Question Number 155806 by SANOGO last updated on 05/Oct/21 Answered by puissant last updated on 05/Oct/21 $$\mathscr{L}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{\mathrm{1}}{\:\sqrt{{n}^{\mathrm{2}} −{k}^{\mathrm{2}} }}\: \\ $$$$=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{0}}…
Question Number 155801 by cortano last updated on 05/Oct/21 $$\:\begin{cases}{\mathrm{m}^{\mathrm{2}} =\mathrm{n}+\mathrm{2}}\\{\mathrm{n}^{\mathrm{2}} =\mathrm{m}+\mathrm{2}}\end{cases}\:\Rightarrow\mathrm{m}\neq\mathrm{n} \\ $$$$\:\mathrm{4mn}−\mathrm{m}^{\mathrm{3}} −\mathrm{n}^{\mathrm{3}} =?\: \\ $$ Answered by Rasheed.Sindhi last updated on 05/Oct/21…
Question Number 24730 by Tinkutara last updated on 25/Nov/17 $$\mathrm{Consider}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{square}\:\mathrm{plate}\:\mathrm{of}\:\mathrm{side} \\ $$$${a}\:\mathrm{and}\:\mathrm{mass}\:{m}.\:\mathrm{The}\:\mathrm{moment}\:\mathrm{of}\:\mathrm{inertia} \\ $$$$\mathrm{of}\:\mathrm{this}\:\mathrm{plate}\:\mathrm{about}\:\mathrm{an}\:\mathrm{axis}\:\mathrm{perpendicular} \\ $$$$\mathrm{to}\:\mathrm{its}\:\mathrm{plane}\:\mathrm{and}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{one}\:\mathrm{of} \\ $$$$\mathrm{its}\:\mathrm{corners}\:\mathrm{is} \\ $$ Commented by ajfour last updated…
Question Number 155803 by cortano last updated on 05/Oct/21 $$\mathrm{proof}\:\mathrm{that}\: \\ $$$$\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\mathrm{n}×\mathrm{n}!\:=\:\mathrm{11}!−\mathrm{1} \\ $$ Answered by som(math1967) last updated on 05/Oct/21 $$\mathrm{1}×\mathrm{1}!+\mathrm{2}×\mathrm{2}!+\mathrm{3}×\mathrm{3}!+…+\mathrm{10}×\mathrm{10}!\:+\mathrm{1}−\mathrm{1} \\…
Question Number 155802 by cortano last updated on 05/Oct/21 $$\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\mathrm{2}×\mathrm{1}!+\mathrm{4}×\mathrm{2}!+\mathrm{6}×\mathrm{3}!+…+\mathrm{200}×\mathrm{100}! \\ $$ Answered by talminator2856791 last updated on 05/Oct/21 $$\:\mathrm{use}\:\mathrm{the}\:\mathrm{information}\:\mathrm{in}\:\mathrm{the}\:\mathrm{post}\: \\ $$$$\:\mathrm{above}\:\mathrm{this}\:\mathrm{post}\:\mathrm{Q}.\mathrm{155803}: \\…
Question Number 24728 by math solver last updated on 25/Nov/17 $$\mathrm{find}\:\mathrm{sum}\:\mathrm{of}\:: \\ $$$$\mathrm{1}^{\mathrm{3}\:} −\:\left(\:\mathrm{1}.\mathrm{5}\right)^{\mathrm{3}} \:+\mathrm{2}^{\mathrm{3}\:} −\left(\mathrm{2}.\mathrm{5}\right)^{\mathrm{3}} +………\:? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 155797 by ajfour last updated on 09/Oct/21 $${a},{b},{c},{d},{e}\:\:\left({kids}\right)\:{are}\:{in}\:{ascending} \\ $$$${order}\:{of}\:{heights}.\:{If}\:{they}\:{are} \\ $$$${to}\:{stand}\:{in}\:{a}\:{circle}\:{in}\:{a}\:{way}\:{so} \\ $$$${that}\:{the}\:{sum}\:{of}\:\mid{difference}\:{in} \\ $$$${heights}\:{of}\:{adjacent}\:{pairs}\mid \\ $$$$\:{is}\:{a}\:{minimum},\:{find}\:{this} \\ $$$$\:{minimum}. \\ $$ Commented…
Question Number 90262 by jagoll last updated on 22/Apr/20 $$\left(\mathrm{y}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\right)\:\mathrm{dx}\:=\:\mathrm{x}\:\mathrm{dy}\: \\ $$ Commented by john santu last updated on 22/Apr/20 $$\left(\frac{{y}}{{x}}+\sqrt{\mathrm{1}+\left(\frac{{y}}{{x}}\right)^{\mathrm{2}} }\right)\:{dx}\:=\:{dy}\: \\…
Question Number 90258 by jagoll last updated on 22/Apr/20 Commented by john santu last updated on 22/Apr/20 $$\left({a}\right){P}\left({X}\leqslant\mathrm{3}\right)\:=\:\underset{{k}\:=\:\mathrm{0}} {\overset{\mathrm{3}} {\sum}}{C}_{{k}} ^{\mathrm{25}} \left(\mathrm{0}.\mathrm{05}\right)^{{k}} \:\left(\mathrm{0}.\mathrm{95}\right)^{\mathrm{3}−{k}} \\ $$$$\left({b}\right){P}\left({X}\geqslant\mathrm{4}\right)\:=\:\mathrm{1}−\underset{{k}\:=\:\mathrm{0}}…
Question Number 90259 by john santu last updated on 22/Apr/20 $${a}\:{function}\:{f}\:{is}\:{defined}\:{on}\: \\ $$$${the}\:{positive}\:{integers}\:{satisfies}\: \\ $$$${f}\left(\mathrm{1}\right)\:=\:\mathrm{1002}\:,\:\&\:{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+ \\ $$$$…\:+{f}\left({n}\right)\:=\:{n}^{\mathrm{2}} \:{f}\left({n}\right)\:. \\ $$$${find}\:{f}\left(\mathrm{2003}\right)\: \\ $$ Answered by mr…