Question Number 175213 by Mastermind last updated on 23/Aug/22 $$\mathrm{Solve}\:\mathrm{by}\:\mathrm{Method}\:\mathrm{of}\:\mathrm{variation}\:\mathrm{parameter} \\ $$$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }−\mathrm{3}\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{2y}=\mathrm{sinx} \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$ Answered by Ar Brandon last…
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Question Number 109619 by Dwaipayan Shikari last updated on 24/Aug/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}!}{{n}^{{n}} } \\ $$ Commented by mnjuly1970 last updated on 24/Aug/20 $${please}\:{solve}\Uparrow\Uparrow \\…
Question Number 44069 by ajfour last updated on 21/Sep/18 $$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}\:=\:? \\ $$ Commented by maxmathsup by imad last updated on 21/Sep/18 $${let}\:{I}\:=\:\int\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}\:\:{changement}\:{x}=\sqrt{\mathrm{2}}{sh}\left({t}\right){give} \\…
Question Number 44051 by Rio Michael last updated on 20/Sep/18 Commented by Rio Michael last updated on 20/Sep/18 $${Two}\:{forces}\:{F}_{\mathrm{1}} \:{and}\:{F}_{\mathrm{2}} \:{are}\:{acting}\:{on}\:{different}\:{directions}, \\ $$$${find}\:{the}\:{resultant}\:{force}\:{F}_{{R}} . \\…
Question Number 175122 by Michaelfaraday last updated on 20/Aug/22 Answered by Ar Brandon last updated on 20/Aug/22 $$\mathscr{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\sqrt[{\mathrm{2022}}]{\mathrm{cos}\left(\mathrm{2021}{x}\right)}}{{x}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\left(\mathrm{1}−\frac{\mathrm{2021}^{\mathrm{2}} {x}^{\mathrm{2}} }{\mathrm{2}}\right)^{\frac{\mathrm{1}}{\mathrm{2022}}}…
Question Number 175108 by Mastermind last updated on 19/Aug/22 Answered by MJS_new last updated on 19/Aug/22 $${y}={px} \\ $$$$\begin{cases}{\left({p}^{\mathrm{4}} +\mathrm{6}{p}^{\mathrm{2}} +\mathrm{1}\right){x}^{\mathrm{4}} =\mathrm{1}}\\{\left({p}+\mathrm{1}\right)^{\mathrm{4}} {x}^{\mathrm{5}} ={x}\left(\mathrm{1}−{p}\right)}\end{cases} \\…
Question Number 44026 by SNILL JAMES last updated on 20/Sep/18 $${ifA}:{B}=\mathrm{3}:\mathrm{6}\:{and}\:{B}:{C}\:=\:\mathrm{7}:\mathrm{8} \\ $$$${find}\:{A}:{B}:{C} \\ $$$${solution} \\ $$$${since}\:{B}\:{is}\:{common}\:{then} \\ $$$$\left.{A}:{B}\:=\mathrm{3}:\mathrm{6}\right\}\mathrm{7} \\ $$$$\left.{B}:{C}=\mathrm{7}:\mathrm{8}\right\}\mathrm{6} \\ $$$${A}:{B}=\mathrm{21}:\mathrm{42} \\ $$$${B}:{C}=\mathrm{42}:\mathrm{48}…
Question Number 175036 by Mastermind last updated on 16/Aug/22 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\left(\mathrm{xy}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{dx}−\left(\mathrm{x}^{\mathrm{2}} \mathrm{y}−\mathrm{1}\right)\mathrm{dy}=\mathrm{0} \\ $$ Answered by ajfour last updated on 17/Aug/22 $${xy}\left({ydx}−{xdy}\right)={dx}−{dy} \\…
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