Question Number 44034 by Dilshad786 last updated on 20/Sep/18 $$\mathrm{Let}\:\:{I}_{\mathrm{1}} =\:\underset{\:\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx}\:\mathrm{and}\:{I}_{\mathrm{2}} =\:\underset{\:\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\frac{\mathrm{1}}{{x}}\:{dx}. \\ $$$$\mathrm{Then} \\ $$ Commented by maxmathsup by…
Question Number 109485 by ZiYangLee last updated on 24/Aug/20 $$\mathrm{If}\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c},\:{g}\left({x}\right)=\:−{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$$\mathrm{where}\:{ac}\:\neq\:\mathrm{0},\:\mathrm{then}\:{f}\left({x}\right){g}\left({x}\right)=\mathrm{0}\:\mathrm{has} \\ $$ Answered by ajfour last updated on 24/Aug/20 $${f}\left({x}\right){g}\left({x}\right)={h}\left({x}\right)=\left({bx}+{c}\right)^{\mathrm{2}} −{a}^{\mathrm{2}}…
Question Number 43787 by kkr1729 last updated on 15/Sep/18 $$\mathrm{The}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{not} \\ $$$$\mathrm{more}\:\mathrm{than}\:\mathrm{20}\:\mathrm{digits}\:\mathrm{that}\:\mathrm{are}\:\mathrm{formed} \\ $$$$\mathrm{by}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\:\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:\mathrm{3}\:\mathrm{and}\:\mathrm{4}\:\mathrm{is} \\ $$ Answered by MrW3 last updated on 17/Sep/18 $${let}\:{number}\:{of}\:{numbers}\:{with}\:{n}\:{digits}={S}\left({n}\right) \\…
Question Number 43767 by peter frank last updated on 15/Sep/18 $$\mathrm{The}\:\mathrm{chance}\:\mathrm{of}\:\mathrm{an}\:\mathrm{event}\:\mathrm{happening}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{square}\:\mathrm{of}\:\mathrm{the}\:\mathrm{chance}\:\mathrm{of}\:\mathrm{a}\:\mathrm{second}\:\mathrm{event} \\ $$$$\mathrm{but}\:\mathrm{the}\:\mathrm{odds}\:\mathrm{against}\:\mathrm{the}\:\mathrm{first}\:\mathrm{are}\:\mathrm{the} \\ $$$$\mathrm{cube}\:\mathrm{of}\:\mathrm{the}\:\mathrm{odds}\:\mathrm{against}\:\mathrm{the}\:\mathrm{second}.\:\mathrm{The} \\ $$$$\mathrm{chances}\:\mathrm{of}\:\mathrm{the}\:\mathrm{events}\:\mathrm{are} \\ $$ Terms of Service Privacy…
Question Number 43766 by peter frank last updated on 15/Sep/18 $$\mathrm{If}\:\mid{a}\mid<\mathrm{1}\:\mathrm{and}\:\mid{b}\mid<\mathrm{1},\:\mathrm{then}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{series}\:{a}\left({a}+{b}\right)+{a}^{\mathrm{2}} \left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)+{a}^{\mathrm{3}} \left({a}^{\mathrm{3}} +{b}^{\mathrm{3}} \right)+… \\ $$$$\mathrm{upto}\:\infty\:\mathrm{is} \\ $$ Answered by…
Question Number 43765 by peter frank last updated on 15/Sep/18 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{integers}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{100}\:\mathrm{that} \\ $$$$\mathrm{are}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{2}\:\mathrm{or}\:\mathrm{5}\:\mathrm{is}\:\_\_\_\_\_. \\ $$ Answered by math1967 last updated on 15/Sep/18 $${sum}\:{of}\:{divisible}\:{by}\:\mathrm{2}={S}_{\mathrm{2}} \\ $$$${sum}\:{of}\:{divisible}\:{by}\:\mathrm{5}={S}_{\mathrm{5}}…
Question Number 43662 by kkr1729 last updated on 13/Sep/18 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{4}\:\mathrm{sides} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{regular}\:\mathrm{tetrahedron}\:\mathrm{can}\:\mathrm{be}\:\mathrm{painted} \\ $$$$\mathrm{with}\:\mathrm{different}\:\mathrm{colours}\:\mathrm{is} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 43642 by gunawan last updated on 13/Sep/18 $$\mathrm{The}\:\mathrm{most}\:\mathrm{general}\:\mathrm{value}\:\mathrm{of}\:\theta\:\mathrm{which} \\ $$$$\mathrm{satisfy}\:\mathrm{both}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{cos}\:\theta=\:−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$$\mathrm{and}\:\:\mathrm{tan}\:\theta=\mathrm{1}\:\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 13/Sep/18 $${cos}\theta=−{ve}\:\:\:{tan}\theta=+{ve}\:\:\:{so}\:\theta\:{lies}\:{in}\:{third}\:{quadrant} \\…
Question Number 43643 by gunawan last updated on 13/Sep/18 $$\mathrm{If}\:\:\mathrm{sin}^{−\mathrm{1}} {x}+\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{1}−{x}\right)\:=\:\mathrm{cos}^{−\mathrm{1}} {x}, \\ $$$$\mathrm{then}\:\:{x}\:= \\ $$ Answered by behi83417@gmail.com last updated on 13/Sep/18 $${x}=\frac{\mathrm{1}}{\mathrm{2}}…
Question Number 43641 by gunawan last updated on 13/Sep/18 $$\mathrm{In}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{one}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{120}°, \\ $$$$\mathrm{the}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{form}\:\mathrm{an}\:\mathrm{AP}. \\ $$$$\mathrm{If}\:\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{side}\:\mathrm{is} \\ $$$$\mathrm{7}\:\mathrm{cm}.,\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is} \\ $$ Answered by $@ty@m last updated on 13/Sep/18…