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 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 $${x}=\frac{\mathrm{1}}{\mathrm{2}}…
Question Number 43642 by gunawan last updated on 13/Sep/18 $$\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 $${cos}\theta=−{ve}\:\:\:{tan}\theta=+{ve}\:\:\:{so}\:\theta\:{lies}\:{in}\:{third}\:{quadrant} \\…
Question Number 43641 by gunawan last updated on 13/Sep/18 $$\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…
Question Number 109169 by ZiYangLee last updated on 21/Aug/20 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+…+{n}\centerdot{n}! \\ $$$$\mathrm{is}\: \\ $$ Answered by Dwaipayan Shikari last updated on 21/Aug/20 $$\underset{{n}=\mathrm{1}} {\overset{{n}} {\sum}}{n}.{n}!=\underset{{n}=\mathrm{1}}…
Question Number 43630 by peter frank last updated on 12/Sep/18 $$\mathrm{If}\:\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$${x}^{\mathrm{3}} −\mathrm{12}{x}^{\mathrm{2}} +\mathrm{39}{x}−\mathrm{28}=\mathrm{0}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP},\:\mathrm{then} \\ $$$$\mathrm{their}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{will}\:\mathrm{be} \\ $$ Answered by $@ty@m last updated on…
Question Number 43629 by peter frank last updated on 12/Sep/18 $$\mathrm{If}\:\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{an}\:\mathrm{infinite}\:\mathrm{GP}\:\mathrm{be}\:\mathrm{3}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{squares}\:\mathrm{of}\:\mathrm{its}\:\mathrm{term}\:\mathrm{is}\:\mathrm{also}\:\mathrm{3}, \\ $$$$\mathrm{then}\:\mathrm{its}\:\mathrm{first}\:\mathrm{term}\:\mathrm{and}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{are} \\ $$ Answered by $@ty@m last updated on 13/Sep/18 $${ATQ},…
Question Number 43628 by peter frank last updated on 12/Sep/18 $$\mathrm{Three}\:\mathrm{numbers}\:\mathrm{form}\:\mathrm{an}\:\mathrm{increasing}\:\mathrm{GP}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{number}\:\mathrm{is}\:\mathrm{doubled},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{new}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}.\:\mathrm{The}\:\mathrm{common}\:\mathrm{ratio} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{is} \\ $$ Answered by $@ty@m last updated on…
Question Number 43627 by peter frank last updated on 12/Sep/18 $$\underset{\:\mathrm{0}} {\overset{\pi^{\mathrm{2}} /\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:\sqrt{{x}}}{\:\sqrt{{x}}}\:{dx}\:= \\ $$ Commented by math khazana by abdo last updated on…