Question Number 203527 by Mastermind last updated on 21/Jan/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} \mathrm{z}^{\mathrm{2}} \:\mathrm{subject}\:\mathrm{to}\:\mathrm{the}\:\mathrm{condition}\:\mathrm{that} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{c}^{\mathrm{2}} ,\:\mathrm{where}\:\mathrm{c}\:\mathrm{is}\:\mathrm{the}\:\mathrm{constant}. \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{in}\:\mathrm{advance}…
Question Number 203554 by Mastermind last updated on 21/Jan/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203480 by mr W last updated on 20/Jan/24 Commented by mr W last updated on 20/Jan/24 $${is}\:{it}\:{possible}\:{that}\:{the}\:{red}\:{lines}\:{divide} \\ $$$${the}\:{square}\:{into}\:\mathrm{4}\:{parts}\:{with}\:{given}\: \\ $$$${areas}?\:{if}\:{yes},\:{find}\:{the}\:{length}\:{of}\:{the} \\ $$$${red}\:{lines}.…
Question Number 203508 by Fridunatjan08 last updated on 20/Jan/24 $${Evaluate}\:{the}\:{given}\:{limit}: \\ $$$$\underset{{n}\rightarrow\infty} {{lim}}\frac{\sqrt[{{n}}]{\mathrm{8}}−\mathrm{1}}{\:\sqrt[{{n}}]{\mathrm{16}}−\mathrm{1}} \\ $$ Answered by esmaeil last updated on 20/Jan/24 $$={Y} \\ $$$$\frac{\mathrm{1}}{{n}}={p}\rightarrow\left({n}\rightarrow\infty\rightarrow{p}\rightarrow\mathrm{0}\right)…
Question Number 203509 by Fridunatjan08 last updated on 20/Jan/24 $${Find}\:{the}\:{value}\:{of}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\frac{\mathrm{2}^{{n}} +\mathrm{1}}{\mathrm{2}^{{n}} −\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203474 by ajfour last updated on 20/Jan/24 $$\frac{{z}^{\mathrm{4}} +\mathrm{4}{z}^{\mathrm{3}} −\mathrm{6}{z}^{\mathrm{2}} −\mathrm{4}{z}+\mathrm{1}}{{z}^{\mathrm{4}} −\mathrm{4}{z}^{\mathrm{3}} −\mathrm{6}{z}^{\mathrm{2}} +\mathrm{4}{z}+\mathrm{1}}=\frac{{z}+\mathrm{1}}{{z}−\mathrm{1}} \\ $$$${Find}\:{z}\in\mathbb{R}. \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 203502 by Frix last updated on 20/Jan/24 $${z}\mathrm{e}^{{z}} =\mathrm{e} \\ $$$$\mathrm{Obviously}\:{z}=\mathrm{1} \\ $$$$\mathrm{Now}\:\mathrm{find}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{solution}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$ Commented by Frix last updated on 22/Jan/24 $$\mathrm{See}\:\mathrm{question}\:\mathrm{203570}…
Question Number 203497 by ajfour last updated on 20/Jan/24 $${x}^{\mathrm{4}} +{cx}+{d}=\mathrm{0} \\ $$$${then}\:\:{find}\:{p}\:\:{from} \\ $$$${p}^{\mathrm{6}} −\mathrm{4}\left(\frac{{d}^{\:\mathrm{3}} }{{c}^{\mathrm{4}} }\right)^{\mathrm{1}/\mathrm{3}} {p}^{\mathrm{2}} −\mathrm{1}=\mathrm{0} \\ $$$${x}=\frac{{c}^{\mathrm{1}/\mathrm{3}} }{\mathrm{2}}\left({p}\pm\sqrt{−{p}^{\mathrm{2}} −\frac{\mathrm{8}}{{p}}}\:\right) \\…
Question Number 203498 by ajfour last updated on 20/Jan/24 $$\frac{{d}^{\mathrm{3}\:} {y}}{{dx}^{\mathrm{3}} }=\mathrm{4}\left({x}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}} −\mathrm{4}{y} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203490 by cortano12 last updated on 20/Jan/24 $$\:\:\:\:\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}×\mathrm{9}×…×\mathrm{2005}\:=\:…\:\left(\mathrm{mod}\:\mathrm{1000}\right) \\ $$ Answered by AST last updated on 20/Jan/24 $${x}=\mathrm{1}×\mathrm{3}×\mathrm{5}…×\mathrm{2005}\equiv\mathrm{0}\left({mod}\:\mathrm{125}\right) \\ $$$${x}\equiv\left(\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}\right)^{\mathrm{250}} ×\mathrm{1}×\mathrm{3}×\mathrm{5}\left({mod}\:\mathrm{8}\right)\equiv\mathrm{7}\left({mod}\:\mathrm{8}\right) \\ $$$${x}=\mathrm{125}{q}\equiv\mathrm{7}\left({mod}\:\mathrm{8}\right)\Rightarrow\mathrm{5}{q}\equiv\mathrm{15}\left({mod}\:\mathrm{8}\right)\Rightarrow{q}\equiv\mathrm{3}\left({mod}\:\mathrm{8}\right)…