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Author: Tinku Tara

Question-18366

Question Number 18366 by ketto last updated on 19/Jul/17 Answered by Tinkutara last updated on 19/Jul/17 $$−\mathrm{4}\:<\:\mathrm{5}\:−\:\mathrm{3}{x}\:\leqslant\:\mathrm{17} \\ $$$$−\mathrm{9}\:<\:−\mathrm{3}{x}\:\leqslant\:\mathrm{12} \\ $$$$−\mathrm{12}\:\leqslant\:\mathrm{3}{x}\:<\:\mathrm{9} \\ $$$$−\mathrm{4}\:\leqslant\:{x}\:<\:\mathrm{3} \\ $$$${x}\:\in\:\left[−\mathrm{4},\:\mathrm{3}\right)…

du-u-2-1-u-

Question Number 83898 by sahnaz last updated on 07/Mar/20 $$\int\frac{\mathrm{du}}{\:\sqrt{\mathrm{u}^{\mathrm{2}} −\mathrm{1}\:}−\mathrm{u}} \\ $$ Commented by john santu last updated on 07/Mar/20 $$\mathrm{let}\:{u}\:=\:\mathrm{sec}\:\theta\:\Rightarrow\:\mathrm{du}\:=\:\mathrm{sec}\:\theta\:\mathrm{tan}\:\theta\:\mathrm{d}\theta \\ $$ Commented…

Defined-a-function-f-x-such-that-f-1-x-2f-x-nx-for-m-n-gt-1-the-value-of-1-m-2n-6f-m-x-dx-is-

Question Number 83899 by john santu last updated on 07/Mar/20 $$\mathrm{Defined}\:\mathrm{a}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{such}\: \\ $$$$\mathrm{that}\:\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)+\mathrm{2f}\left(\mathrm{x}\right)=\:\mathrm{nx}\: \\ $$$$\mathrm{for}\:\mathrm{m}\:,\mathrm{n}\:>\:\mathrm{1}\:,\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\int\underset{\mathrm{1}} {\overset{\:\mathrm{m}} {\:}}\left(\mathrm{2n}+\mathrm{6f}\left(\frac{\mathrm{m}}{\mathrm{x}}\right)\right)\:\mathrm{dx}\:\mathrm{is}\:… \\ $$ Commented by john santu…

N-propositions-are-judged-by-2k-1-people-Each-person-assigns-true-to-exactly-M-propositions-and-false-to-the-other-N-M-M-N-To-say-a-proposition-is-approved-means-it-is-true-according-to-at

Question Number 18361 by diofanto last updated on 19/Jul/17 $${N}\:\mathrm{propositions}\:\mathrm{are}\:\mathrm{judged}\:\mathrm{by}\:\mathrm{2}{k}−\mathrm{1}\:\mathrm{people}. \\ $$$$\mathrm{Each}\:\mathrm{person}\:\mathrm{assigns}\:“\mathrm{true}''\:\mathrm{to} \\ $$$$\mathrm{exactly}\:{M}\:\mathrm{propositions}\:\mathrm{and}\:“\mathrm{false}'' \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{other}\:{N}−{M}\:\left({M}\:\leqslant\:{N}\right). \\ $$$$\mathrm{To}\:\mathrm{say}\:\mathrm{a}\:\mathrm{proposition}\:\mathrm{is}\:“\mathrm{approved}''\:\mathrm{means} \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{true}\:\mathrm{according}\:\mathrm{to}\:\mathrm{at}\:\mathrm{least}\:{k}\:\mathrm{judges}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\:\mathrm{numbers} \\ $$$$\mathrm{of}\:\mathrm{approved}\:\mathrm{propositions}\:\mathrm{given}\:{N},\:{M}\:\mathrm{and}\:{k}. \\…