Question Number 127127 by mr W last updated on 27/Dec/20 Commented by mr W last updated on 27/Dec/20 $${This}\:{question}\:{was}\:{once}\:{asked}. \\ $$$$ \\ $$$${Find}\:{the}\:{radius}\:{of}\:{circle}\:{in}\:{terms}\:{of} \\ $$$${parameters}\:{a}\:{and}\:{b}\:{of}\:{the}\:{ellipse}.…
Question Number 192663 by Mingma last updated on 24/May/23 Answered by cherokeesay last updated on 24/May/23 Commented by Mingma last updated on 25/May/23 Perfect �� Terms…
Question Number 192652 by beto last updated on 24/May/23 $${lim}_{{x}\rightarrow\mathrm{0}} \frac{\mathrm{1}−\sqrt{{cos}\left({x}\right)}}{\mathrm{1}+{cos}\left(\sqrt{{x}}\right)} \\ $$ Answered by MM42 last updated on 24/May/23 $$\mathrm{0} \\ $$ Answered by…
Question Number 127119 by liberty last updated on 27/Dec/20 $${The}\:{barometric}\:{pressure}\:{p}\:{at}\:{an}\:{altitude} \\ $$$${of}\:{h}\:{miles}\:{above}\:{sea}\:{level}\:{satisfies}\:{the} \\ $$$${differential}\:{equation}\:\frac{{dp}}{{dh}}\:=\:−\mathrm{0}.\mathrm{2}{p}\:. \\ $$$${If}\:{the}\:{pressure}\:{at}\:{sea}\:{level}\:{is}\:\mathrm{29}.\mathrm{92}\:{inches} \\ $$$${of}\:{mercury},\:{find}\:{the}\:{barometric}\: \\ $$$${preassure}\:{at}\:\mathrm{17},\mathrm{000}\:{ft}\: \\ $$$$\left({A}\right)\:\mathrm{56}.\mathrm{97}\:{in}\:\:\:\:\:\:\left({B}\right)\:\mathrm{15}.\mathrm{71}\:{in} \\ $$$$\left({C}\right)\:\mathrm{7}.\mathrm{86}\:{in}\:\:\:\:\:\:\:\:\:\:\left({D}\right)\:\mathrm{1}\:{in} \\…
Question Number 127116 by physicstutes last updated on 27/Dec/20 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{sequence}\:\left({u}_{{n}} \right)\:\mathrm{defined}\:\mathrm{reculsively}\:\mathrm{by} \\ $$$$\:{u}_{{n}+\mathrm{1}} \:=\:\mathrm{3}{u}_{{n}} +\:\mathrm{4}{u}_{{n}−\mathrm{1}} ,\:\:{u}_{\mathrm{0}} =\:\mathrm{1}\:,\:{u}_{\mathrm{2}} \:=\:\mathrm{3} \\ $$$$\:\mathrm{show}\:\mathrm{that}\:\:{u}_{{n}+\mathrm{1}} −\mathrm{4}{u}_{{n}} \:=\:\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \left(\mathrm{3}{u}_{\mathrm{0}} −\mathrm{4}{u}_{\mathrm{1}} \right)…
Question Number 192648 by pascal889 last updated on 24/May/23 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\right) \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{1} \\ $$ Answered by Skabetix last updated on…
Question Number 192651 by beto last updated on 24/May/23 $$ \\ $$$${lim}_{{x}\rightarrow\mathrm{0}} \frac{\mathrm{2}−\sqrt{{cos}\left({x}\right)}−{cos}\left({x}\right)}{{x}^{\mathrm{2}} } \\ $$ Answered by cortano12 last updated on 24/May/23 $$\:\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}−\sqrt{\mathrm{cos}\:\mathrm{x}}\right)+\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}}…
Question Number 192650 by beto last updated on 24/May/23 $$ \\ $$$$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} \frac{{x}−{sen}\left({x}\right)}{{tan}^{\mathrm{3}} \left({x}\right)} \\ $$$${without}\:{lhopital}\:{rule} \\ $$ Answered by MM42 last updated on 24/May/23…
Question Number 127110 by benjo_mathlover last updated on 26/Dec/20 $$\:\:\int\:\left(\mathrm{arcsin}\:{x}\right)^{\mathrm{2}} \:{dx}\:=? \\ $$ Answered by liberty last updated on 27/Dec/20 $$\:{letting}\:\mathrm{arcsin}\:{x}\:=\:\ell\:\Rightarrow{x}\:=\:\mathrm{sin}\:\ell\:\wedge\:{dx}\:=\:\mathrm{cos}\:\ell\:{d}\ell \\ $$$${I}=\:\int\:\ell^{\mathrm{2}} \mathrm{cos}\:\ell\:{d}\ell\:=\:\ell^{\mathrm{2}} \mathrm{sin}\:\ell\:+\mathrm{2}\ell\:\mathrm{cos}\:\ell−\mathrm{2sin}\:\ell\:+\:{c}…
Question Number 127111 by benjo_mathlover last updated on 26/Dec/20 $$\:{find}\:{the}\:{value}\:{of}\:{x}\:{such}\:{that}\: \\ $$$$\:\begin{cases}{{x}=\mathrm{2}\:\left({mod}\:\mathrm{5}\right)}\\{{x}=\mathrm{3}\:\left({mod}\:\mathrm{8}\right)\:}\\{{x}=\mathrm{2}\:\left({mod}\:\mathrm{3}\right)}\end{cases} \\ $$ Answered by liberty last updated on 04/Jan/21 $${given}\:\begin{cases}{{x}=\mathrm{2}\:\left({mod}\:\mathrm{5}\right)…\left({i}\right)}\\{{x}=\mathrm{3}\:\left({mod}\:\mathrm{8}\right)…\left({ii}\right)}\\{{x}=\mathrm{2}\:\left({mod}\:\mathrm{3}\right)…\left({iii}\right)}\end{cases} \\ $$$${for}\left({i}\right)\:\Rightarrow\:\mathrm{24}{a}\:\equiv\:\mathrm{2}\:\left({mod}\:\mathrm{5}\right)\: \\…