Question Number 221955 by Nicholas666 last updated on 13/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{ln}\left(\mathrm{sin}\:\left({x}\right)\right.}{{x}}\right)\:\mathrm{d}{x} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221919 by fantastic last updated on 12/Jun/25 $${Acable}\:{can}\:{stand}\:{a}\:{maximum}\:{weight}\:{of}\:\mathrm{25kg}\: \\ $$$${If}\:{the}\:{length}\:{of}\:{wire}\:{is}\:{halved}\:{what}\:{is}\:{the} \\ $$$${maximum}\:{weight}\:{thsn}\:{can}\:{be}\:{hung}\:{from}\:{it}?? \\ $$ Commented by mr W last updated on 12/Jun/25 $$\sim\:\mathrm{50}\:{kg}…
Question Number 221913 by Tawa11 last updated on 12/Jun/25 A man standing 10m away from a plane mirror moves towards the mirror with a speed…
Question Number 221882 by MrGaster last updated on 12/Jun/25 $$\mathrm{Prove}:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{sin}\:{x}\:{K}^{\mathrm{2}} \:\mathrm{sin}\:{x}\:{dx}=\frac{\pi^{\mathrm{4}} }{\mathrm{16}}\:_{\mathrm{7}} {F}_{\mathrm{6}} \left(\frac{\mathrm{1}}{\:\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{5}}{\mathrm{4}};\mathrm{1},\mathrm{1},\mathrm{1},\mathrm{1},\mathrm{1},\frac{\mathrm{1}}{\mathrm{4}};\mathrm{1}\right) \\ $$ Answered by wewji12 last updated on 12/Jun/25…
Question Number 221907 by alvan545 last updated on 12/Jun/25 Answered by fantastic last updated on 12/Jun/25 Commented by fantastic last updated on 12/Jun/25 $${CD}^{\mathrm{2}} ={CN}×{CF}…
Question Number 221902 by alvan545 last updated on 12/Jun/25 Answered by mahdipoor last updated on 12/Jun/25 $${x}−\mathrm{5}={u}\:\:\:\:\:\:\:{dx}={du} \\ $$$${x}=\mathrm{10}\equiv{u}=\mathrm{5}\:\:\:\:\:\:{x}=\mathrm{0}\equiv{u}−\mathrm{5} \\ $$$$\left.\int_{−\mathrm{5}} ^{\:\mathrm{5}} \left({u}+{u}^{\mathrm{2}} +{u}^{\mathrm{3}} \right){du}=\frac{{u}^{\mathrm{2}}…
Question Number 221896 by fantastic last updated on 12/Jun/25 $${If}\:\mathrm{log}\underset{\mathrm{10}} {\:}\mathrm{7}={a}\:,{then}\:\mathrm{log}\underset{\mathrm{10}} {\:}\left(\frac{\mathrm{1}}{\mathrm{70}}\right)=? \\ $$ Answered by fantastic last updated on 12/Jun/25 $$\mathrm{log}\underset{\mathrm{10}} {\:}\mathrm{7}={a} \\ $$$$\:{so}\:\mathrm{10}^{{a}}…
Question Number 221899 by universe last updated on 12/Jun/25 $$\:\:\:{let}\:{a}\in\left[\mathrm{0},\mathrm{1}\right]\:{find}\:{all}\:{continuous}\:{function} \\ $$$$\:\:\:\:\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\left[\mathrm{0},\infty\right)\:{such}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx}\:=\:\mathrm{1}\:\:, \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {xf}\left({x}\right){dx}\:=\:{a}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} {f}\left({x}\right){dx}\:=\:{a}^{\mathrm{2}} \\ $$$$\:\:\:\:{how}\:{many}\:{such}\:{function}\:{are}\:{there}\:? \\ $$$$…
Question Number 221853 by fantastic last updated on 11/Jun/25 $${find}\:{x}\:{where} \\ $$$$\mathrm{log}\underset{\mathrm{8}} {\:}{x}−\mathrm{log}\underset{\mathrm{4}} {\:}{x}−\mathrm{log}\underset{\mathrm{2}} {\:}{x}=\mathrm{11} \\ $$ Commented by Tawa11 last updated on 11/Jun/25 $$\mathrm{log}_{\mathrm{2}^{\mathrm{3}}…
Question Number 221848 by ajfour last updated on 11/Jun/25 Commented by ajfour last updated on 11/Jun/25 Commented by ajfour last updated on 11/Jun/25 Terms of…