Question Number 144899 by mnjuly1970 last updated on 30/Jun/21 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\Omega\::=\:\int\:\frac{\sqrt{\mathrm{1}−{sin}\left({x}\right)}}{{cos}\:\left({x}\right)}\:{e}\:^{−\frac{\mathrm{1}}{\mathrm{2}}\:{x}} =\:? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 13806 by ajfour last updated on 23/May/17 $${Prove}\:{that}\:{for}\:−\frac{\pi}{\mathrm{2}}<{x}<\frac{\pi}{\mathrm{2}}\:, \\ $$$$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }\mathrm{cos}\:{x}−\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }\mathrm{cos}\:\mathrm{3}{x}+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{3}} }\mathrm{cos}\:\mathrm{5}{x}−….{to}\:{infinity} \\ $$$$\:\:=\frac{\pi}{\mathrm{8}}\left(\frac{\pi^{\mathrm{2}} }{\mathrm{4}}−{x}^{\mathrm{2}} \right)\:. \\ $$ Commented by prakash jain…
Question Number 13751 by Nayon last updated on 23/May/17 $$\frac{{ds}}{{dt}}={v},\frac{{dv}}{{dt}}={a},\frac{{da}}{{dt}}={b},\frac{{db}}{{dt}}={e},\frac{{de}}{{dt}}={f} \\ $$$$\frac{{df}}{{dt}}={g},\frac{{dg}}{{dt}}={h},\frac{{dh}}{{dt}}={i},\frac{{di}}{{dt}}={j},\frac{{dj}}{{dt}}={k},….. \\ $$$${now}\:{if}\:{we}\:{continue}\:{this}\:{process}\:{to} \\ $$$${infinity}..{and}\:{if}\:{v}_{\mathrm{0}} ,{v},{a},{b},{e},{f},{g},{h},{i}, \\ $$$${j},…………….=\mathrm{1}\:.{then}\:{calculate} \\ $$$${the}\:{formula}\:{of}\:{v}\:{and}\:{s}\:… \\ $$$$ \\ $$…
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…