Question Number 64726 by aliesam last updated on 20/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 130257 by pete last updated on 23/Jan/21 $${n}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer} \\ $$$$\mathrm{prove}\:\mathrm{algebraically}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{n}\left({n}+\mathrm{1}\right)\:\mathrm{and}\:\frac{\mathrm{1}}{\mathrm{2}}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\:\mathrm{is}\:\mathrm{always} \\ $$$$\mathrm{a}\:\mathrm{square}\:\mathrm{number}. \\ $$$$\mathrm{note}:\:{write}\:{your}\:{expression}\:{in}\:{a}\:{form} \\ $$$${that}\:{clearly}\:{shows}\:{a}\:{square}\:{number}. \\ $$ Commented by Dwaipayan…
Question Number 130254 by Eric002 last updated on 23/Jan/21 $${prove} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{ln}^{\mathrm{2}} \left({x}\right){ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\mathrm{7}\pi}{\mathrm{4}}\zeta\left(\mathrm{3}\right)+\frac{\pi^{\mathrm{3}} {ln}\left(\mathrm{2}\right)}{\mathrm{4}} \\ $$$${where}\:\zeta\left(\mathrm{3}\right)\:{is}\:{a}\:{pery}^{\:,} {s}\:{constant} \\ $$ Answered by…
Question Number 130255 by stelor last updated on 23/Jan/21 $$\mathrm{please}\:\:….\:\mathrm{I}\:\mathrm{am}\:\mathrm{confiouse}….\:\:\:\mathrm{1}\:\mathrm{and}\:\mathrm{2}. \\ $$$$\mathrm{1}.\:\:\:\:\:\:\:\int\mid{x}\mid\mathrm{d}{x}\:=\:?\:? \\ $$$$\mathrm{2}.\:\:\:\:\:\mathrm{with}\:\left(\mathrm{F}\left({x}\right)\right)^{'} \:=\mathrm{f}\left({x}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\mid\mathrm{f}\left({x}\right)\mid{dx}\:=\:?? \\ $$$$ \\ $$ Answered by Olaf last updated on…
Question Number 130244 by Adel last updated on 23/Jan/21 Commented by mr W last updated on 23/Jan/21 $${it}'{s}\:{not}\:{to}\:{understand}:\:{this}\:{question} \\ $$$${is}\:{asked}\:{already}\:{four}\:{times},\:{three} \\ $$$${times}\:{alone}\:{from}\:{you}!\:{what}'{s}\:{the} \\ $$$${sense}?\:{if}\:{you}\:{don}'{t}\:{understand}\:{the} \\…
Question Number 64709 by ajfour last updated on 20/Jul/19 Commented by ajfour last updated on 20/Jul/19 $${If}\:{regions}\:{A}\:{and}\:{B}\:{have}\:{the}\:{same} \\ $$$${area},\:{and}\:{both}\:{parabolas}\:{have} \\ $$$${the}\:{same}\:{shape}\:{but}\:{their}\:{axis}\:\bot\:{to} \\ $$$${each}\:{other},\:{then}\:{determine} \\ $$$${the}\:{equation}\:{of}\:{the}\:{red}\:{parabola}.…
Question Number 130245 by mohammad17 last updated on 23/Jan/21 Commented by mohammad17 last updated on 23/Jan/21 $${please}\:{sir}\:{can}\:{help}\:{me}\:{now}\:{i}\:{want}\:{this}? \\ $$ Answered by PRITHWISH SEN 2 last…
Question Number 130242 by Raxreedoroid last updated on 23/Jan/21 $$\mathrm{Find}\:\:\:{m} \\ $$$${n}=\left({p}_{\mathrm{1}} {p}_{\mathrm{2}} \right)^{{m}} \\ $$$$\mathrm{2}{n}=\left({p}_{\mathrm{1}} ^{\mathrm{1}+{log}_{{p}_{\mathrm{1}} {p}_{\mathrm{2}} } {n}} \right)\left({p}_{\mathrm{2}} ^{\mathrm{1}+{log}_{{p}_{\mathrm{1}} {p}_{\mathrm{2}} } {n}}…
Question Number 130241 by mr W last updated on 23/Jan/21 Commented by mr W last updated on 23/Jan/21 $${three}\:{circles}\:{with}\:{radii}\:{p},\:{q},\:{r}\:{have} \\ $$$${the}\:{same}\:{center}.\:\left({p}<{q}<{r}\right) \\ $$$${what}\:{is}\:{the}\:{side}\:{length}\:{of}\:{the}\:{smallest} \\ $$$${and}\:{the}\:{largest}\:{square}\:{which}\:{has}…
Question Number 64702 by Tanmay chaudhury last updated on 20/Jul/19 Answered by Tanmay chaudhury last updated on 20/Jul/19 $${abstaining}={a}\:\:\:\:{voting}={v}\:\: \\ $$$${a}=\mathrm{1}+{v}=\mathrm{7} \\ $$$${a}=\mathrm{2}+{v}=\mathrm{6} \\ $$$$……