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Question Number 69229 by naka3546 last updated on 21/Sep/19 $${a},\:{b},\:{c}\:\:\in\:\:{nonnegative}\:\:{real}\:\:{numbers} \\ $$$$\sqrt{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:\mathrm{1}}\:+\:\sqrt{{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:+\:\mathrm{1}}\:+\:\sqrt{{c}^{\mathrm{2}} \:+\:{a}^{\mathrm{2}} \:+\:\mathrm{1}}\:\:\geqslant\:\:\mathrm{2}\:+\:\sqrt{\mathrm{2}\left({a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \right)\:+\:\mathrm{1}} \\ $$$${Find}\:\:{all}\:\:{triplets}\:\left({a},\:{b},\:{c}\right)\:\:{so}\:\:{that}\:\:{inequality}\:\:{above}\:\:{hold}\:. \\ $$…
Question Number 134752 by mathocean1 last updated on 06/Mar/21 $${In}\:{a}\:{locality},\:\mathrm{20\%}\:{of}\:{population}\:{have} \\ $$$${a}\:{chronic}\:{disease}.\:{Among}\:{these}\: \\ $$$${people}\:{who}\:{has}\:{a}\:{chronic}\:{disease},\:\mathrm{2}.\mathrm{5}\:\% \\ $$$${have}\:{COVID}−\mathrm{19}.\:{Among}\:{the}\:{people} \\ $$$${who}\:{don}'{t}\:{have}\:{a}\:{chronic}\:{disease},\:\mathrm{99\%} \\ $$$${have}\:{not}\:{COVID}−\mathrm{19}. \\ $$$$\boldsymbol{{C}}{alculate}\:{the}\:{probability}\:{that}\:{one}\:{person} \\ $$$${of}\:{this}\:{locality}\:{has}\:{COVID}−\mathrm{19}\:{and}\:{a} \\…
Question Number 134753 by mathocean1 last updated on 06/Mar/21 $${f}\:{is}\:{defined}\:{in}\:\left[\mathrm{0};\:+\infty\left[.\right.\right. \\ $$$$\begin{cases}{\:}\\{}\\{{f}\left(\mathrm{0}\right)={ln}\mathrm{2}}\end{cases}{f}\left({x}\right)=\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{e}^{−{t}} }{{t}}{dt}\:\:{for}\:{x}>\mathrm{0} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{Given}\:\mathrm{0}\leqslant{f}\left({x}\leqslant\frac{{e}^{−{x}} −{e}^{−\mathrm{2}{x}} }{{x}}.\right. \\ $$$${Calcule}\:{the}\:{lim}\:{f}\left({x}\right)\:{at}\:\mathrm{0}\:{and}\:+\infty. \\ $$$$\left.\mathrm{2}\right)\:{Calculate}\:{f}\:'\left({x}\right)\:,\:{give}\:{its}\:{variation}…
Question Number 134758 by rs4089 last updated on 07/Mar/21 Commented by rs4089 last updated on 07/Mar/21 $${prove}\:{it} \\ $$ Answered by mnjuly1970 last updated on…
Question Number 134751 by mathocean1 last updated on 06/Mar/21 $$\:{In}\:{my}\:{house},\:{there}\:{is}\:\mathrm{250}\:{laptops}:\: \\ $$$$\mathrm{40}\:{are}\:{new},\:\mathrm{100}\:{are}\:{recent}\:{and}\:{the}\: \\ $$$${others}\:{are}\:{old}.\:{A}\:{statistic}\:{showed}\:{that} \\ $$$$\mathrm{4\%}\:{of}\:{new}\:{laptops}\:{are}\:{faulty},\:\mathrm{12\%}\:{of} \\ $$$${recent}\:{ones}\:{are}\:{faulty}\:{and}\:\mathrm{25\%}\:{of}\:{old} \\ $$$${ones}\:{are}\:{faulty}. \\ $$$${Calculate}\:{the}\:{probability}\:{that}\:\mathrm{1}\:{laptop}\:{be} \\ $$$${new}\:,\:{knowing}\:{that}\:{it}\:{is}\:{faulty}. \\…
Question Number 134737 by CutieJanab last updated on 06/Mar/21 Answered by floor(10²Eta[1]) last updated on 07/Mar/21 $$\mathrm{if}\:\mathrm{g}=\mathrm{gcd}\left(\mathrm{a},\mathrm{b}\right)\Rightarrow\mathrm{g}\mid\mathrm{a},\:\mathrm{g}\mid\mathrm{b}\Rightarrow\mathrm{g}\mid\mathrm{ax}+\mathrm{by}\Rightarrow\mathrm{g}\mid\mathrm{d} \\ $$ Commented by CutieJanab last updated on…
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Question Number 134721 by 0731619177 last updated on 06/Mar/21 Commented by CutieJanab last updated on 06/Mar/21 $${i}\:{want}\:{to}\:{shre}\:{my}\:{queztion}\:{but}\:{i}\:{dont}\:{know}\:{how}\:{can}\:{i}\:{upload}\:{my}\:{wuestion}\:{cam}\:{you}\:{help}\:{me}… \\ $$ Commented by mr W last updated…