Question Number 205515 by aba last updated on 23/Mar/24 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{decomposition}\:\mathrm{into}\:\mathrm{cycles} \\ $$$$\mathrm{with}\:\mathrm{disjoints}\:\mathrm{support}\:\mathrm{of}\:\mathrm{c}^{\mathrm{k}} ,\:\mathrm{where}\:\mathrm{c}=\left(\mathrm{123}…\mathrm{n}\right)\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205492 by BaliramKumar last updated on 22/Mar/24 Answered by cortano12 last updated on 22/Mar/24 $$\:\Rightarrow\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{5}} {\prod}}\mathrm{T}_{\mathrm{i}\:} =\:\mathrm{T}_{\mathrm{3}} ^{\mathrm{5}} \:=\:\mathrm{3}^{\mathrm{5}} =\:\mathrm{243} \\ $$…
Question Number 205490 by mnjuly1970 last updated on 22/Mar/24 $$ \\ $$$$\:\:\:\:{If},{f}\left({x}\right)=\:\sqrt{\mathrm{2}\:+\:{x}}\:+\:{a}\:\sqrt{{x}\:−\:\mathrm{1}}\: \\ $$$$\:\:\:\:{is}\:{monotone}\:{function}\:. \\ $$$$\:\:\:\:{find}\:{the}\:{range}\:{of}\:\:''\:{a}\:'' \\ $$$$ \\ $$ Answered by mr W last…
Question Number 205471 by Fridunatjan08 last updated on 21/Mar/24 $${Solve}\:{the}\:{equation}:\:\frac{{x}}{\mathrm{21}}+\frac{{x}}{\mathrm{77}}+\frac{{x}}{\mathrm{165}}+\frac{{x}}{\mathrm{285}}=\mathrm{200} \\ $$ Answered by Rasheed.Sindhi last updated on 23/Mar/24 $$\frac{{x}}{\mathrm{21}}+\frac{{x}}{\mathrm{77}}+\frac{{x}}{\mathrm{165}}+\frac{{x}}{\mathrm{285}}=\mathrm{200} \\ $$$${x}\left(\frac{\mathrm{1}}{\mathrm{21}}+\frac{\mathrm{1}}{\mathrm{77}}+\frac{\mathrm{1}}{\mathrm{165}}+\frac{\mathrm{1}}{\mathrm{285}}\right)=\mathrm{200} \\ $$$${x}\left(\:\frac{\mathrm{1}}{\mathrm{7}}\left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{11}}\right)+\frac{\mathrm{1}}{\mathrm{15}}\left(\frac{\mathrm{1}}{\mathrm{11}}+\frac{\mathrm{1}}{\mathrm{19}}\right)\right)=\mathrm{200} \\…
Question Number 205432 by hardmath last updated on 21/Mar/24 $$\mathrm{Find}:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{2}\boldsymbol{\pi}} \:\mathrm{ln}\:\left(\mathrm{sinx}\:+\:\sqrt{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{x}}\right)\:\mathrm{dx} \\ $$ Answered by MathedUp last updated on 21/Mar/24 $$\mathrm{0} \\ $$$$\mathrm{cauz}\:−{f}\left({z}\right)={f}\left(−{z}\right)\:,\:{f}\left({z}+\pi\right)=−{f}\left({z}\right)\:,\:{f}\left({z}+\mathrm{2}\pi\right)={f}\left({z}\right)…
Question Number 205460 by hardmath last updated on 21/Mar/24 $$\mathrm{If}\:\:\mathrm{3cosx}\:=\:\mathrm{8sin}\left(\mathrm{30}°\:−\:\mathrm{x}\right) \\ $$$$\mathrm{Find}:\:\:\mathrm{tanx}\:=\:? \\ $$ Answered by MM42 last updated on 21/Mar/24 $$\mathrm{3}{cosx}=\mathrm{4}{cosx}−\mathrm{4}\sqrt{\mathrm{3}}{sinx} \\ $$$$\Rightarrow{cosx}=\mathrm{4}\sqrt{\mathrm{3}}{sinx}\Rightarrow{tanx}=\frac{\sqrt{\mathrm{3}}}{\mathrm{12}}\:\:\checkmark \\…
Question Number 205430 by hardmath last updated on 21/Mar/24 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\frac{\mathrm{1}}{\mathrm{sinA}}\:+\:\frac{\mathrm{1}}{\mathrm{sinB}}\:+\:\frac{\mathrm{1}}{\mathrm{sinC}}\:\leqslant\:\frac{\mathrm{2}}{\mathrm{3}}\:\left(\mathrm{cot}\frac{\mathrm{A}}{\mathrm{2}}\:+\:\mathrm{cot}\frac{\mathrm{B}}{\mathrm{2}}\:+\:\mathrm{cot}\frac{\mathrm{C}}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205431 by hardmath last updated on 21/Mar/24 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\frac{\mathrm{cotA}\:\mathrm{cotB}\:\mathrm{cotC}}{\mathrm{sinA}\:\mathrm{sinB}\:\mathrm{sinC}}\:\leqslant\:\frac{\mathrm{8}}{\mathrm{27}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205420 by hardmath last updated on 20/Mar/24 $$\mathrm{If} \\ $$$$\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:\geqslant\:\mathrm{2} \\ $$ Answered…
Question Number 205422 by hardmath last updated on 20/Mar/24 $$\mathrm{If} \\ $$$$\left(\mathrm{a}\:+\:\mathrm{1}\right)\left(\mathrm{b}\:+\:\mathrm{1}\right)\left(\mathrm{c}\:+\:\mathrm{1}\right)\:=\:\mathrm{8} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\geqslant\:\mathrm{3} \\ $$ Answered by A5T last…