Question Number 201681 by jabarsing last updated on 10/Dec/23 $${f}\left({x}+\mathrm{1}\right)−{f}\left({x}\right)=\mathrm{3}{f}\left({x}\right)×{f}\left({x}+\mathrm{1}\right) \\ $$$${D}_{{f}} ={N} \\ $$$$\mathrm{2023}×{f}\left(\mathrm{1402}\right)=\mathrm{1} \\ $$$${have}\:{equation}\:{f}\left({x}\right)=\mathrm{1}\:{solution}? \\ $$ Answered by Frix last updated on…
Question Number 201683 by aurpeyz last updated on 10/Dec/23 $${Starting}\:{from}\:{substituting}\:{z}={x}+{iy}.\:{Identify} \\ $$$${the}\:{maximal}\:{region}\:{within}\:{which}\:{f}\left({z}\right)\:{is}\:{analytic} \\ $$$${f}\left({z}\right)=\frac{\mathrm{1}}{{z}\left({z}+\mathrm{1}\right)}.\: \\ $$$$ \\ $$$${Note}.\:{Do}\:{not}\:{start}\:{by}\:{just}\:{differentiating}\:{f}\left({z}\right).\: \\ $$$${Start}\:{by}\:\:{doing}\:{a}\:{substitution}\:{of}\:{x}\:{and}\:{iy}\:{and}\: \\ $$$${then}\:{verify}\:{Cauchy}\:{Rieman}\:{theorem}. \\ $$$$ \\…
Question Number 201679 by cherokeesay last updated on 10/Dec/23 Answered by Rasheed.Sindhi last updated on 10/Dec/23 $$\sqrt[{\mathrm{6}}]{\mathrm{1}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:+\sqrt[{\mathrm{6}}]{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:−\mathrm{1}}\:=\mathrm{1} \\ $$$${a}+{b}=\mathrm{1}\Rightarrow{b}=\mathrm{1}−{a} \\ $$$${a}^{\mathrm{6}} +{b}^{\mathrm{6}} =\mathrm{1}−\sqrt{{x}^{\mathrm{2}}…
Question Number 201629 by ali009 last updated on 09/Dec/23 Commented by ali009 last updated on 09/Dec/23 $${how}\:{is}\:{that}\:{cslculated}? \\ $$ Commented by aleks041103 last updated on…
Question Number 201631 by professorleiciano last updated on 09/Dec/23 Answered by mr W last updated on 10/Dec/23 $${totally}\:{number}\:{of}\:{words}:\:\mathrm{6}!=\mathrm{720} \\ $$$$ \\ $$$${number}\:{of}\:{words}\:{in}\:{which}\:\mathrm{3}\:{vowels} \\ $$$${are}\:{together}:\:\mathrm{4}!\mathrm{3}!=\mathrm{144} \\…
Question Number 201599 by mr W last updated on 09/Dec/23 Commented by AST last updated on 09/Dec/23 $${Are}\:{those}\:{numbers}\:{areas}\:{or}\:{lengths}? \\ $$ Commented by mr W last…
Question Number 201561 by Mingma last updated on 09/Dec/23 Answered by ajfour last updated on 11/Dec/23 Commented by ajfour last updated on 11/Dec/23 $$\mathrm{2}\theta+\mathrm{2}\phi=\frac{\pi}{\mathrm{2}} \\…
Question Number 201562 by Mingma last updated on 09/Dec/23 Answered by mr W last updated on 09/Dec/23 $${r}={radius}\:{of}\:{quarter}\:{circle} \\ $$$${a}={side}\:{length}\:{of}\:{square} \\ $$ Commented by mr…
Question Number 201627 by professorleiciano last updated on 09/Dec/23 Answered by mr W last updated on 10/Dec/23 $${for}\:\mathrm{200}\:{meals}\:\mathrm{6}\:{cooks}\:{each}\:{working}\: \\ $$$$\mathrm{6}\:{hours}\:{are}\:{needed},\:{i}.{e}.\:{totally} \\ $$$$\mathrm{36}\:{working}\:{hours}\:{are}\:{needed}\:{for}\: \\ $$$$\mathrm{200}\:{meals}. \\…
Question Number 201595 by mokys last updated on 09/Dec/23 $$\left.\mathrm{1}\right)\:\:\mid\frac{\mathrm{3}+\mathrm{2}{x}}{\mathrm{3}{x}}\mid\:\leq\mathrm{1} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\mathrm{1}\leq\:\mid\:\frac{{x}−\mathrm{3}}{\mathrm{1}−\mathrm{2}{x}}\mid\leq\:\mathrm{2} \\ $$$$ \\ $$$$\left.\mathrm{3}\right)\:\frac{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{35}}{{x}+\mathrm{2}}\:>\:\mathrm{0} \\ $$$$ \\ $$$$\left.\mathrm{4}\right)\:−\mathrm{1}\:\leq\:\frac{{x}+\mathrm{1}}{{x}−\mathrm{2}}\:\leq\mathrm{2} \\ $$…