Question Number 221264 by fantastic last updated on 28/May/25 $${A}\:{wooden}\:{block}\:{and}\:{a}\:{solid}\:{lead}\:{ball}\:{are}\: \\ $$$${placed}\:{in}\:{a}\:{container}\:{fully}\:{filled}\:{with}\:{water} \\ $$$${Now}\:{if}\:{the}\:{lead}\:{ball}\:{is}\:{placed}\:{on}\:{top}\:{of}\:{the} \\ $$$${floating}\:{wooden}\:{block},{what}\:{is}\:{the}\:{change} \\ $$$${in}\:{water}\:{level}\:{in}\:{the}\:{container}?? \\ $$ Commented by mr W last…
Question Number 221233 by Nicholas666 last updated on 28/May/25 $$ \\ $$$$\:\mathrm{if}\:{a},{b},{c},{d},{e},{f}\:>\:\mathrm{0}\:\mathrm{and}\:{abcdef}\:=\:\mathrm{1}\:, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{then} \\ $$$$\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{ad}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{be}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{cf}}}\:\leqslant\:\frac{\mathrm{3}}{\:\sqrt{\mathrm{2}}}\: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Profosed}\:\mathrm{by}\:\mathrm{Craciun}\:\mathrm{Georghe} \\ $$ Commented by Rasheed.Sindhi…
Question Number 221234 by Nicholas666 last updated on 28/May/25 $$ \\ $$$$\:\:\mathrm{let}\:\mathrm{0}\:\leqslant\:{a},{b},{c},\:\leqslant\:\mathrm{2}\:,\:\mathrm{and}\:{a}\:+\:{b}\:+\:{c}\:=\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Prove}\:\mathrm{that}; \\ $$$$\:\:\frac{\mathrm{3}}{\mathrm{2}}\:\leqslant\:\frac{\mathrm{1}}{{a}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{{b}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{{c}\:+\mathrm{1}\:}\:\leqslant\:\frac{\mathrm{11}}{\mathrm{6}} \\ $$$$ \\ $$ Commented by Frix last updated…
Question Number 221260 by mnjuly1970 last updated on 28/May/25 Answered by maths2 last updated on 30/May/25 $$=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\sqrt{{n}}.\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\frac{\mathrm{2}^{\mathrm{2}{n}} \left({n}!\right)^{\mathrm{2}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!} \\ $$$${n}!\sim\sqrt{\mathrm{2}\pi{n}}.\left(\frac{{n}}{{e}}\right)^{{n}} ..…
Question Number 221262 by Nicholas666 last updated on 28/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{if}\:{a},\:{b},\:{c},\:>\:\mathrm{0}\:\:,\:\mathrm{show}\:\mathrm{that}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{5}} }{{b}^{\mathrm{2}} }\:+\:\frac{{b}}{{c}}\:+\:\frac{{c}^{\mathrm{3}} }{{a}^{\mathrm{2}} }\:>\:\mathrm{2}{a} \\ $$$$ \\ $$ Commented by mr…
Question Number 221256 by Nicholas666 last updated on 28/May/25 $$ \\ $$$$\:\:\int\int\int_{\:\left[\mathrm{0},\mathrm{1}\right]} \:\frac{\mathrm{ln}\left[\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{y}\right)\left(\mathrm{1}+{z}\right]\right.}{\mathrm{1}\:+\:{xyz}}\:{dxdydz}\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221254 by Nicholas666 last updated on 28/May/25 $$\:\:\int\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} } \:\frac{\mathrm{1}}{\left(\mathrm{1}−{xyz}\right)\left(\mathrm{1}−{xy}\right)\left(\mathrm{1}−{yz}\right)\left(\mathrm{1}−{zx}\right)}\:{dxdydz}\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221255 by MATHEMATICSAM last updated on 28/May/25 $$\mathrm{Let}\:\mathrm{X}\:\mathrm{be}\:\mathrm{a}\:\mathrm{point}\:\mathrm{inside}\:\mathrm{a}\:\mathrm{square}\:\mathrm{ABCD},\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{XA}\:=\:\mathrm{10}\:\mathrm{cm},\:\mathrm{XB}\:=\:\mathrm{6}\:\mathrm{cm}\:\mathrm{and} \\ $$$$\mathrm{XC}\:=\:\mathrm{14}\:\mathrm{cm}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}. \\ $$ Commented by mr W last updated on 28/May/25 $${see}\:{also}\:{Q}\mathrm{72294}…
Question Number 221228 by Nicholas666 last updated on 27/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\underset{{m}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left({m}^{\mathrm{2}} \:+\:{n}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by…
Question Number 221218 by MATHEMATICSAM last updated on 27/May/25 Commented by MATHEMATICSAM last updated on 27/May/25 $$\left.\mathrm{1}\right)\:\mathrm{Three}\:\mathrm{blocks}\:\mathrm{are}\:\mathrm{arranged}\:\mathrm{as}\:\mathrm{shown}\:\mathrm{in}\: \\ $$$$\mathrm{the}\:\mathrm{figure}.\:\mathrm{The}\:\mathrm{whole}\:\mathrm{system}\:\mathrm{is}\:\mathrm{placed}\:\mathrm{on} \\ $$$$\mathrm{a}\:\mathrm{smooth}\:\mathrm{horizontal}\:\mathrm{plane}.\:\mathrm{Coefficient}\:\mathrm{of} \\ $$$$\mathrm{friction}\:\mathrm{between}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{and}\:\mathrm{5}\:\mathrm{kg}\:\mathrm{block} \\ $$$$\mathrm{is}\:\mathrm{0}.\mathrm{1},\:\mathrm{between}\:\mathrm{the}\:\mathrm{5}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{3}\:\mathrm{kg}\:\mathrm{block}\:\mathrm{is}…