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 205487 by MathedUp last updated on 22/Mar/24 $${f}\left({t}\right)={t}\centerdot\int_{\mathrm{0}} ^{\infty} \:{e}^{−{st}+\mathrm{tanh}\left({t}\right)} \mathrm{d}{t} \\ $$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\left({t}\right)=??? \\ $$$$\mathrm{g}\left({t}\right)=\frac{\mathrm{1}}{{t}}{f}\left({t}\right) \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left\{\mathrm{g}\left({n}\right)−\underset{{h}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{h}}\right\}=??? \\ $$…
Question Number 205479 by cortano12 last updated on 22/Mar/24 Answered by mr W last updated on 22/Mar/24 Commented by mr W last updated on 22/Mar/24…
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 $$\mathrm{3}{cosx}=\mathrm{4}{cosx}−\mathrm{4}\sqrt{\mathrm{3}}{sinx} \\ $$$$\Rightarrow{cosx}=\mathrm{4}\sqrt{\mathrm{3}}{sinx}\Rightarrow{tanx}=\frac{\sqrt{\mathrm{3}}}{\mathrm{12}}\:\:\checkmark \\…
Question Number 205428 by mr W last updated on 21/Mar/24 Answered by Rasheed.Sindhi last updated on 21/Mar/24 Commented by Rasheed.Sindhi last updated on 21/Mar/24 $${White}\:{area}\:{of}\:\Box{ABCD}\:{is}\:{composed}…
Question Number 205461 by mr W last updated on 21/Mar/24 Commented by mr W last updated on 21/Mar/24 $${find}\:{the}\:{area}\:{of}\:{the}\:{third}\:{part}\: \\ $$$${between}\:{two}\:{squares}. \\ $$ Answered by…
Question Number 205429 by mnjuly1970 last updated on 21/Mar/24 $$ \\ $$$$\:\mathrm{I}{f},\:\:\varphi\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\left(\pi\:−{cos}^{\:−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{4}}\:\right)\right) \\ $$$$ \\ $$$$\:\:\:\Rightarrow\:\mathrm{log}_{\:\mathrm{2}} \left(\:\frac{\:\mathrm{1}+\:{cos}\left(\mathrm{6}\varphi\:\right)}{{cos}^{\mathrm{6}} \left(\varphi\:\right)}\:\right)\:=? \\ $$$$ \\ $$ Answered by…