Question Number 16839 by arnabpapu550@gmail.com last updated on 27/Jun/17 $$\int\mathrm{x}^{\mathrm{e}^{\mathrm{x}} } \mathrm{dx} \\ $$ Commented by prakash jain last updated on 01/Jul/17 $$\mathrm{This}\:\mathrm{does}\:\mathrm{not}\:\mathrm{integrate}\:\mathrm{to}\:\mathrm{a}\:\mathrm{standard} \\ $$$$\mathrm{function}.…
Question Number 82375 by M±th+et£s last updated on 20/Feb/20 $${if}\:\:{x}+{y}=\mathrm{8}\:\:\:\:\:,,{x},{y}\in\mathbb{R}^{+} \\ $$$${prove}\:{that}\: \\ $$$$\left({x}+\frac{\mathrm{1}}{{y}}\right)^{\mathrm{2}} +\left({y}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} \geqslant\frac{\mathrm{289}}{\mathrm{8}} \\ $$ Answered by MJS last updated on 21/Feb/20…
Question Number 16836 by tawa tawa last updated on 26/Jun/17 $$\mathrm{Find}\:\mathrm{how}\:\mathrm{many}\:\mathrm{number}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{2},\mathrm{500}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\mathrm{the}\:\mathrm{digit} \\ $$$$\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4}\:\:\mathrm{if}\:\mathrm{no}\:\mathrm{digit}\:\mathrm{can}\:\mathrm{be}\:\mathrm{used}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once}. \\ $$ Answered by mrW1 last updated on 27/Jun/17 $$\mathrm{2}×\mathrm{4}×\mathrm{3}×\mathrm{2}=\mathrm{48} \\ $$…
Question Number 147905 by puissant last updated on 24/Jul/21 Answered by Olaf_Thorendsen last updated on 24/Jul/21 $${x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:=\:\mathrm{13} \\ $$$$\mathrm{2}{xdx}+\mathrm{2}{ydy}\:=\:\mathrm{0} \\ $$$${x}+{y}\frac{{dy}}{{dx}}\:=\:\mathrm{0} \\ $$$$\bullet\:\mathrm{En}\:\left(\mathrm{2},−\mathrm{3}\right)\::…
Question Number 16835 by tawa tawa last updated on 26/Jun/17 Answered by sandy_suhendra last updated on 27/Jun/17 $$\left.\mathrm{1}\right) \\ $$$$\mathrm{5C3}×\mathrm{5C3}×\mathrm{4C2} \\ $$$$=\:\mathrm{10}×\mathrm{10}×\mathrm{6} \\ $$$$=\:\mathrm{600}\:\mathrm{ways} \\…
Question Number 147904 by puissant last updated on 24/Jul/21 Answered by Olaf_Thorendsen last updated on 24/Jul/21 $$\mathrm{Il}\:\mathrm{y}\:\mathrm{a}\:\mathrm{6}\:\mathrm{valeurs}\:\mathrm{de}\:{x}\:\left({x}_{\mathrm{0}} \:\mathrm{a}\:{x}_{\mathrm{5}} \right),\:\mathrm{ce}\:\mathrm{qui} \\ $$$$\mathrm{definit}\:\mathrm{5}\:\mathrm{intervalles}\:\mathrm{qui}\:\mathrm{correspondent} \\ $$$$\mathrm{a}\:\mathrm{5}\:\mathrm{trapezes}. \\ $$$$\mathrm{Chaque}\:\mathrm{trapeze}\:{k}\:\mathrm{a}\:\mathrm{une}\:\mathrm{surface}\:\mathrm{egale}…
Question Number 16834 by sushmitak last updated on 26/Jun/17 $$\mathrm{If}\:\alpha<\beta<\gamma<\mathrm{2}\pi\:\mathrm{and} \\ $$$$\mathrm{cos}\:\left({x}+\alpha\right)+\mathrm{cos}\:\left({x}+\beta\right)+\mathrm{cos}\:\left({x}+\gamma\right)=\mathrm{0} \\ $$$$\mathrm{for}\:\mathrm{all}\:{x}\in\mathbb{R},\:\mathrm{then}\:\mathrm{is} \\ $$$$\gamma−\alpha=\frac{\mathrm{2}\pi}{\mathrm{3}}? \\ $$ Commented by ajfour last updated on 27/Jun/17…
Question Number 147906 by Odhiambojr last updated on 24/Jul/21 $$\mathrm{4}\:{bad}\:{apples}\:{are}\:{mixed}\:{accidentally} \\ $$$${with}\:\mathrm{20}\:{good}\:{apples}.\:{Obtain}\:{the} \\ $$$$\:{probability}\:{distribution}\:{of}\:{the}\: \\ $$$${numbers}\:{of}\:{bad}\:{apples}\:{in}\:{a}\:{draw}\:{of}\: \\ $$$$\mathrm{2}\:{apples}\:{at}\:{random} \\ $$ Answered by Olaf_Thorendsen last updated…
Question Number 16829 by tawa tawa last updated on 26/Jun/17 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$\mathrm{6}\left(\mathrm{4}^{\mathrm{x}} \:+\:\mathrm{9}^{\mathrm{x}} \right)\:=\:\left(\mathrm{13}.\mathrm{6}\right)^{\mathrm{x}} \\ $$ Commented by mrW1 last updated on 26/Jun/17 $$\mathrm{please}\:\mathrm{check}\:\mathrm{the}\:\mathrm{question}.…
Question Number 82365 by M±th+et£s last updated on 20/Feb/20 Commented by mr W last updated on 21/Feb/20 $${a}_{{n}} =\mathrm{1}+\frac{\mathrm{3}\left({n}−\mathrm{1}\right){n}}{\mathrm{2}} \\ $$ Commented by mr W…