Question Number 223179 by hardmath last updated on 16/Jul/25 $$\mathrm{If}:\:\:\:\mathrm{xy}\:=\:\boldsymbol{\mathrm{e}}^{\frac{\boldsymbol{\pi}}{\mathrm{4}}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{tg}\:\left(\mathrm{ln}\:\left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{y}}\right)\right)\:\centerdot\:\mathrm{tg}\:\left(\mathrm{ln}\:\left(\frac{\mathrm{y}^{\mathrm{3}} }{\mathrm{x}}\right)\right)\:=\:? \\ $$ Commented by hardmath last updated on 16/Jul/25 $$\mathrm{no}\:\mathrm{dear}\:\mathrm{professor},\:\mathrm{answer}: \\…
Question Number 223189 by behi834171 last updated on 16/Jul/25 $$\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}\right)\left(\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{3}\right)\left(\boldsymbol{{x}}^{\mathrm{4}} −\mathrm{4}\right)=\mathrm{36} \\ $$$$\boldsymbol{{x}}=? \\ $$ Commented by Ghisom last updated on 17/Jul/25 $$\mathrm{you}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate}…
Question Number 223110 by Rojarani last updated on 15/Jul/25 Answered by fantastic last updated on 15/Jul/25 $$\frac{\left({x}^{\mathrm{11}} −\frac{\mathrm{1}}{{x}^{\mathrm{11}} }\right)−\left({x}^{\mathrm{9}} −\frac{\mathrm{1}}{{x}^{\mathrm{9}} }\right)}{\left({x}^{\mathrm{10}} −\frac{\mathrm{1}}{{x}^{\mathrm{10}} }\right)−\left({x}^{\mathrm{8}} −\frac{\mathrm{1}}{{x}^{\mathrm{8}} }\right)}…
Question Number 223044 by hardmath last updated on 13/Jul/25 Commented by hardmath last updated on 13/Jul/25 $$ \\ $$Find the voltmeter reading in the electrical…
Question Number 222889 by Tawa11 last updated on 10/Jul/25 Commented by mr W last updated on 10/Jul/25 $${such}\:{a}\:{bench}: \\ $$ Commented by mr W last…
Question Number 222885 by gabthemathguy25 last updated on 10/Jul/25 Answered by MrGaster last updated on 10/Jul/25 Commented by gabthemathguy25 last updated on 10/Jul/25 nice Answered…
Question Number 222847 by OmoloyeMichael last updated on 09/Jul/25 $$\boldsymbol{{let}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\mathrm{1}.\mathrm{013}\boldsymbol{{x}}^{\mathrm{5}} −\mathrm{5}.\mathrm{262}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{0}.\mathrm{01732}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{0}.\mathrm{8389}\boldsymbol{{x}} \\ $$$$−\mathrm{1}.\mathrm{912}.\:\boldsymbol{{Evaluate}}\:\boldsymbol{{f}}\left(\mathrm{2}.\mathrm{279}\right)\:\boldsymbol{{by}}\:\boldsymbol{{first}}\:\boldsymbol{{calculating}} \\ $$$$\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{2}} ,\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{3}} ,\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{4}} \boldsymbol{{and}}\left(\mathrm{2}.\mathrm{279}\right)^{\mathrm{5}} \:\boldsymbol{{using}} \\ $$$$\boldsymbol{{four}}−\boldsymbol{{digit}}\:\boldsymbol{{round}}\:\boldsymbol{{arithmetic}}.\:\boldsymbol{{hence}},\boldsymbol{{compute}} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{absolute}}\:\boldsymbol{{and}}\:\boldsymbol{{relative}}\:\boldsymbol{{errors}}.…
Question Number 222856 by OmoloyeMichael last updated on 09/Jul/25 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{possible}}\:\boldsymbol{{root}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{{x}}+\mathrm{6}=\mathrm{0} \\ $$$$\boldsymbol{{using}}\:\boldsymbol{{the}}\:\boldsymbol{{fixed}}\:\boldsymbol{{point}}\:\boldsymbol{{iteration}}\:\boldsymbol{{method}}? \\ $$ Answered by AntonCWX8 last updated on 09/Jul/25 $${x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}}…
Question Number 222829 by hardmath last updated on 08/Jul/25 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{3x}\:+\:\left[\mathrm{x}\right]}{\mathrm{2x}} \\ $$$$\mathrm{Find}\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow−\mathrm{5}^{+} } {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:−\:\underset{\boldsymbol{\mathrm{x}}\rightarrow−\mathrm{5}^{−} } {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$ Answered by mehdee7396 last updated on 08/Jul/25…
Question Number 222777 by hardmath last updated on 07/Jul/25 $$\mathrm{Simplify}: \\ $$$$\frac{\left(\mathrm{cos214}°\:+\:\boldsymbol{\mathrm{i}}\:\mathrm{sin146}°\right)\centerdot\left(\mathrm{cos10}°\:+\:\boldsymbol{\mathrm{i}}\:\mathrm{sin10}°\right)}{\left(\mathrm{cos66}°\:−\:\boldsymbol{\mathrm{i}}\:\mathrm{sin246}°\right)}\:=\:? \\ $$ Answered by Frix last updated on 07/Jul/25 $$\mathrm{cos}\:\mathrm{214}°\:+\mathrm{i}\:\mathrm{sin}\:\mathrm{146}°\:=\mathrm{e}^{\mathrm{i}\frac{\mathrm{73}\pi}{\mathrm{90}}} \\ $$$$\mathrm{cos}\:\mathrm{10}°\:+\mathrm{i}\:\mathrm{sin}\:\mathrm{10}°\:=\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{18}}} \\…