Question Number 9516 by Joel575 last updated on 12/Dec/16 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\lfloor\mathrm{log}_{\mathrm{2}} \:{k}\rfloor\:=\:\mathrm{2018} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{n}\:? \\ $$ Commented by sou1618 last updated on 12/Dec/16 $$\ast{K}=\lfloor{log}_{\mathrm{2}}…
Question Number 9515 by Joel575 last updated on 12/Dec/16 $$\mathrm{cos}\:\left({x}+\mathrm{2}{y}\right)\:=\:{a} \\ $$$$\mathrm{cos}\:\left({x}+{y}\right)\:=\:{b} \\ $$$$ \\ $$$$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{sin}^{\mathrm{2}} \:\left(\mathrm{2}{x}+\mathrm{3}{y}\right)\:\:\mathrm{is}\:… \\ $$ Answered by mrW last updated on…
Question Number 140587 by mathsuji last updated on 09/May/21 $${a};{b}>\mathrm{0}\:{and}\:\forall{x};{y}\in\mathbb{R} \\ $$$${find}\:{all}\:{functions}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:;\:{such}\:{that} \\ $$$${f}\left({ax}\right){f}\left({by}\right)={abf}\left({bx}+{ay}\right)+{x}^{{a}} {y}^{{b}} {f}\left({x}^{{b}} {y}^{{a}} \right) \\ $$ Terms of Service Privacy Policy…
Question Number 75048 by mathocean1 last updated on 06/Dec/19 $$\mathrm{I}\:\mathrm{would}\:\mathrm{like}\:\mathrm{that}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\: \\ $$$$\mathrm{show}\:\mathrm{this}\:\mathrm{equality}: \\ $$$$\mathrm{16cos}\:\frac{\Pi}{\mathrm{24}}\mathrm{cos}\frac{\mathrm{5}\Pi}{\mathrm{24}}\mathrm{cos}\frac{\mathrm{7}\Pi}{\mathrm{24}}\mathrm{cos}\frac{\mathrm{11}\Pi}{\mathrm{24}}=\mathrm{1} \\ $$ Commented by mind is power last updated on 06/Dec/19…
Question Number 140581 by bounhome last updated on 09/May/21 $${prove}\:\:\int{sec}^{\mathrm{2}} {xdx}={tanx} \\ $$ Answered by MJS_new last updated on 09/May/21 $$\mathrm{tan}\:{x}\:=\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}} \\ $$$$\frac{{d}}{{dx}}\left[\frac{{u}\left({x}\right)}{{v}\left({x}\right)}\right]=\frac{{u}'\left({x}\right){v}\left({x}\right)−{u}\left({x}\right){v}'\left({x}\right)}{\left({v}\left({x}\right)\right)^{\mathrm{2}} } \\…
Question Number 75046 by aliesam last updated on 06/Dec/19 Commented by mind is power last updated on 06/Dec/19 $$\mathrm{O}\:\mathrm{is}\:\mathrm{center}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{wich}\:\mathrm{pass}\:\mathrm{tbrow}\:\mathrm{A},\mathrm{B},\mathrm{C}\:? \\ $$ Commented by aliesam last…
Question Number 9510 by FilupSmith last updated on 11/Dec/16 $$\mathrm{Prove}\:\mathrm{if}\:\mathrm{a}\:\mathrm{rational}\:\mathrm{times}\:\mathrm{an}\:\mathrm{irrational} \\ $$$$\mathrm{can}\:\mathrm{result}\:\mathrm{in}\:\mathrm{a}\:\mathrm{rational}. \\ $$ Answered by geovane10math last updated on 11/Dec/16 $${A}\:{rational}\:{times}\:{an}\:{irrational}\:\boldsymbol{{alyaws}}\: \\ $$$${is}\:{a}\:{irrational}.\: \\…
Question Number 140576 by SOMEDAVONG last updated on 09/May/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\underset{\mathrm{n}=\mathrm{1}} {\overset{+\propto} {\sum}}\frac{\mathrm{2}^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} }=? \\ $$ Answered by Dwaipayan Shikari last updated on 09/May/21 $${Li}_{\mathrm{3}}…
Question Number 75040 by mathocean1 last updated on 06/Dec/19 $$\mathrm{Please}\:\mathrm{can}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\: \\ $$$$\mathrm{to}\:\mathrm{show}\:\mathrm{that}: \\ $$$$\mathrm{cos}\:\frac{\mathrm{47}\Pi}{\mathrm{13}}=\mathrm{sin}\:\frac{\mathrm{23}\Pi}{\mathrm{26}}=\mathrm{sin}\frac{\mathrm{3}\Pi}{\mathrm{26}} \\ $$ Answered by Kunal12588 last updated on 06/Dec/19 $${cos}\frac{\mathrm{47}\pi}{\mathrm{13}}={cos}\left(\frac{\mathrm{52}\pi−\mathrm{5}\pi}{\mathrm{13}}\right)={cos}\left(\mathrm{4}\pi−\frac{\mathrm{5}\pi}{\mathrm{13}}\right) \\…
Question Number 75041 by ~blr237~ last updated on 06/Dec/19 $$\left.\mathrm{1}\left.\right)\left.\:\mathrm{Show}\:\mathrm{that}\:\:\mathrm{for}\:\mathrm{a}\in\right]\mathrm{01}\right]\mathrm{the}\:\mathrm{function}\:\:\mathrm{f}_{\mathrm{a}} \::\mathbb{R}_{+} \rightarrow\mathbb{R}\:\mathrm{defined}\:\mathrm{by}\:\mathrm{f}_{\mathrm{a}} \left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{a}} \: \\ $$$$\mathrm{is}\:\:\:\mathrm{a}−\mathrm{holder}\:\mathrm{function}\:\:\mathrm{in}\:\mathrm{other}\:\mathrm{way}\:\:\mathrm{there}\:\mathrm{exist}\:\:\mathrm{K}>\mathrm{0}\:\mathrm{such}\:\mathrm{as}\:\forall\:\mathrm{x},\mathrm{y}>\mathrm{0}\: \\ $$$$\mid\mathrm{f}_{\mathrm{a}} \left(\mathrm{x}\right)−\mathrm{f}_{\mathrm{a}} \left(\mathrm{y}\right)\mid\leqslant\mathrm{K}\mid\mathrm{x}−\mathrm{y}\mid^{\mathrm{a}} \:\: \\ $$$$ \\ $$…