Question Number 144684 by mnjuly1970 last updated on 27/Jun/21 $$ \\ $$ Answered by mindispower last updated on 27/Jun/21 $${M}:={xyz}−\left({xy}+{yz}+{zx}\right)+{x}+{y}+{z}−\mathrm{1} \\ $$$$\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}=\mathrm{1}{xyz}={xy}+{yz}+{zx} \\ $$$${M}={x}+{y}+{z}−\mathrm{1} \\…
Question Number 79126 by ~blr237~ last updated on 22/Jan/20 $${Study}\:\:\:{f}\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{x}^{{n}} {sin}\left({nx}\right)}{{n}} \\ $$$${Find}\:{out}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \:\frac{{sin}\left({n}\right)}{{n}}\:\:\:{and}\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}\right)}{{n}}\: \\ $$ Commented by mathmax…
Question Number 79127 by ~blr237~ last updated on 22/Jan/20 $$\:{Solve}\:\:{on}\:\mathbb{R}\ast\mathbb{R}\:\:{the}\:{following}\:{system} \\ $$$$\left\{_{\mathrm{9}^{{A}} +\mathrm{9}^{{B}} +\mathrm{9}^{{C}} =\mathrm{1}} ^{\mathrm{3}^{{A}} +\mathrm{3}^{{B}} +\mathrm{3}^{{C}} =\sqrt{\mathrm{3}}} \:\:\:\right. \\ $$ Commented by jagoll…
Question Number 79124 by ~blr237~ last updated on 22/Jan/20 $${Prove}\:{that}\: \\ $$$$\:\mathrm{16}{arctan}\left(\frac{\mathrm{1}}{\mathrm{5}}\right)−\mathrm{4}{arctan}\left(\frac{\mathrm{1}}{\mathrm{239}}\right)=\pi \\ $$$$ \\ $$ Commented by mind is power last updated on 23/Jan/20…
Question Number 144554 by imjagoll last updated on 26/Jun/21 Answered by Olaf_Thorendsen last updated on 26/Jun/21 $$\left.{a}\right)\:\Delta\:=\:\left[\mathrm{O}{x}\right) \\ $$$$\mathrm{I}_{\Delta} \:=\:\int{r}^{\mathrm{2}} {dm}\:=\:\int{r}^{\mathrm{2}} \delta{dS} \\ $$$$\mathrm{I}_{\Delta} \:=\:\delta\int_{\mathrm{0}}…
Question Number 144532 by EDWIN88 last updated on 26/Jun/21 $$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{box},\mathrm{open}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{top}\:\mathrm{is}\:\mathrm{to}\:\mathrm{have}\:\mathrm{a}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{32}\:\mathrm{cube}\:\mathrm{feet} \\ $$$$\mathrm{What}\:\mathrm{must}\:\mathrm{be}\:\mathrm{the}\:\mathrm{dimensions} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{total}\:\mathrm{surface}\:\mathrm{is}\:\mathrm{a}\:\mathrm{minimum}? \\ $$ Answered by liberty last updated on 26/Jun/21…
Question Number 144534 by imjagoll last updated on 26/Jun/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance}\:\mathrm{from}\: \\ $$$$\mathrm{the}\:\mathrm{origin}\:\mathrm{to}\:\mathrm{the}\:\mathrm{hyperbola}\: \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{8xy}+\mathrm{7y}^{\mathrm{2}} =\mathrm{225}\:,\mathrm{z}=\mathrm{0}\: \\ $$ Answered by liberty last updated on 26/Jun/21…
Question Number 144525 by imjagoll last updated on 26/Jun/21 $$\:\mathrm{If}\:\mathrm{y}=\mathrm{cosh}\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{1}\right) \\ $$$$\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:=? \\ $$ Answered by EDWIN88 last updated on 26/Jun/21 $$\:\mathrm{let}\:\mathrm{q}\:=\:\mathrm{x}^{\mathrm{2}}…
Question Number 78974 by ~blr237~ last updated on 22/Jan/20 $$\left\{_{\mathrm{3e}^{\mathrm{2x}} −\mathrm{y}^{\mathrm{2}} =\mathrm{2}\:\:\:} ^{\mathrm{e}^{\mathrm{x}} −\mathrm{y}^{\mathrm{2}} =\mathrm{2lny}−\mathrm{x}} \right. \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{on}\:\mathbb{R}\ast\mathbb{R} \\ $$ Commented by jagoll last updated…
Question Number 13429 by sergiosba last updated on 20/May/17 Commented by prakash jain last updated on 20/May/17 $${x}=−\mathrm{2cos}\:\theta \\ $$$${y}=\mathrm{3sin}\:\theta \\ $$$$\mathrm{cos}\:\theta=−\frac{{x}}{\mathrm{2}} \\ $$$$\mathrm{sin}\:\theta=\frac{{y}}{\mathrm{3}} \\…