Question Number 88014 by ajfour last updated on 07/Apr/20 $${If}\:{there}\:{is}\:{no}\:{second}'{s}\:{hand}\:{on} \\ $$$${a}\:{clock}\:{and}\:{the}\:{minute}\:{and}\:{hour} \\ $$$${hand}\:{move}\:{in}\:{continuous}\:{fashion}, \\ $$$${then}\:{exactly}\:{at}\:{what}\:{time}\:{between} \\ $$$$\mathrm{02}:\mathrm{10}\:\:{and}\:\mathrm{02}:\mathrm{15}\:{does}\:{the}\:{position} \\ $$$${of}\:{the}\:{two}\:{hands}\:{exactly}\:{coincide}? \\ $$ Answered by mr…
Question Number 22474 by Tinkutara last updated on 19/Oct/17 $$\mathrm{Let}\:{R}\:=\:\left(\mathrm{5}\sqrt{\mathrm{5}}\:+\:\mathrm{11}\right)^{\mathrm{2}{n}+\mathrm{1}} \:\mathrm{and}\:{f}\:=\:{R}\:−\:\left[{R}\right], \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:{Rf}\:=\:\mathrm{4}^{\mathrm{2}{n}+\mathrm{1}} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 22472 by Tinkutara last updated on 18/Oct/17 $$\mathrm{If}\:{x}^{{x}} \centerdot{y}^{{y}} \centerdot{z}^{{z}} \:=\:{x}^{{y}} \centerdot{y}^{{z}} \centerdot{z}^{{x}} \:=\:{x}^{{z}} \centerdot{y}^{{x}} \centerdot{z}^{{y}} \:\mathrm{such} \\ $$$$\mathrm{that}\:{x},\:{y}\:\mathrm{and}\:{z}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{greater}\:\mathrm{than}\:\mathrm{1},\:\mathrm{then}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{true}\:\mathrm{for}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the}…
Question Number 22468 by Tinkutara last updated on 18/Oct/17 $$\mathrm{If}\:{a}_{{r}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{r}} \:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\left(\mathrm{1}\:+\:{x}\:+\:{x}^{\mathrm{2}} \right)^{{n}} ,\:\mathrm{then} \\ $$$${a}_{\mathrm{1}} \:−\:\mathrm{2}{a}_{\mathrm{2}} \:+\:\mathrm{3}{a}_{\mathrm{3}} \:−\:…….\:\mathrm{2}{na}_{\mathrm{2}{n}} \:= \\ $$ Terms…
Question Number 22463 by Tinkutara last updated on 18/Oct/17 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:{x}: \\ $$$$\frac{\mathrm{1}}{\left[{x}\right]}\:+\:\frac{\mathrm{1}}{\left[\mathrm{2}{x}\right]}\:=\:\left({x}\right)\:+\:\frac{\mathrm{1}}{\mathrm{3}}, \\ $$$$\mathrm{where}\:\left[{x}\right]\:\mathrm{is}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{or}\:\mathrm{equal}\:\mathrm{to}\:{x}\:\mathrm{and}\:\left({x}\right)\:=\:{x}\:−\:\left[{x}\right], \\ $$$$\left[\mathrm{e}.\mathrm{g}.\:\left[\mathrm{3}.\mathrm{4}\right]\:=\:\mathrm{3}\:\mathrm{and}\:\left(\mathrm{3}.\mathrm{4}\right)\:=\:\mathrm{0}.\mathrm{4}\right]. \\ $$ Answered by ajfour last updated…
Question Number 87988 by M±th+et£s last updated on 07/Apr/20 $${solve}\:{the}\:{PDE} \\ $$$$\mathrm{1}−{Z}={px}+{py}−{q}\sqrt{{pq}} \\ $$$$\mathrm{2}−{Z}={px}+{qy}+{sin}\left({p}+{q}\right) \\ $$$$\mathrm{3}−{p}\left(\mathrm{1}+{q}^{\mathrm{2}} \right)={q}\left({Z}−{a}\right) \\ $$$$\mathrm{4}−{Z}={xyp}^{\mathrm{2}} \\ $$ Terms of Service Privacy…
Question Number 153513 by yeti123 last updated on 08/Sep/21 $$\left(\frac{{x}}{\mathrm{5}}\:+\:\frac{{y}}{\mathrm{3}}\right)\left(\frac{\mathrm{5}}{{x}}\:+\:\frac{\mathrm{3}}{{y}}\right)\:=\:\mathrm{139},\:\forall{x},{y}\:\in\:\mathbb{R}_{>\mathrm{0}} \\ $$$$\mathrm{find}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum}\:\mathrm{of}\:\:\frac{{x}\:+\:{y}}{\:\sqrt{{xy}}} \\ $$ Answered by liberty last updated on 08/Sep/21 $$\Rightarrow\frac{{x}+{y}}{\:\sqrt{{xy}}}\:=\:\sqrt{\frac{{x}}{{y}}}+\sqrt{\frac{{y}}{{x}}}=\sqrt{\frac{\mathrm{5}\lambda}{\mathrm{3}}}+\sqrt{\frac{\mathrm{3}}{\mathrm{5}\lambda}} \\ $$$${from}\:{condition} \\…
Question Number 153508 by mathdanisur last updated on 07/Sep/21 Answered by maged last updated on 08/Sep/21 $${x}=\mathrm{2},{y}=\mathrm{2},{z}=\mathrm{2}\Rightarrow\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} =\mathrm{12} \\ $$$${S}_{{min}} =\mathrm{2}+\mathrm{2}+\mathrm{2}+\mathrm{8}+\frac{\mathrm{1}}{\mathrm{4}+\mathrm{4}+\mathrm{4}} \\ $$$${S}_{{min}}…
Question Number 153505 by mathdanisur last updated on 07/Sep/21 Commented by MJS_new last updated on 08/Sep/21 $$\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{5}}−\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{5}}=\mathrm{5}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solution}\:\in\mathbb{C} \\ $$ Answered by…
Question Number 153500 by Engr_Jidda last updated on 07/Sep/21 $${Evaluate}\:{the}\:{line}\:{integral}\:{space} \\ $$$${if}\:{f}\left({r}\right)={Zi}+{Xj}+{Yk}\:{and}\:{C}\:{is}\:{a}\:{helix} \\ $$$${given}\:{by}\:{C}:\:{r}\left({t}\right)=\left({cost},{sint},−\mathrm{3}{t}\right)\:\:\mathrm{0}\leqslant{t}\leqslant\mathrm{2}\pi \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com