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Question Number 135230 by benjo_mathlover last updated on 11/Mar/21 $${A}\:{hockey}\:{team}\:{plays}\:{in}\:{an}\:{arena}\:{that} \\ $$$${has}\:{a}\:{seating}\:{capacity}\:{of}\:\mathrm{15},\mathrm{000} \\ $$$${spectators}.\:{With}\:{the}\:{ticket}\:{price} \\ $$$${seat}\:{at}\:\$\mathrm{14},\:{average}\:{attendance} \\ $$$${at}\:{recent}\:{games}\:{has}\:{been}\:\mathrm{9500}. \\ $$$${A}\:{market}\:{survey}\:{indicates}\:{that} \\ $$$${for}\:{each}\:{dollar}\:{the}\:{ticket}\:{price} \\ $$$${is}\:{lowered}\:,{the}\:{average}\:{attendance} \\…
Question Number 4156 by Yozzii last updated on 30/Dec/15 $${Let}\:{I}\left({n}\right)=\int_{\mathrm{0}} ^{{n}} \left\{\sqrt{{a}+{coshx}}−\sqrt{{a}+{sinhx}}\right\}{dx} \\ $$$${with}\:\mathrm{0}<{a}<\mathrm{1}\:{and}\:{define}\:{I}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}{I}\left({n}\right). \\ $$$${Does}\:{I}\:{exist}?\: \\ $$ Commented by 123456 last updated on…
Question Number 135223 by benjo_mathlover last updated on 11/Mar/21 $${Limit}\: \\ $$$$\left({a}\right)\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{tan}\:^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)\right)=? \\ $$$$\left({b}\right)\:\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{108}\left({x}^{\mathrm{2}} +\mathrm{2}{x}\right)\left({x}+\mathrm{1}\right)^{\mathrm{3}} }{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{1}\right)}=? \\ $$ Answered…
Question Number 135217 by benjo_mathlover last updated on 11/Mar/21 Commented by mr W last updated on 11/Mar/21 $${please}\:{explain}\:{what}\:{you}\:{mean}\:{with} \\ $$$$“{there}\:{is}\:{exactly}\:{only}\:{a}\:{circle}\:{that} \\ $$$${has}\:\mathrm{6}\:{girls}''! \\ $$$${when}\:{a}\:{circle}\:{has}\:{exactly}\:\mathrm{6}\:{girls}, \\…
Question Number 135216 by mohammad17 last updated on 11/Mar/21 $${lim}_{{x}\rightarrow\mathrm{3}^{+} } \frac{\left[{x}\right]^{\mathrm{2}} −\mathrm{9}}{{x}−\mathrm{3}} \\ $$ Answered by Olaf last updated on 11/Mar/21 $$\underset{{x}\rightarrow\mathrm{3}^{+} } {\mathrm{lim}}\:\frac{\left[{x}\right]^{\mathrm{2}}…
Question Number 69680 by 20190927 last updated on 26/Sep/19 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{sinx}} \:\:,\:\mathrm{0}<\mathrm{x}<\frac{\pi}{\mathrm{2}}\:\:\:\mathrm{find}\:\mathrm{f}'\left(\mathrm{x}\right) \\ $$ Answered by MJS last updated on 26/Sep/19 $$\frac{{d}}{{dx}}\left[{u}^{{v}} \right]={u}^{{v}} \left(\frac{{u}'{v}}{{u}}+{v}'\mathrm{ln}\:{u}\right) \\ $$$$\Rightarrow…
Question Number 135218 by benjo_mathlover last updated on 11/Mar/21 $$\mathrm{Permutation} \\ $$How many ways can 10 men and 7 women sit at a round table…
Question Number 69681 by ajfour last updated on 26/Sep/19 Commented by ajfour last updated on 26/Sep/19 $${Q}.\mathrm{69496}\:\:\:\left({A}\:{try}..\right) \\ $$ Commented by ajfour last updated on…
Question Number 135213 by mr W last updated on 11/Mar/21 Commented by mr W last updated on 11/Mar/21 $${if}\:{the}\:{truck}\:{can}\:{start}\:{with}\:{an} \\ $$$${acceleration}\:{a},\:{find}\:{the}\:{friction} \\ $$$${coefficient}\:{between}\:{tires}\:{and}\:{ground}. \\ $$…