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Question Number 169569 by mnjuly1970 last updated on 03/May/22 $$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)\:=\:{x}\:−\lfloor\frac{{x}}{\mathrm{2}}\rfloor−\lfloor\frac{{x}}{\mathrm{3}}\rfloor−\lfloor\frac{{x}}{\mathrm{6}}\rfloor \\ $$$$\:\:\:\:\:\:\:\:\:\:{R}_{\:{f}} \:=\:? \\ $$$$\:\:\:\:\: \\ $$ Answered by mahdipoor last updated on…
Question Number 104037 by bramlex last updated on 19/Jul/20 $$\left(\mathrm{1}\right)\begin{cases}{{x}^{\mathrm{3}} +{y}^{\mathrm{6}} \:=\:\mathrm{91}}\\{{x}+{y}^{\mathrm{2}} \:=\:\mathrm{7}\:}\end{cases} \\ $$$${find}\:{x}−{y}^{\mathrm{6}} \:. \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}{a}+\frac{\mathrm{2}}{{a}}\:=\:\mathrm{8}\:\Rightarrow\:\frac{{a}^{\mathrm{6}} +\mathrm{1}}{{a}^{\mathrm{3}} }\:? \\ $$ Answered by bemath…
Question Number 104023 by I want to learn more last updated on 18/Jul/20 Commented by I want to learn more last updated on 18/Jul/20 .A man answers 10 maths problems, one after the other. He answers the first problem correctly and the second problem incorrectly, for each of the remaining 8 problems the probability that he answers the problem correctly equals to the ratio of the number of problems that he has already answered correctly to the total number of problems that he has already answered. What is the probability that he answers exactly 5 out of 10 problems correctly…
Question Number 38477 by Sr@2004 last updated on 26/Jun/18 Answered by $@ty@m last updated on 26/Jun/18 $$\frac{{a}−{b}}{{c}}+\frac{{b}−{c}}{{a}}+\frac{{c}+{a}}{{b}}=\mathrm{1} \\ $$$$\Rightarrow\frac{{a}−{b}}{{c}}+\frac{{c}+{a}}{{b}}=\mathrm{1}−\frac{{b}−{c}}{{a}} \\ $$$$\Rightarrow\frac{{b}\left({a}−{b}\right)+{c}\left({c}+{a}\right)}{{bc}}=\frac{{a}−{b}+{c}}{{a}} \\ $$$$\Rightarrow\frac{\left({a}−{b}+{c}\right)\left({b}+{c}\right)}{{bc}}=\frac{{a}−{b}+{c}}{{a}} \\ $$$$\Rightarrow\frac{{b}+{c}}{{bc}}=\frac{\mathrm{1}}{{a}}…
Question Number 169539 by Shrinava last updated on 02/May/22 Commented by mr W last updated on 02/May/22 $$\frac{{R}}{{OI}}=\sqrt{\frac{\mathrm{3}}{\mathrm{2}}}\:? \\ $$ Commented by Shrinava last updated…
Question Number 169533 by cortano1 last updated on 02/May/22 $$\:\:\begin{cases}{{x}+\frac{\mathrm{1}}{{y}}=\mathrm{1}}\\{\frac{\mathrm{1}}{{x}}+{y}=\mathrm{2}}\end{cases}\Rightarrow{x}^{\mathrm{2022}} +\frac{\mathrm{1}}{{y}^{\mathrm{2022}} }\:=? \\ $$ Commented by greougoury555 last updated on 02/May/22 $$\:\:{x}=\frac{{y}−\mathrm{1}}{{y}}\:\wedge\:\frac{{y}}{{y}−\mathrm{1}}+{y}\:=\:\mathrm{2} \\ $$$$\Rightarrow{y}+{y}^{\mathrm{2}} −{y}\:=\:\mathrm{2}{y}−\mathrm{2}…
Question Number 38459 by ajfour last updated on 25/Jun/18 $${x}^{\mathrm{2}} \left({x}−{b}^{\mathrm{2}} \right)+{a}^{\mathrm{2}} {b}^{\mathrm{2}} \left({x}−{a}^{\mathrm{2}} \right)=\mathrm{0} \\ $$$${Solve}\:{for}\:{x}. \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on…
Question Number 103983 by I want to learn more last updated on 18/Jul/20 $$\mathrm{If}\:\:\alpha\:\:\mathrm{and}\:\:\beta\:\:\mathrm{are}\:\mathrm{two}\:\mathrm{unequal}\:\mathrm{angle},\:\mathrm{which}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}, \\ $$$$\:\:\:\:\mathrm{a}\:\mathrm{cos}\left(\alpha\right)\:\:+\:\:\mathrm{b}\:\mathrm{sin}\left(\beta\right)\:\:=\:\:\mathrm{c},\:\:\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:\:\:\:\mathrm{sin}\left(\frac{\alpha\:\:+\:\beta}{\mathrm{2}}\right)\:\mathrm{sec}\left(\frac{\alpha\:\:−\:\:\beta}{\mathrm{2}}\right)\:\:=\:\:\frac{\mathrm{b}}{\mathrm{c}} \\ $$$$\left(\mathrm{ii}\right)\:\:\:\:\:\mathrm{tan}\left(\frac{\alpha}{\mathrm{2}}\right)\:\mathrm{tan}\left(\frac{\beta}{\mathrm{2}}\right)\:\:=\:\:\frac{\mathrm{c}\:\:−\:\:\mathrm{a}}{\mathrm{c}\:\:+\:\:\mathrm{a}} \\ $$ Terms of Service…