Question Number 223000 by MrGaster last updated on 12/Jul/25 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{1}}{{e}}\left(\frac{{n}+\mathrm{1}}{{n}}\right)^{{n}} \right)^{\left(−\mathrm{1}\right)^{{n}} } =\frac{{e}\centerdot\sqrt{\pi}\centerdot\sqrt[{\mathrm{6}}]{\mathrm{2}}}{{A}^{\mathrm{6}} } \\ $$ Commented by MathematicalUser2357 last updated on 22/Jul/25…
Question Number 222996 by MrGaster last updated on 12/Jul/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{2}−{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} {dx} \\ $$ Answered by MrGaster last updated on 12/Jul/25 Answered by…
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Question Number 222993 by dr1001sa last updated on 12/Jul/25 Commented by dr1001sa last updated on 12/Jul/25 $${help},{please} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 222961 by Jubr last updated on 12/Jul/25 Answered by mr W last updated on 12/Jul/25 Commented by mr W last updated on 12/Jul/25…
Question Number 222995 by Jubr last updated on 12/Jul/25 Answered by mr W last updated on 12/Jul/25 $${T}={tension}\:{string}\:{around}\:{the}\:{pulley} \\ $$$${A}={acceleration}\:{of}\:{block}\:{M} \\ $$$${a}={acceleration}\:{of}\:{block}\:{m} \\ $$$${assume}\:{there}\:{is}\:{no}\:{friction}. \\…
Question Number 222924 by chidera last updated on 11/Jul/25 Answered by gabthemathguy25 last updated on 11/Jul/25 $$\mathrm{8}×\mathrm{70}=\mathrm{560}\:{kg} \\ $$$$\mathrm{1}\:\mathrm{tonne}\:=\:\mathrm{1000}\:\mathrm{kg} \\ $$$$\Rightarrow\frac{\mathrm{560}}{\mathrm{1000}}=\mathrm{0}.\mathrm{56}\:\mathrm{tonnes} \\ $$ Answered by…
Question Number 222958 by mr W last updated on 11/Jul/25 Commented by mr W last updated on 12/Jul/25 $${find}\:{the}\:{area}\:{of}\:{the}\:{smallest}\: \\ $$$${inscribed}\:{equilateral}\:{triangle}\:{of}\:{a} \\ $$$${given}\:{triangle}\:{with}\:{sides}\:{of}\:{lengthes} \\ $$$$\mathrm{3},\:\mathrm{5},\:\mathrm{7}\:{respectively}.…
Question Number 222943 by Rajakumarselvi last updated on 11/Jul/25 $$\mathrm{11}.\:\mathrm{If}\:\sqrt{\mathrm{5}}\:=\:\mathrm{2}.\mathrm{236}\:\mathrm{and}\:\sqrt{\mathrm{10}}\:=\:\mathrm{3}.\mathrm{162}\:\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{15}}{\:\sqrt{\mathrm{10}}+\sqrt{\mathrm{20}}+\sqrt{\mathrm{40}}−\sqrt{\mathrm{5}}−\sqrt{\mathrm{80}}}\:\mathrm{is} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{5}.\mathrm{398}\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{4}.\mathrm{398}\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{3}.\mathrm{398}\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{6}.\mathrm{398} \\ $$$$\mathrm{12}.\:\mathrm{If}\:\mathrm{x}=\frac{\sqrt{\mathrm{3}}+\mathrm{1}}{\mathrm{3}}\:\:\mathrm{then}\:\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} \:}=? \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{28}\sqrt{\mathrm{3}}\:+\mathrm{15}}{\mathrm{8}}\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{28}\sqrt{\mathrm{3}}−\mathrm{15}}{\mathrm{8}}\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\frac{\mathrm{27}\sqrt{\mathrm{3}}−\mathrm{35}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\frac{\mathrm{27}\sqrt{\mathrm{3}}+\mathrm{35}}{\mathrm{4}} \\ $$$$\mathrm{13}.\:\mathrm{Simplify}\:\:\sqrt[{\mathrm{5}}]{\mathrm{x}^{\mathrm{4}} \sqrt[{\mathrm{4}}]{\mathrm{x}^{\mathrm{3}_{\:} } \sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}}}}} \\…
Question Number 222927 by MrGaster last updated on 11/Jul/25 $$\int\int\int_{{V}} \bigtriangledown\centerdot\boldsymbol{\mathrm{F}}{dV}=\int\int_{\partial{V}} \boldsymbol{\mathrm{F}}\centerdot\mathrm{d}\boldsymbol{{S}} \\ $$$$\boldsymbol{\mathrm{F}}=−\bigtriangledown\phi \\ $$$$\bigtriangledown\centerdot\left(−\bigtriangledown\phi\right)=−\bigtriangledown^{\mathrm{2}} \phi \\ $$$$\int\int\int_{{V}} \left(−\bigtriangledown^{\mathrm{2}} \phi\right){dV}=\int\int_{\partial{V}} \left(−\bigtriangledown\phi\right)\centerdot\mathrm{d}\boldsymbol{{S}} \\ $$$$−\int\int\int_{{V}} \bigtriangledown^{\mathrm{2}}…