Question Number 210574 by ChantalYah last updated on 13/Aug/24 $${if}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$${x}^{\mathrm{2}} +\left({k}+\mathrm{1}\right){x}+{k}=\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta, \\ $$$$\:{find}\:{the}\:{value}\:{of}\:{the} \\ $$$$\:{real}\:{constant}\:{k}\:{for} \\ $$$${which}\:\alpha=\mathrm{2}\beta \\ $$ Answered by…
Question Number 210607 by peter frank last updated on 13/Aug/24 Answered by A5T last updated on 14/Aug/24 $$\mathrm{75}\left(\mathrm{5}^{\mathrm{3}{log}_{\mathrm{2}} {x}} \right)=\mathrm{75}\left(\mathrm{2}^{{log}_{\mathrm{2}} \mathrm{5}} \right)^{{log}_{\mathrm{2}} {x}×\mathrm{3}} =\mathrm{75}\left(\mathrm{2}^{{log}_{\mathrm{2}} {x}}…
Question Number 210601 by mnjuly1970 last updated on 13/Aug/24 $$ \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:{Find}\:\:{the}\:\:{value}\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\sqrt{\:{x}^{\:\mathrm{2}} \:+{y}^{\:\mathrm{2}} }}…
Question Number 210593 by efronzo1 last updated on 13/Aug/24 $$\:\:\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}{\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{2x}}\:+\:\sqrt{\mathrm{cos}\:\mathrm{2x}}}\:\mathrm{dx}\:=? \\ $$$$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{sec}\:\mathrm{x}\:\sqrt[{\mathrm{2}}]{\mathrm{sin}\:\mathrm{x}}\:+\:\mathrm{cos}\:\mathrm{x}\:\sqrt[{\mathrm{3}}]{\mathrm{cosec}\:^{\mathrm{5}} \mathrm{x}}}\:=? \\ $$ Answered by Sutrisno last updated on 30/Aug/24 $${misal} \\ $$$${cos}\mathrm{2}{x}={y}^{\mathrm{6}}…
Question Number 210559 by mathlove last updated on 12/Aug/24 $${deg}\:\left[{p}\left({x}^{\mathrm{2}} \right)\centerdot{q}\left({x}\right)\right]=\mathrm{20} \\ $$$${deg}\left[\frac{{p}\left({x}\right)^{\mathrm{3}} }{{q}\left({x}\right)^{\mathrm{2}} }\right]=\mathrm{2} \\ $$$${then}\:{deg}\:\:{q}\left({x}\right)=? \\ $$ Answered by mr W last updated…
Question Number 210554 by Batmath last updated on 12/Aug/24 Answered by MrGaster last updated on 02/Nov/24 $$\int_{\mathrm{0}} ^{\infty} \left[\frac{\mathrm{1}}{\mathrm{2}}−{S}\left({px}\right)\right]{x}^{\mathrm{2}{q}−\mathrm{1}} {dx}=\int_{\mathrm{0}} ^{\infty} \left[\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\left({tpx}\right)}{{t}}{dt}\right]{x}^{\mathrm{2}{q}−\mathrm{1}} {dx}…
Question Number 210549 by universe last updated on 12/Aug/24 $$\mathrm{let}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{be}\:\mathrm{difined}\:\mathrm{as} \\ $$$$\:\mathrm{a}_{\mathrm{n}} =\:\mathrm{a}_{\mathrm{n}−\mathrm{1}} \:+\:\frac{\mathrm{2cos}\:\left(\frac{\mathrm{a}_{\mathrm{n}−\mathrm{1}} }{\mathrm{2}}\right)}{\mathrm{2sin}\:\left(\frac{\mathrm{a}_{\mathrm{n}−\mathrm{1}} }{\mathrm{2}}\right)−\mathrm{1}}\:\:,\:\mathrm{a}_{\mathrm{0}\:} =\:\mathrm{0} \\ $$$$\mathrm{find}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{a}_{\mathrm{n}\:} \:=\:? \\ $$ Answered by…
Question Number 210572 by Spillover last updated on 12/Aug/24 Answered by mathmax last updated on 13/Aug/24 $${I}=\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{4}} }{dx}\:\:{changement}\:{x}={t}^{\frac{\mathrm{1}}{\mathrm{4}}} {give} \\ $$$${I}=\frac{\mathrm{1}}{\mathrm{16}}\int_{\mathrm{0}} ^{\infty}…
Question Number 210573 by Spillover last updated on 12/Aug/24 Answered by mathmax last updated on 13/Aug/24 $$\mathrm{2}{I}=\int_{−\infty} ^{+\infty} \frac{{dx}}{{x}^{\mathrm{4}} +{ix}^{\mathrm{2}} +\mathrm{2}}\:\left({fonction}\:{paire}\right) \\ $$$${roots}\:\:\:\:\:\:{x}^{\mathrm{2}} ={t}\rightarrow{t}^{\mathrm{2}} +{it}+\mathrm{2}…
Question Number 210542 by SANOGO last updated on 12/Aug/24 Commented by Rasheed.Sindhi last updated on 12/Aug/24 $${x}+{y}+{z}=\mathrm{1}\Rightarrow\left({x}+{y}+{z}\right)^{\mathrm{2}} =\mathrm{1} \\ $$ Commented by Frix last updated…