Question Number 76307 by Master last updated on 26/Dec/19 Answered by mr W last updated on 26/Dec/19 $${x}\neq\mathrm{1} \\ $$$$\mathrm{125}\left(\mathrm{1}+{x}^{\mathrm{5}} \right)=\mathrm{11}\left(\mathrm{1}+{x}\right)^{\mathrm{5}} \\ $$$$\mathrm{125}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +{x}^{\mathrm{4}}…
Question Number 10768 by 2525 last updated on 24/Feb/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{differential}\:\mathrm{equations}\: \\ $$$$\mathrm{by}\:\mathrm{power}\:\mathrm{series}. \\ $$$${y}^{//} −\mathrm{2}{y}\:=\:\mathrm{4}{x}^{\mathrm{2}} {e}^{{x}^{\mathrm{2}} } \\ $$ Commented by 2525 last updated on…
Question Number 76302 by john santuy last updated on 26/Dec/19 $${given}\:{vektor}\:{a}=\left(\mathrm{3},{x},−\mathrm{2}\right) \\ $$$${b}=\left(−\mathrm{6},−\mathrm{2},{y}\right)\:.\:{what}\:{the}\:{value}\:{x}\: \\ $$$${and}\:{y}\:{if}\:{a}\:{and}\:{b}\:{are}\:{parallel}? \\ $$ Answered by benjo last updated on 26/Dec/19 $$\mathrm{a}×\mathrm{b}\:=\mathrm{0}…
Question Number 76303 by arkanmath7@gmail.com last updated on 26/Dec/19 $${In}\:{the}\:{symmetric}\:{group}\:\left({S}_{{n}} \:,\:{o}\right),\:{let} \\ $$$${H}\:{denotes}\:{the}\:{set}\:{of}\:{permutations}\: \\ $$$${leaving}\:{the}\:{integer}\:{n}\:{fixed}: \\ $$$$\:\:\:{H}\:=\:\left\{{f}\in{S}_{{n}} \:\mid\:{f}\left({n}\right)\:=\:{n}\right\} \\ $$$${Show}\:{that}\:{the}\:{pair}\:\left({H},\:{o}\right)\:{is}\:{subgroup} \\ $$$${of}\:\left({S}_{{n}} ,{o}\right). \\ $$$$'{note}:\:{the}\:{operation}\:{is}\:{composition}'…
Question Number 76298 by benjo last updated on 26/Dec/19 $$\int\sqrt{\:\mathrm{tanx}+\mathrm{cotxdx}} \\ $$ Commented by benjo last updated on 26/Dec/19 Commented by john santuy last updated…
Question Number 10762 by 2525 last updated on 24/Feb/17 $$\mathrm{in}\:\mathrm{eac}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{problems}\:\mathrm{you}\:{are} \\ $$$$\mathrm{given}\:\mathrm{a}\:\mathrm{function}\:\mathrm{on}\:\mathrm{the}\:\mathrm{interval}\:\:−\pi<{x}<\pi. \\ $$$$\mathrm{Sketch}\:\mathrm{several}\:\mathrm{periods}\:\mathrm{of}\:\mathrm{the}\:\mathrm{corresponding} \\ $$$$\mathrm{periodic}\:\mathrm{function}\:\mathrm{of}\:\mathrm{period}\:\mathrm{2}\pi.\:\mathrm{Expand}\:\mathrm{the} \\ $$$$\mathrm{periodic}\:\mathrm{function}\:\mathrm{in}\:\mathrm{a}\:\mathrm{sine}−\mathrm{consine}\:\mathrm{Fourier} \\ $$$$\mathrm{series}.\:\: \\ $$$$ \\ $$$${F}\left({x}\right)\:=\:\left\{\overset{{x}+\pi} {\:}_{\mathrm{0}}…
Question Number 10761 by 2525 last updated on 24/Feb/17 $$\mathrm{Express}\:\mathrm{the}\:\mathrm{following}\:\Gamma\:\mathrm{function}\:\mathrm{using}\:\mathrm{tables} \\ $$$$\mathrm{and}\:\mathrm{evaluate}\:\mathrm{them}\:\mathrm{using}\:\mathrm{a}\:\mathrm{table}\:\mathrm{or}\:\Gamma\:\mathrm{functions}. \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} {x}^{−\mathrm{1}/\mathrm{3}} {e}^{−\mathrm{8}{x}\:} {dx} \\ $$ Terms of Service…
Question Number 10760 by Saham last updated on 24/Feb/17 $$\mathrm{A}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2}.\mathrm{0kg}\:\mathrm{resting}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{horizontal}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{acted} \\ $$$$\mathrm{upon}\:\mathrm{simultaneously}\:\mathrm{by}\:\mathrm{two}\:\mathrm{forces}\:\mathrm{10N}\:\mathrm{due}\:\mathrm{north}\:\mathrm{and}\:\mathrm{10N}\:\mathrm{due}\:\mathrm{east}. \\ $$$$\mathrm{The}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{produce}\:\mathrm{by}\:\mathrm{the}\:\mathrm{force}\:\mathrm{on}\:\mathrm{the}\:\mathrm{block}. \\ $$ Commented by chux last updated on 24/Feb/17 $$\mathrm{please}\:\mathrm{are}\:\mathrm{you}\:\mathrm{a}\:\mathrm{nigerian} \\…
Question Number 141825 by Rankut last updated on 23/May/21 $$\boldsymbol{\mathrm{If}}\:\:\boldsymbol{\mathrm{P}}=\left(\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} ,\:\boldsymbol{\mathrm{when}}\:\boldsymbol{\mathrm{x}}=\mathrm{2},\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{is}} \\ $$$$\boldsymbol{\mathrm{decreased}}\:\boldsymbol{\mathrm{by}}\:\mathrm{3\%}.\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{approximate}} \\ $$$$\boldsymbol{\mathrm{percentage}}\:\boldsymbol{\mathrm{change}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{P}}. \\ $$$$\boldsymbol{\mathrm{Help}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{out}}\:\boldsymbol{\mathrm{pls}} \\ $$ Terms of Service Privacy Policy…
Question Number 76290 by benjo last updated on 26/Dec/19 $$\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{x}^{\mathrm{y}} \:+\mathrm{y}^{\mathrm{x}} \:\geqslant\mathrm{1}\:,\:\mathrm{x},\mathrm{y}\:\in\mathbb{R} \\ $$$$\mathrm{x},\mathrm{y}\:>\:\mathrm{0} \\ $$ Commented by MJS last updated on 26/Dec/19 $$\mathrm{we}\:\mathrm{can}\:\mathrm{exchange}\:{x}\:\mathrm{and}\:{y}\:\Rightarrow\:\mathrm{let}\:{x}\leqslant{y} \\…