Question Number 187869 by BaliramKumar last updated on 23/Feb/23 $$\frac{\mathrm{41}!}{\mathrm{47}}\:{find}\:{remaider} \\ $$ Answered by Rasheed.Sindhi last updated on 23/Feb/23 $${According}\:{to}\:{Wilson}'{s}\:{theorem}: \\ $$$$\left(\mathrm{47}−\mathrm{1}\right)!\equiv−\mathrm{1}\left({mod}\:\mathrm{47}\right) \\ $$$$\mathrm{46}!\equiv−\mathrm{1}+\mathrm{47}\left({mod}\:\mathrm{47}\right) \\…
Question Number 56785 by Runzzy last updated on 23/Mar/19 Commented by tanmay.chaudhury50@gmail.com last updated on 24/Mar/19 $${rechek}\:{question} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 56763 by Tawa1 last updated on 23/Mar/19 $$\left(\mathrm{a}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{rectangle}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{inscribed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{circle}\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:\:=\:\:\mathrm{a}^{\mathrm{2}} \:. \\ $$$$ \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Name}\:\mathrm{the}\:\mathrm{rectangle}\:\mathrm{so}\:\mathrm{formed} \\ $$ Answered by kaivan.ahmadi last…
Question Number 56711 by Tawa1 last updated on 22/Mar/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{shotest}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{line} \\ $$$$\:\:\:\:\:\:\:\frac{\mathrm{x}\:−\:\mathrm{8}}{\mathrm{3}}\:=\:\frac{\mathrm{y}\:−\:\mathrm{2}}{\mathrm{4}}\:=\:\frac{\mathrm{z}\:+\:\mathrm{1}}{\mathrm{1}}\:,\:\:\:\:\:\:\:\frac{\mathrm{x}\:−\:\mathrm{3}}{\mathrm{3}}\:=\:\frac{\mathrm{y}\:+\:\mathrm{4}}{\mathrm{5}}\:=\:\frac{\mathrm{z}\:−\mathrm{2}}{\mathrm{2}} \\ $$ Answered by mr W last updated on 23/Mar/19 $${using}\:{vector}\:{method}: \\ $$$$…
Question Number 56597 by Tawa1 last updated on 19/Mar/19 Commented by Tawa1 last updated on 19/Mar/19 $$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{an}\:\mathrm{arithmetico}\:−\:\mathrm{geometric}\:\mathrm{series}, \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{infinity}.\:\:\: \\ $$$$\boldsymbol{\mathrm{Again}} \\ $$$$\:\:\:\:\mathrm{How}\:\mathrm{does}\:\mathrm{the}\:\mathrm{3x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{above}\:\mathrm{solution}\:\mathrm{disappear}. \\ $$$$\mathrm{From}\:\:\:\:\:\:\:\mathrm{3x}\:+\:\left(\mathrm{2x}^{\mathrm{2}}…
Question Number 56594 by Joel578 last updated on 19/Mar/19 $$\mathrm{Find}\:\mathrm{the}\:{n}\mathrm{th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence} \\ $$$$\left({a}\right)\:\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{1}}{\mathrm{4}},\:\frac{\mathrm{1}}{\mathrm{8}},\:\frac{\mathrm{7}}{\mathrm{62}},\:… \\ $$$$\left({b}\right)\:\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{1}}{\mathrm{4}},\:\frac{\mathrm{1}}{\mathrm{8}},\:\mathrm{0},\:… \\ $$ Answered by MJS last updated on 19/Mar/19 $$\mathrm{there}\:\mathrm{are}\:\mathrm{always}\:\infty\:\mathrm{possibilities} \\…
Question Number 187619 by BaliramKumar last updated on 19/Feb/23 $$\mathrm{32}^{\mathrm{32}^{\mathrm{32}} } \:\equiv\:{r}\:\left({mod}\:\:\:\mathrm{7}\right) \\ $$$${r}\:=\:? \\ $$ Answered by SEKRET last updated on 19/Feb/23 $$\left(\mathrm{32}\right)^{\mathrm{32}^{\mathrm{32}} }…
Question Number 122036 by physicstutes last updated on 13/Nov/20 $$\mathrm{Let}\:\:{f}\left({x}\right)\:=\:\left(\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\right)\:\mathrm{and}\:\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\left[{f}\left({x}\right)\right]^{{r}} \:\mathrm{be}\:\mathrm{a}\:\mathrm{convergent}\:\mathrm{series} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\right)^{{r}} \right]^{{n}} \:=\:\mathrm{4}\: \\ $$…
Question Number 187560 by Mingma last updated on 18/Feb/23 Answered by mr W last updated on 19/Feb/23 $${i}\:{think}\:{there}\:{is}\:{only}\:{one}\:{possibility}. \\ $$$${blue}\:{numbers}\:{show}\:{the}\:{order}\:{in}\:{which} \\ $$$${i}\:{determined}\:{the}\:{red}\:{numbers}. \\ $$$$\mathrm{62}/\mathrm{2}=\mathrm{31}\:\:\left(\mathrm{2}\right) \\…
Question Number 121949 by liberty last updated on 12/Nov/20 $$\:\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{sum}\:\:\frac{\mathrm{2}}{\mathrm{3}+\mathrm{1}}\:+\:\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{3}^{\mathrm{2}} +\mathrm{1}}\:+\:\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{3}^{\mathrm{4}} +\mathrm{1}}+\:…+\:\frac{\mathrm{2}^{\mathrm{n}+\mathrm{1}} }{\mathrm{3}^{\mathrm{2}^{\mathrm{n}} } \:+\mathrm{1}}\:. \\ $$ Answered by bobhans last updated on…