by MJS last updated on 05/Apr/20 $${a}=\frac{\mathrm{49}}{\mathrm{76}}\pm\frac{\mathrm{457}\sqrt{\mathrm{87}}}{\mathrm{6612}} \\ $$$${b}=\frac{\mathrm{49}}{\mathrm{76}}\mp\frac{\mathrm{457}\sqrt{\mathrm{87}}}{\mathrm{6612}} \\ $$$${x}=−\mathrm{7}\pm\sqrt{\mathrm{87}} \\ $$$${y}=−\mathrm{7}\mp\sqrt{\mathrm{87}} \\…
Question Number 87530 by mathmax by abdo last updated on 04/Apr/20 $$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{e}^{−{n}\left[{x}\right]} {sin}\left(\frac{\pi{x}}{{n}}\right){dx}\:\:{nnatural}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right){determine}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by mathmax by abdo…
Question Number 21994 by Tinkutara last updated on 08/Oct/17 $$\mathrm{Suppose}\:{N}\:\mathrm{is}\:\mathrm{an}\:{n}-\mathrm{digit}\:\mathrm{positive} \\ $$$$\mathrm{integer}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{all}\:\mathrm{the}\:{n}-\mathrm{digits}\:\mathrm{are}\:\mathrm{distinct};\:\mathrm{and} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{any}\:\mathrm{three}\:\mathrm{consecutive} \\ $$$$\mathrm{digits}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:{n}\:\mathrm{is}\:\mathrm{at}\:\mathrm{most}\:\mathrm{6}.\:\mathrm{Further}, \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{starting}\:\mathrm{with}\:\mathrm{any}\:\mathrm{digit}\:\mathrm{one} \\ $$$$\mathrm{can}\:\mathrm{find}\:\mathrm{a}\:\mathrm{six}-\mathrm{digit}\:\mathrm{number}\:\mathrm{with}\:\mathrm{these} \\…
Question Number 87526 by mathmax by abdo last updated on 04/Apr/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left[{nx}\right]} \:{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 87527 by mathmax by abdo last updated on 04/Apr/20 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{3}{x}\right)}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 21990 by hi147 last updated on 08/Oct/17 $${i}\:{still}\:{search}\:{about}\:{a}\:{general}\:{and}\: \\ $$$${complete}\:{solution}\:{about}\:{this} \\ $$$${determine}\:{x}\:{in}\:{N}\:{where}\:\mathrm{7}\:{divise}\:\mathrm{2}^{{x}} +\mathrm{3}^{{x}} \\ $$$${note}\:=\:{it}\:{is}\:{just}\:{an}\:{exercise}\:{in}\:{secondary} \\ $$$${so}\:{dont}\:{go}\:{away}… \\ $$$${maybe}\:{we}\:{must}\:{use}\:{separation}\:{of}\:{cases} \\ $$$${methode}…. \\ $$…
Question Number 153063 by talminator2856791 last updated on 04/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\: \\ $$$$\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:\:{dx} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{is}\:\mathrm{unsolvable} \\ $$$$\:…
Question Number 153057 by DELETED last updated on 04/Sep/21 Answered by DELETED last updated on 04/Sep/21 $$\mathrm{i}_{\mathrm{1}} +\mathrm{i}_{\mathrm{2}} =\mathrm{i}_{\mathrm{3}} \:…..\left(\mathrm{1}\right) \\ $$$$\Sigma\mathrm{E}+\Sigma\mathrm{i}.\mathrm{R}=\mathrm{0}\:\:\mathrm{hk}\:\mathrm{kirchoff}\:\mathrm{II} \\ $$$$\mathrm{loop}\:\mathrm{1}\:\left(\mathrm{searah}\:\mathrm{jarum}\:\mathrm{jam}\right) \\…
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