Question Number 56075 by Kunal12588 last updated on 10/Mar/19 $${Prove}\:{that}\:{If}\:{a}\:{set}\:{consist}\:{of}\:{n}\:{number}\:{of} \\ $$$${terms}\:{then}\:{its}\:{Power}\:{Set}\:{would}\:{contain} \\ $$$$\mathrm{2}^{{n}} \:{number}\:{of}\:{terms}. \\ $$$$\left[{Use}\:{formulas}\:{of}\:{sequence}\:{and}\:{series}\right] \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 121612 by Khalmohmmad last updated on 10/Nov/20 Commented by MJS_new last updated on 10/Nov/20 $$\mathrm{the}\:\mathrm{problem}\:\mathrm{why}\:\mathrm{you}\:\mathrm{got}\:\mathrm{no}\:\mathrm{answer}\:\mathrm{might} \\ $$$$\mathrm{be}\:\mathrm{that}\:\mathrm{nobody}\:\mathrm{knows}\:\mathrm{what}\:“\mathrm{the}\:\left({a}_{\mathrm{4}} =?\right)'' \\ $$$$\mathrm{means}.\:\mathrm{your}\:\mathrm{question}\:\mathrm{is}\:\mathrm{like}\:\mathrm{this}\:\mathrm{one}: \\ $$$${the}\:{ship}\:{is}\:\mathrm{25}{m}\:{long}.\:{how}\:{old}\:{is}\:{Peter}? \\…
Question Number 121608 by naka3546 last updated on 10/Nov/20 $$\left(\mathrm{6}^{\mathrm{2020}} \:+\:\mathrm{8}^{\mathrm{2020}} \right)\:{mod}\:\mathrm{49}\:\:? \\ $$$${Show}\:\:{your}\:\:{elegant}\:\:{workings}\:,\:{please}. \\ $$$${Thanks}\:\:{a}\:{lot}. \\ $$ Answered by mr W last updated on…
Question Number 56074 by Kunal12588 last updated on 10/Mar/19 $${In}\:{a}\:{sequence}\:{if}\:{r}^{{th}} \:{term}\:{is}\:{given}\:{by} \\ $$$${T}_{{r}} =\mathrm{2}×{T}_{{r}−\mathrm{1}} +\mathrm{1} \\ $$$${then}\:{give}\:{it}'{s}\:{n}^{{th}} \:{term}\:{in}\:{terms}\:{of}\:\:{it}'{s}\:\mathrm{1}^{{st}} \:{term} \\ $$$$\left[{Given}\::\:\:\:\:\:{T}_{\mathrm{1}} =\mathrm{2}\right] \\ $$ Commented…
Question Number 56053 by naka3546 last updated on 09/Mar/19 $$\underset{\mathrm{0}} {\int}\overset{\mathrm{1}} {\:}\:\:\frac{{x}^{\mathrm{17}} \:−\:\mathrm{1}}{{x}^{\mathrm{19}} \:−\:\mathrm{1}}\:\:{dx}\:\:=\:\:? \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 10/Mar/19 Terms of…
Question Number 121587 by Maclaurin Stickker last updated on 09/Nov/20 Commented by Maclaurin Stickker last updated on 09/Nov/20 $${O}_{\mathrm{2}} ,\:{O}_{\mathrm{1}} \:{and}\:{O}\:{are}\:{centers}\:{of}\:{circles}.\: \\ $$$${B}\:{and}\:{O}_{\mathrm{2}} \:{are}\:{tangency}\:{points}. \\…
Question Number 56051 by naka3546 last updated on 09/Mar/19 Answered by mr W last updated on 09/Mar/19 Commented by mr W last updated on 10/Mar/19…
Question Number 121585 by Algoritm last updated on 09/Nov/20 Commented by Algoritm last updated on 09/Nov/20 $$\boldsymbol{\mathrm{answer}}:\:\boldsymbol{\mathrm{x}}=\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{3} \\ $$ Commented by MJS_new last updated on…
Question Number 187091 by Humble last updated on 13/Feb/23 $$ \\ $$$$\lfloor{x}^{\mathrm{2}} \rfloor\:\:−\:\:\lfloor{x}\rfloor^{\mathrm{2}} \:=\mathrm{100} \\ $$$${x}\in\mathbb{R} \\ $$$${min}\left({x}\right)=? \\ $$ Answered by MJS_new last updated…
Question Number 187088 by mustafazaheen last updated on 13/Feb/23 $$\mathrm{prove}\:\mathrm{to}\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{0}}{\mathrm{0}}=\mathrm{2} \\ $$ Commented by Frix last updated on 13/Feb/23 $$\frac{\mathrm{0}}{\mathrm{0}}\:\mathrm{is}\:\mathrm{not}\:\mathrm{defined}\:\Rightarrow\:\mathrm{no}\:\mathrm{proof}\:\mathrm{possible}. \\ $$$${f}\left({r}\right)=\mathrm{0}\wedge{g}\left({r}\right)=\mathrm{0}:\:\underset{{x}\rightarrow{r}} {\mathrm{lim}}\:\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}\:={L} \\ $$$${L}\:\mathrm{can}\:\mathrm{be}\:\mathrm{undefined}\:\mathrm{or}\:\mathrm{have}\:\mathrm{any}\:\mathrm{value}…