Question Number 62585 by Jmasanja last updated on 23/Jun/19 $${find}\:{the}\:{resultant}\:{force}\:{of}\:{a}\:{system} \\ $$$${of}\:{three}\:{forces}\:\overset{−} {{O}}\overset{\rightarrow} {{P}}\:=\mathrm{9}{N},\overset{−} {{O}}\overset{\rightarrow} {{R}}\:=\mathrm{10}{N}\:{and}\:\overset{−} {{O}}\overset{\rightarrow} {{Q}}\:\mathrm{10}{N}\: \\ $$$${acting}\:{at}\:{point}\:{O}\:{where}\:{angle}\:{POR}\:{is} \\ $$$$\mathrm{135}°,{angle}\:{POQ}\:{is}\:\mathrm{135}°\:\:{and}\:{QOR}\:{is}\: \\ $$$$\mathrm{90}° \\…
Question Number 62583 by Jmasanja last updated on 23/Jun/19 $${find}\:{the}\:{vector}\:{sum}\:{of}\:{two}\:{vectors} \\ $$$${of}\:{magnitude}\:{of}\:\mathrm{7}\:{and}\:\mathrm{8}\:{making}\:{an} \\ $$$${angle}\:{of}\:\mathrm{120}°\:{to}\:{each}\:{other} \\ $$ Answered by MJS last updated on 23/Jun/19 $$\begin{pmatrix}{\mathrm{7}}\\{\mathrm{0}}\end{pmatrix}+\begin{pmatrix}{\mathrm{8}}\\{\mathrm{8sin}\:\mathrm{120}°}\end{pmatrix}=\begin{pmatrix}{\mathrm{15}}\\{\mathrm{4}\sqrt{\mathrm{3}}}\end{pmatrix} \\…
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Question Number 128112 by AgnibhoMukhopadhyay last updated on 04/Jan/21 $$\:\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:\mathrm{4}\:+\:…..\:+\:\mathrm{100}\:=\:? \\ $$ Answered by Olaf last updated on 04/Jan/21 $$\mathrm{A}\:\left({n}+\mathrm{1}\right)×\left({n}+\mathrm{1}\right)\:\mathrm{squared}\:\mathrm{chess}\:\mathrm{board} \\ $$$$\mathrm{contains}\:\left({n}+\mathrm{1}\right)^{\mathrm{2}} \:\mathrm{squares}. \\ $$$$…
Question Number 62577 by Sr@2004 last updated on 23/Jun/19 Commented by Sr@2004 last updated on 23/Jun/19 $${please}\:{solve}\:\mathrm{12} \\ $$ Answered by som(math1967) last updated on…
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Question Number 128110 by Dwaipayan Shikari last updated on 04/Jan/21 $$\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{sinx}\:{sin}\left({x}+{y}\right)}{{x}\left({x}+{y}\right)}{dxdy} \\ $$ Answered by Olaf last updated on 04/Jan/21 $$\Omega\:=\:\int_{\mathrm{0}}…
Question Number 128109 by bemath last updated on 04/Jan/21 $$\emptyset\:=\:\int\:\left(\mathrm{x}−\mathrm{2}\right)\:\sqrt{\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}}\:\mathrm{dx}\: \\ $$ Answered by liberty last updated on 04/Jan/21 $$\:\phi\:=\:\int\:\frac{\left(\mathrm{x}−\mathrm{2}\right)\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}{\mathrm{x}−\mathrm{1}}\:\mathrm{dx}\: \\ $$$$\:\mathrm{let}\:\mathrm{x}\:=\:\mathrm{sec}\:\mathrm{t}\: \\ $$$$\:\emptyset\:=\:\int\:\frac{\left(\mathrm{sec}\:\mathrm{t}−\mathrm{2}\right).\mathrm{tan}\:\mathrm{t}}{\mathrm{sec}\:\mathrm{t}−\mathrm{1}}.\:\left(\mathrm{sec}\:\mathrm{t}\:\mathrm{tan}\:\mathrm{t}\:\right)\:\mathrm{dt}\:…
Question Number 128106 by bemath last updated on 04/Jan/21 $$\:\mathrm{yy}'\:+\:\mathrm{b}\left(\mathrm{x}−\mathrm{a}\right)=\:\frac{\mathrm{ay}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\: \\ $$ Commented by mr W last updated on 05/Jan/21 $${once}\:{i}\:{asked}\:{this}\:{question}\:{due}\:{to} \\ $$$${Q}\mathrm{127997},\:{but}\:{then}\:{i}\:{could}\:{solve}\:{it}\:{myself}…
Question Number 62571 by Joel122 last updated on 23/Jun/19 $$\mathrm{Find} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left({n}\left(\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{3}\right)^{\mathrm{2}} }\:+\:…\:+\:\frac{\mathrm{1}}{\left(\mathrm{4}{n}−\mathrm{1}\right)^{\mathrm{2}} }\right)\right) \\ $$ Commented by Prithwish sen last updated on…