Question Number 108369 by mathdave last updated on 16/Aug/20 Answered by Rasheed.Sindhi last updated on 16/Aug/20 $${Fractions}:\:\frac{{x}}{\mathrm{8}},\frac{{y}}{\mathrm{8}} \\ $$$$ \\ $$$$\frac{{x}}{\mathrm{8}}+\frac{{y}}{\mathrm{8}}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow{x}+{y}=\frac{\mathrm{8}}{\mathrm{2}}=\mathrm{4}…..\left({i}\right) \\ $$$$\frac{{x}}{\mathrm{8}}+\frac{\mathrm{5}{y}}{\mathrm{8}}=\mathrm{2}\Rightarrow{x}+\mathrm{5}{y}=\mathrm{16}……..\left({ii}\right) \\ $$$$\left({ii}\right)−\left({i}\right):…
Question Number 108365 by mathdave last updated on 16/Aug/20 Answered by JDamian last updated on 16/Aug/20 $${S}\:=\underset{{n}=\mathrm{1}} {\overset{\mathrm{2019}} {\sum}}\frac{\mathrm{1}+\mathrm{2}+\mathrm{3}+\:\centerdot\centerdot\centerdot\:+\:{n}}{\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +\:\centerdot\centerdot\centerdot\:+\mathrm{2019}^{\mathrm{3}} }\:= \\ $$$$=\frac{\underset{{n}=\mathrm{1}}…
Question Number 173874 by akolade last updated on 20/Jul/22 Answered by a.lgnaoui last updated on 21/Jul/22 $$\mathrm{I}=\int_{\pi/\mathrm{4}} ^{\mathrm{15}\pi/\mathrm{4}} \left(\mathrm{sin}\:{x}\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{3sin}^{\mathrm{2}} {x}\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{4sin}^{\mathrm{5}} {x}\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{2sin}^{\mathrm{3}} {x}\right){dx}=…
Question Number 108326 by abony1303 last updated on 16/Aug/20 Commented by abony1303 last updated on 16/Aug/20 $$\mathrm{pls}\:\mathrm{help} \\ $$ Answered by mr W last updated…
Question Number 108320 by Khalmohmmad last updated on 16/Aug/20 Answered by Dwaipayan Shikari last updated on 16/Aug/20 $${T}_{{n}} ={n}.\mathrm{2}{n}.\mathrm{4}{n}=\mathrm{8}{n}^{\mathrm{3}} \\ $$$${And} \\ $$$${T}_{{n}} ^{'} ={n}.\mathrm{3}{n}.\mathrm{9}{n}=\mathrm{27}{n}^{\mathrm{3}}…
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Question Number 173839 by Khalmohmmad last updated on 19/Jul/22 $${x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0} \\ $$ Commented by mr W last updated on 19/Jul/22 $${x}_{{k}} =\mathrm{cos}\:\frac{\mathrm{2}{k}\pi}{\mathrm{5}}+{i}\:\mathrm{sin}\:\frac{\mathrm{2}{k}\pi}{\mathrm{5}}\:\:\:\:\left({k}=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\right)…
Question Number 108298 by bachamohamed last updated on 16/Aug/20 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} +\mathrm{1}}=\:? \\ $$ Answered by Dwaipayan Shikari last updated on 16/Aug/20 $$\underset{{n}=\mathrm{1}}…
Question Number 42730 by Rio Michael last updated on 01/Sep/18 $${Given}\:{that}\:{f}\left({x}\right)\:=\:\sqrt{\mathrm{1}−{x}}\:{Find} \\ $$$$\left.{a}\right)\:{D}_{{f}} \:{for}\:{the}\:{arranged}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.{b}\right)\:{fg}\:{if}\:{fh}=\:{g}\left({x}\right)\:{and}\:{h}\left({x}\right)=\:\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4} \\ $$$$\left.{c}\right)\:{A}\left({x}\right)=\:\begin{cases}{\sqrt{\mathrm{1}−{x}}\:,\:{x}\neq\:\mathrm{1}}\\{{x}^{\mathrm{2}} ,{x}\neq\mathrm{0}}\end{cases} \\ $$$${find}\:{A}^{−\mathrm{1}} . \\ $$$$…
Question Number 173807 by mokys last updated on 18/Jul/22 Answered by aleks041103 last updated on 18/Jul/22 $${h}\left({t}\right)=\underset{\mathrm{0}} {\overset{\:{t}} {\int}}{f}\left({x}\right){g}\left({t}−{x}\right){dx} \\ $$$${h}\:{is}\:{the}\:{convolution}\:{of}\:{f}\:{and}\:{g}. \\ $$$${for}\:{convolution}\:{and}\:{the}\:{laplace}\:{transform} \\ $$$${it}'{s}\:{true}\:{that}:…