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Question Number 14811 by Nayon last updated on 04/Jun/17 $${why}\:\:\:\:\:\sqrt{{x}^{\mathrm{2}} }=\mid{x}\mid\:\:\:\:?\: \\ $$ Answered by mrW1 last updated on 04/Jun/17 $${if}\:{x}\geqslant\mathrm{0},\:\sqrt{{x}^{\mathrm{2}} }={x}=\mid{x}\mid \\ $$$${if}\:{x}<\mathrm{0},\:\sqrt{{x}^{\mathrm{2}} }=\sqrt{\left(−{x}\right)^{\mathrm{2}}…
Question Number 80347 by jagoll last updated on 02/Feb/20 $${let}\:{x}\:{and}\:{y}\:{be}\:{positif}\:{real}\:{number} \\ $$$${such}\:{that}\:\mathrm{1}\leqslant{x}+{y}\leqslant\mathrm{9}\:{and} \\ $$$${x}\leqslant\mathrm{2}{y}\leqslant\mathrm{3}{x}.\:{what}\:{is}\:{the}\: \\ $$$${largest}\:{value}\:{of}\:\:\:\frac{\mathrm{9}−{y}}{\mathrm{9}−{x}} \\ $$$$ \\ $$ Commented by john santu last…
Question Number 145879 by mathdanisur last updated on 09/Jul/21 Answered by mr W last updated on 09/Jul/21 $${let}\:{u}={f}\left({f}\left({x}\right)\right) \\ $$$${f}\left({u}\right)\leqslant\mathrm{0} \\ $$$$\Rightarrow\frac{\mathrm{1}−{u}}{\mathrm{1}+{u}^{\mathrm{2}} }\leqslant\mathrm{0} \\ $$$$\Rightarrow\mathrm{1}−{u}\leqslant\mathrm{0}…
Question Number 145852 by mathdanisur last updated on 08/Jul/21 $${sin}\frac{\pi}{\mathrm{24}}\centerdot{cos}\frac{\pi}{\mathrm{24}}\centerdot{cos}\frac{\pi}{\mathrm{12}}=? \\ $$ Answered by waiphyoemaung last updated on 08/Jul/21 $$\mathrm{solution} \\ $$$$\mathrm{sin}\frac{\pi}{\mathrm{24}}.\mathrm{cos}\frac{\pi}{\mathrm{24}}.\mathrm{cos}\frac{\pi}{\mathrm{12}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}.\left(\mathrm{2sin}\frac{\pi}{\mathrm{24}}\mathrm{cos}\frac{\pi}{\mathrm{24}}\right)\mathrm{cos}\frac{\pi}{\mathrm{12}} \\…
Question Number 145856 by mathdanisur last updated on 08/Jul/21 Commented by mr W last updated on 08/Jul/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(…\right){dv}={C}={constant} \\ $$$${f}\left({x}\right)=\frac{{d}}{{dx}}\left({C}\right)=\mathrm{0} \\ $$$${f}'\left({x}\right)=\mathrm{0} \\…
Question Number 145851 by mathdanisur last updated on 08/Jul/21 $${if}\:\:\underset{{x}\rightarrow\infty} {{lim}}\frac{\left({a}-\mathrm{3}\right){x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} +{cx}+\mathrm{4}}{{bx}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{7}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${find}\:\:{a}+{b}=? \\ $$ Answered by Olaf_Thorendsen last updated on 08/Jul/21…
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Question Number 80306 by Power last updated on 02/Feb/20 Commented by mr W last updated on 02/Feb/20 $${use}\:{your}\:{calculator}\:{and}\:{you}\:{will}\:{get} \\ $$$${something}\:{like}\:\mathrm{0}.\mathrm{71828}….\:{which}\:{is} \\ $$$${nearly}\:{equal}\:{to}\:{e}−\mathrm{2},\:{but}\:{only}\:{nearly}. \\ $$ Terms…
Question Number 14775 by tawa tawa last updated on 04/Jun/17 $$\mathrm{Using}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{factorize}\:\mathrm{completely}\:\mathrm{the}\:\mathrm{expression}\: \\ $$$$\mathrm{x}^{\mathrm{3}} \left(\mathrm{y}\:−\:\mathrm{z}\right)\:+\:\mathrm{y}^{\mathrm{3}} \left(\mathrm{z}\:−\:\mathrm{x}\right)\:+\:\mathrm{z}^{\mathrm{3}} \left(\mathrm{x}\:−\:\mathrm{y}\right)\: \\ $$ Answered by ajfour last updated on 04/Jun/17…