Question Number 70252 by Shamim last updated on 02/Oct/19 $$\mathrm{If},\:\mathrm{log}\:\mathrm{x}^{\mathrm{y}} \:=\:\mathrm{6}\:\mathrm{and}\:\mathrm{log}\:\mathrm{14x}^{\mathrm{8y}} \:=\:\mathrm{3}\:\mathrm{then}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x},\:\mathrm{y}. \\ $$ Answered by MJS last updated on 02/Oct/19 $$\mathrm{log}\:{x}^{{y}} =\mathrm{6}\:\Rightarrow\:{y}\mathrm{log}\:{x}\:=\mathrm{6}…
Question Number 135790 by benjo_mathlover last updated on 16/Mar/21 $${Find}\:{the}\:{component}\:{form}\:{of} \\ $$$${the}\:{vector}\:{that}\:{reprecents}\:{the} \\ $$$${velocity}\:{of}\:{an}\:{airplane}\:{descending} \\ $$$${at}\:{speed}\:{of}\:\mathrm{150}\:{miles}\:{per}\:{hour} \\ $$$${at}\:{angle}\:\mathrm{20}°\:{below}\:{the}\:{horizontal} \\ $$ Terms of Service Privacy Policy…
Question Number 70253 by oyemi kemewari last updated on 02/Oct/19 Commented by mathmax by abdo last updated on 02/Oct/19 $${let}\:{I}\:=\int\:{u}^{\mathrm{2}} \sqrt{{u}^{\mathrm{2}} −\mathrm{2}}{du}\:{changement}\:{u}=\sqrt{\mathrm{2}}{ch}\left({x}\right)\:{give} \\ $$$${I}\:=\int\:\mathrm{2}{ch}^{\mathrm{2}} \left({x}\right)\sqrt{\mathrm{2}}{sh}\left({x}\right)\sqrt{\mathrm{2}}{sh}\left({x}\right){dx}…
Question Number 4716 by 123456 last updated on 28/Feb/16 $$\mathrm{lets}\:{f}:\left[\mathrm{0},\mathrm{T}\right]\rightarrow\mathbb{R} \\ $$$$\mathrm{does}? \\ $$$$\frac{\mathrm{1}}{\mathrm{T}}\underset{\mathrm{0}} {\overset{\mathrm{T}} {\int}}{f}\left({t}\right){dt}\leqslant\sqrt{\frac{\mathrm{1}}{\mathrm{T}}\underset{\mathrm{0}} {\overset{\mathrm{T}} {\int}}\left[{f}\left({t}\right)\right]^{\mathrm{2}} {dt}}\leqslant\frac{\mathrm{1}}{\mathrm{T}}\underset{\mathrm{0}} {\overset{\mathrm{T}} {\int}}\mid{f}\left({t}\right)\mid{dt} \\ $$ Commented by…
Question Number 135785 by Chhing last updated on 16/Mar/21 $$ \\ $$$$\:\:\mathrm{Solve}\:\mathrm{differential}\:\mathrm{equations} \\ $$$$\:\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\mathrm{y}'+\mathrm{6xy}=\mathrm{lnx} \\ $$$$\:\mathrm{help}\:\mathrm{me} \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 135784 by benjo_mathlover last updated on 16/Mar/21 $${Given}\:\begin{cases}{{f}\left(\mathrm{3}\right)=\mathrm{4}\:,\:{f}\:'\left(\mathrm{3}\right)=−\mathrm{2}}\\{{f}\left(\mathrm{8}\right)=\mathrm{5}\:,\:{f}\:'\left(\mathrm{8}\right)=\mathrm{3}}\end{cases} \\ $$$${find}\:\int_{\mathrm{3}} ^{\:\mathrm{8}} \:{x}\:{f}\:''\left({x}\right)\:{dx}\:. \\ $$ Answered by Ar Brandon last updated on 16/Mar/21 $$\int_{\mathrm{3}}…
Question Number 4714 by 123456 last updated on 28/Feb/16 $$\mathrm{lets}\:{f}:\left[\mathrm{0},\mathrm{T}\right]\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{T}} {\int}}\left[{f}\left({t}\right)\right]^{\mathrm{2}} {dt}<+\infty \\ $$$$\omega\mathrm{T}=\mathrm{2}\pi \\ $$$$\mathrm{if}\:{a}\left({n}\right)=\frac{\mathrm{2}}{\mathrm{T}}\underset{\mathrm{0}} {\overset{\mathrm{T}} {\int}}{f}\left({t}\right)\mathrm{cos}\left(\omega{nt}\right){dt} \\ $$$$\mathrm{and}\:{b}\left({n}\right)=\frac{\mathrm{2}}{\mathrm{T}}\underset{\mathrm{0}} {\overset{\mathrm{T}} {\int}}{f}\left({t}\right)\mathrm{sin}\:\left(\omega{nt}\right){dt}…
Question Number 135786 by JulioCesar last updated on 16/Mar/21 Commented by Ar Brandon last updated on 16/Mar/21 $$\mathrm{You}\:\mathrm{mean}\: \\ $$$$\mathrm{H}=\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}} }}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{9}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}} }}\:??? \\ $$…
Question Number 4712 by paonky last updated on 28/Feb/16 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{1}−\mathrm{sin}{x}} −{e}^{\mathrm{1}−\mathrm{tan}{x}} }{\mathrm{tan}{x}−\mathrm{sin}{x}}=? \\ $$ Answered by Yozzii last updated on 28/Feb/16 $${Let}\:{l}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{1}−{sinx}} −{e}^{\mathrm{1}−{tanx}}…
Question Number 135780 by bramlexs22 last updated on 15/Mar/21 $${If}\:{g}\left(\mathrm{0}\right)=\mathrm{2}\:,\:{g}\:'\left(\mathrm{0}\right)=\mathrm{1}\:{and}\: \\ $$$${f}\left({x}\right)\:=\:{e}^{\mathrm{2}{x}} {g}\left({x}\right).\:{What}\:{the}\:{value} \\ $$$${of}\:{f}^{−\mathrm{1}} \left(\mathrm{2}\right). \\ $$ Commented by bramlexs22 last updated on 16/Mar/21…