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y-t-g-sin-y-t-0-L-s-y-t-g-L-s-sin-y-t-0-0-y-t-e-st-dt-g-0-sin-y-t-e-st-dt-0-0-y-t-g-y-t-y-t-3-3-y-t-5-5-e

Question Number 201740 by MathedUp last updated on 12/Dec/23 $${y}''\left({t}\right)+\frac{\mathrm{g}}{\ell}\centerdot\mathrm{sin}\left({y}\left({t}\right)\right)=\mathrm{0} \\ $$$$\boldsymbol{\mathcal{L}}_{{s}} \left\{{y}''\left({t}\right)\right\}+\frac{\mathrm{g}}{\ell}\boldsymbol{\mathcal{L}}_{{s}} \left\{\mathrm{sin}\left({y}\left({t}\right)\right)\right\}=\mathrm{0} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} {y}''\left({t}\right){e}^{−{st}} \mathrm{d}{t}+\frac{\mathrm{g}}{\ell}\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{sin}\left({y}\left({t}\right)\right){e}^{−{st}} \mathrm{d}{t}=\mathrm{0} \\ $$$$\int_{\mathrm{0}} ^{\:\infty}…

Question-201654

Question Number 201654 by mokys last updated on 10/Dec/23 Answered by aleks041103 last updated on 10/Dec/23 $${First}\:{part}: \\ $$$${M}=\begin{pmatrix}{\mathrm{4}}&{\mathrm{3}}\\{\mathrm{1}}&{−\mathrm{2}}\end{pmatrix}\: \\ $$$${eigenvals}: \\ $$$${det}\left({M}−{xI}\right)=\begin{vmatrix}{\mathrm{4}−{x}}&{\mathrm{3}}\\{\mathrm{1}}&{−\mathrm{2}−{x}}\end{vmatrix}=\mathrm{0} \\ $$$$\Rightarrow\left({x}−\mathrm{4}\right)\left({x}+\mathrm{2}\right)−\mathrm{3}=\mathrm{0}…

Starting-from-substituting-z-x-iy-Identify-the-maximal-region-within-which-f-z-is-analytic-f-z-1-z-z-1-Note-Do-not-start-by-just-differentiating-f-z-Start-by-doing-a-substitution-of-x-

Question Number 201683 by aurpeyz last updated on 10/Dec/23 $${Starting}\:{from}\:{substituting}\:{z}={x}+{iy}.\:{Identify} \\ $$$${the}\:{maximal}\:{region}\:{within}\:{which}\:{f}\left({z}\right)\:{is}\:{analytic} \\ $$$${f}\left({z}\right)=\frac{\mathrm{1}}{{z}\left({z}+\mathrm{1}\right)}.\: \\ $$$$ \\ $$$${Note}.\:{Do}\:{not}\:{start}\:{by}\:{just}\:{differentiating}\:{f}\left({z}\right).\: \\ $$$${Start}\:{by}\:\:{doing}\:{a}\:{substitution}\:{of}\:{x}\:{and}\:{iy}\:{and}\: \\ $$$${then}\:{verify}\:{Cauchy}\:{Rieman}\:{theorem}. \\ $$$$ \\…

Question-201631

Question Number 201631 by professorleiciano last updated on 09/Dec/23 Answered by mr W last updated on 10/Dec/23 $${totally}\:{number}\:{of}\:{words}:\:\mathrm{6}!=\mathrm{720} \\ $$$$ \\ $$$${number}\:{of}\:{words}\:{in}\:{which}\:\mathrm{3}\:{vowels} \\ $$$${are}\:{together}:\:\mathrm{4}!\mathrm{3}!=\mathrm{144} \\…

Question-201627

Question Number 201627 by professorleiciano last updated on 09/Dec/23 Answered by mr W last updated on 10/Dec/23 $${for}\:\mathrm{200}\:{meals}\:\mathrm{6}\:{cooks}\:{each}\:{working}\: \\ $$$$\mathrm{6}\:{hours}\:{are}\:{needed},\:{i}.{e}.\:{totally} \\ $$$$\mathrm{36}\:{working}\:{hours}\:{are}\:{needed}\:{for}\: \\ $$$$\mathrm{200}\:{meals}. \\…

1-3-2x-3x-1-2-1-x-3-1-2x-2-3-x-2-2x-35-x-2-gt-0-4-1-x-1-x-2-2-

Question Number 201595 by mokys last updated on 09/Dec/23 $$\left.\mathrm{1}\right)\:\:\mid\frac{\mathrm{3}+\mathrm{2}{x}}{\mathrm{3}{x}}\mid\:\leq\mathrm{1} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\mathrm{1}\leq\:\mid\:\frac{{x}−\mathrm{3}}{\mathrm{1}−\mathrm{2}{x}}\mid\leq\:\mathrm{2} \\ $$$$ \\ $$$$\left.\mathrm{3}\right)\:\frac{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{35}}{{x}+\mathrm{2}}\:>\:\mathrm{0} \\ $$$$ \\ $$$$\left.\mathrm{4}\right)\:−\mathrm{1}\:\leq\:\frac{{x}+\mathrm{1}}{{x}−\mathrm{2}}\:\leq\mathrm{2} \\ $$…