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…
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…
Question Number 150277 by mathdanisur last updated on 10/Aug/21 $$\mathrm{Laplace}\:\mathrm{Metodu}\:\left(\mathrm{solution}\right) \\ $$$$\mathrm{y}^{''} \:+\:\mathrm{5y}^{'} \:+\:\mathrm{6y}\:=\:\mathrm{cos}\left(\mathrm{t}\right) \\ $$$$\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$ Commented by amin96 last updated on…
Question Number 19215 by Tinkutara last updated on 07/Aug/17 $$\mathrm{STATEMENT}-\mathrm{1}\::\:\mathrm{For}\:\mathrm{every}\:\mathrm{natural} \\ $$$$\mathrm{number}\:{n}\:\geqslant\:\mathrm{2},\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:+\:…..\:\frac{\mathrm{1}}{\:\sqrt{{n}}}\:>\:\sqrt{{n}} \\ $$$$\boldsymbol{\mathrm{and}} \\ $$$$\mathrm{STATEMENT}-\mathrm{2}\::\:\mathrm{For}\:\mathrm{every}\:\mathrm{natural} \\ $$$$\mathrm{number}\:{n}\:\geqslant\:\mathrm{2},\:\sqrt{{n}\left({n}\:+\:\mathrm{1}\right)}\:<\:{n}\:+\:\mathrm{1} \\ $$ Answered by 433 last updated…
Question Number 19204 by malwaan last updated on 06/Aug/17 $$\mathrm{If}\:\mathrm{L}=\begin{bmatrix}{\mathrm{1}\:\:\mathrm{0}\:\:\mathrm{0}}\\{\mathrm{3}\:\:\mathrm{1}\:\:\mathrm{0}}\\{\mathrm{2}\:\:\mathrm{4}\:\:\mathrm{1}}\end{bmatrix}\mathrm{and}\:\mathrm{B}=\begin{bmatrix}{\mathrm{3}}\\{\mathrm{2}}\\{\mathrm{1}}\end{bmatrix} \\ $$$$\mathrm{x}_{\mathrm{1}} =−\mathrm{2}\:;\:\mathrm{x}_{\mathrm{2}} =\mathrm{1}\:;\:\mathrm{x}_{\mathrm{3}} =\mathrm{5} \\ $$$$\mathrm{find}\:\mathrm{U} \\ $$$$\left(\mathrm{numerical}\:\mathrm{analysis}\right) \\ $$$$ \\ $$ Commented by…
Question Number 19198 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{integer}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{system}: \\ $$$$\mathrm{35}{x}\:+\:\mathrm{63}{y}\:+\:\mathrm{45}{z}\:=\:\mathrm{1},\:\mid{x}\mid\:<\:\mathrm{9},\:\mid{y}\mid\:<\:\mathrm{5}, \\ $$$$\mid{z}\mid\:<\:\mathrm{7}. \\ $$ Commented by mrW1 last updated on 09/Aug/17 $$\left(−\mathrm{10},\mathrm{2},\mathrm{5}\right) \\…
Question Number 84728 by mr W last updated on 15/Mar/20 $${y}={x}\left[{x}\left[{x}\right]\right]\:{with}\:{x}\in{R}^{+} \\ $$$${find}\:{the}\:{range}\:{of}\:{function} \\ $$$${and}\:{solve}\:{x}\left[{x}\left[{x}\right]\right]=\mathrm{150}. \\ $$ Commented by MJS last updated on 16/Mar/20 Commented…
Question Number 150259 by mathdanisur last updated on 10/Aug/21 $$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{e}^{−\boldsymbol{\mathrm{st}}} \left(\mathrm{cosh}\left(\mathrm{2t}\right)−\mathrm{cosh}\left(\mathrm{5t}\right)\right)\mathrm{dt}}{\mathrm{t}}=? \\ $$ Answered by Ar Brandon last updated on 10/Aug/21 $${I}\left({s}\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 84711 by M±th+et£s last updated on 15/Mar/20 Commented by mr W last updated on 15/Mar/20 $${x}\lceil{x}\left[{x}\right]\rceil=\mathrm{35}\:\Rightarrow\:{no}\:{solution}! \\ $$$$ \\ $$$${x}\left[{x}\left[{x}\right]\right]=\mathrm{35}\:\Rightarrow\:{solution}\:{x}=\mathrm{3}.\mathrm{5} \\ $$ Commented…
Question Number 150247 by mathdanisur last updated on 10/Aug/21 $$\underset{\:\mathrm{2}} {\overset{\:\mathrm{6}} {\int}}\:\left(\mathrm{x}-\mathrm{1}\right)\left(\mathrm{x}-\mathrm{2}\right)\left(\mathrm{x}-\mathrm{3}\right)…\left(\mathrm{x}-\mathrm{9}\right)\:\mathrm{dx}\:=\:? \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{1}\left.\:\left.\:\:\:\:\mathrm{b}\right)\mathrm{0}\:\:\:\:\:\mathrm{c}\right)\mathrm{6}!\:\:\:\:\:\mathrm{d}\right)-\mathrm{2}\:\:\:\:\mathrm{e}\right)\mathrm{4}! \\ $$ Commented by amin96 last updated on 10/Aug/21 $$\int_{\mathrm{2}} ^{\mathrm{6}}…