Question Number 226554 by Spillover last updated on 03/Dec/25 Answered by peace2 last updated on 03/Dec/25 $$=\frac{\mathrm{1}}{{n}}\int\frac{{nx}^{{n}−\mathrm{1}} {dx}}{{x}^{{n}} \left(\mathrm{1}+{x}^{{n}} \right)}=\frac{\mathrm{1}}{{n}}\int\frac{{dy}}{{y}\left(\mathrm{1}+{y}\right)}=\frac{\mathrm{1}}{{n}}\int\frac{\mathrm{1}}{{y}}−\frac{\mathrm{1}}{\mathrm{1}+{y}}{dy} \\ $$$$=\frac{\mathrm{1}}{{n}}{ln}\left(\frac{{y}}{\mathrm{1}+{y}}\right)+\mathrm{c};{y}={x}^{{n}} \\ $$ Answered…
Question Number 226550 by gregori last updated on 03/Dec/25 $$\:\:\:\: {a}+{b}+{c}\:=\:{x}\: \\ $$$$\:\:\:\: \underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} }{{abc}}\:=? \\ $$ Answered by peace2 last updated…
Question Number 226524 by wongb1506 last updated on 02/Dec/25 Answered by som(math1967) last updated on 02/Dec/25 $$\:\alpha=\mathrm{3}{x}\:\:\beta=\mathrm{2}{x} \\ $$$$\mathrm{5}{x}=\mathrm{90}\Rightarrow{x}=\mathrm{18}=\alpha−\beta \\ $$$$\:\:\left({D}\right) \\ $$ Terms of…
Question Number 226525 by wongb1506 last updated on 02/Dec/25 Answered by som(math1967) last updated on 02/Dec/25 $${AF}=\sqrt{\mathrm{160}}\:,{AE}=\sqrt{\mathrm{180}}\:,\:{EF}=\sqrt{\mathrm{100}} \\ $$$${Cosx}=\frac{\mathrm{160}+\mathrm{180}−\mathrm{100}}{\mathrm{2}×\sqrt{\mathrm{180}×\mathrm{160}}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$$\:{x}=\mathrm{45}° \\ $$ Answered by…
Question Number 226526 by wongb1506 last updated on 02/Dec/25 Answered by som(math1967) last updated on 02/Dec/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 226536 by hardmath last updated on 02/Dec/25 $$\mathrm{If}\:\:\:\left(\mathrm{x}+\left(\mathrm{2a}^{\mathrm{2}} +\mathrm{5}\right)\right)\left(\mathrm{x}−\left(\mathrm{2a}^{\mathrm{2}} +\mathrm{7}\right)\right)\:\leqslant\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\mathrm{x}\in\left[−\left(\mathrm{a}^{\mathrm{2}} +\mathrm{8a}−\mathrm{10}\right)\:;\:\left(\mathrm{a}^{\mathrm{2}} +\mathrm{9a}−\mathrm{11}\right)\right] \\ $$$$\mathrm{Find}:\:\boldsymbol{\mathrm{a}}\:=\:? \\ $$ Answered by gregori last updated…
Question Number 226538 by mr W last updated on 02/Dec/25 Answered by mr W last updated on 07/Dec/25 $${length}\:{of}\:{cylinder}\:={L} \\ $$$${cross}−{section}\:=\mathrm{2}{RL} \\ $$$${at}\:{speed}\:{v} \\ $$$${Mv}=\left({M}+\mathrm{2}{RLnmvdt}\right)\left({v}+{dv}\right)…
Question Number 226533 by mr W last updated on 02/Dec/25 Answered by mr W last updated on 03/Dec/25 $${cube}\:{roots}\:{of}\:{unit}:\:\mathrm{1},\:\omega,\:\omega^{\mathrm{2}} \\ $$$$\mathrm{1}+\omega+\omega^{\mathrm{2}} =\mathrm{0} \\ $$$${e}^{{x}} =\underset{{n}=\mathrm{0}}…
Question Number 226534 by ajfour last updated on 02/Dec/25 Commented by ajfour last updated on 02/Dec/25 $${If}\:{AB}=\mathrm{2}\theta,\:{find}\:{everything}! \\ $$ Commented by mr W last updated…
Question Number 226509 by hardmath last updated on 01/Dec/25 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}\centerdot\left(\mathrm{2n}\:+\:\mathrm{1}\right)^{\mathrm{2}} }\:=\:? \\ $$ Answered by mr W last updated on 01/Dec/25 $$\frac{\mathrm{1}}{{n}\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{{A}}{{n}}+\frac{{B}}{\mathrm{2}{n}+\mathrm{1}}+\frac{{C}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}}…