Question Number 84770 by jagoll last updated on 16/Mar/20 $$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{30}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}}\:=\:\mathrm{2}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{x}\:\&\:\mathrm{y}\:? \\ $$ Commented by Tony Lin last updated on…
Question Number 84766 by jagoll last updated on 15/Mar/20 $$\int\:\frac{\mathrm{dx}}{\left(\mathrm{16}+\mathrm{9sin}\:\mathrm{x}\right)^{\mathrm{2}} } \\ $$$$ \\ $$ Commented by jagoll last updated on 16/Mar/20 $$\int\:\mathrm{sec}\:\:\mathrm{x}\:\left[\:\frac{\mathrm{cos}\:\:\mathrm{x}}{\left(\mathrm{16}+\mathrm{9sin}\:\mathrm{x}\right)^{\mathrm{2}} }\right]\:\mathrm{dx}\:= \\…
Question Number 84767 by naka3546 last updated on 16/Mar/20 $${Find}\:\:{all}\:\:{solutions}\:\:{of} \\ $$$$\:\:\:\:\:\:\:\mathrm{2020}{x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:\:=\:\:\mathrm{6059} \\ $$$${x},\:{y}\:<\:\:\mathrm{2020}\:\:,\:\:\:{x},\:{y}\:\:\in\:\:\mathbb{N} \\ $$ Answered by mr W last updated on…
Question Number 19230 by tawa tawa last updated on 07/Aug/17 Answered by ajfour last updated on 07/Aug/17 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)=\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{f}\left(\mathrm{x}\right)\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{f}\left(\mathrm{x}−\mathrm{2}\right)\sqrt[{\mathrm{3}}]{\mathrm{1}+…}}}}\: \\ $$$$\Rightarrow\:\left[\mathrm{g}\left(\mathrm{x}\right)\right]^{\mathrm{3}} =\mathrm{1}+\mathrm{f}\left(\mathrm{x}\right)\mathrm{g}\left(\mathrm{x}−\mathrm{1}\right) \\ $$$$\Rightarrow\:\mathrm{degree}\:\mathrm{of}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{1}. \\ $$$$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{Ax}+\mathrm{B}…
Question Number 150303 by mathdanisur last updated on 10/Aug/21 $$\mathrm{If}\:\:\:\mathrm{x};\mathrm{y};\mathrm{z}\in\left[\mathrm{0};\infty\right)\:\:\mathrm{then}: \\ $$$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} +\mathrm{2}^{\boldsymbol{\mathrm{y}}} +\mathrm{2}^{\boldsymbol{\mathrm{z}}} +\mathrm{2}^{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}} \:\geqslant\:\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{xy}}}} +\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{yz}}}} +\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{zx}}}} +\mathrm{1} \\ $$ Answered by aleks041103 last…
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Question Number 150299 by otchereabdullai@gmail.com last updated on 10/Aug/21 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{73}\:\mathrm{and}\:\mathrm{xy}=\mathrm{12}\:,\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} \\ $$ Answered by cherokeesay last updated on 10/Aug/21 $${x}^{\mathrm{2}} +{y}^{\mathrm{2}}…
Question Number 19223 by Tinkutara last updated on 07/Aug/17 $$\mathrm{A}\:\mathrm{particle}\:{P}\:\mathrm{is}\:\mathrm{sliding}\:\mathrm{down}\:\mathrm{a}\:\mathrm{frictionless} \\ $$$$\mathrm{hemispherical}\:\mathrm{bowl}.\:\mathrm{It}\:\mathrm{passes}\:\mathrm{the}\:\mathrm{point} \\ $$$${A}\:\mathrm{at}\:{t}\:=\:\mathrm{0}.\:\mathrm{At}\:\mathrm{this}\:\mathrm{instant}\:\mathrm{of}\:\mathrm{time},\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{component}\:\mathrm{of}\:\mathrm{its}\:\mathrm{velocity}\:\mathrm{is} \\ $$$${v}.\:\mathrm{A}\:\mathrm{bead}\:{Q}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{mass}\:\mathrm{as}\:{P}\:\mathrm{is} \\ $$$$\mathrm{ejected}\:\mathrm{from}\:{A}\:\mathrm{at}\:{t}\:=\:\mathrm{0}\:\mathrm{along}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{direction},\:\mathrm{with}\:\mathrm{the}\:\mathrm{speed}\:{v}. \\ $$$$\mathrm{Friction}\:\mathrm{between}\:\mathrm{the}\:\mathrm{bead}\:\mathrm{and}\:\mathrm{the} \\…
Question Number 84759 by mathmax by abdo last updated on 15/Mar/20 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by mind is power last updated…
Question Number 150289 by mathdanisur last updated on 10/Aug/21 $$\mathrm{If}\:\:\:_{\boldsymbol{\mathrm{n}}} \mathrm{C}_{\mathrm{3}} \:−\:_{\boldsymbol{\mathrm{n}}} \mathrm{C}_{\mathrm{2}} \:=\:\mathrm{14} \\ $$$$\mathrm{Find}\:\:\:_{\boldsymbol{\mathrm{n}}} \mathrm{P}_{\mathrm{2}} \:=\:? \\ $$ Answered by Ar Brandon last…