Question Number 147091 by aliibrahim1 last updated on 17/Jul/21 Answered by Olaf_Thorendsen last updated on 18/Jul/21 $${f}\left({x},{y}+{z}\right)\:=\:{f}\left({x},{y}\right){f}\left({x},{z}\right) \\ $$$${y}\:=\:{z} \\ $$$${f}\left({x},\mathrm{2}{y}\right)\:=\:{f}\left({x},{y}\right){f}\left({x},{y}\right)\:=\:{f}^{\mathrm{2}} \left({x},{y}\right) \\ $$$$\Rightarrow\:{f}\left({x},\mathrm{2}^{{n}} {y}\right)\:=\:{f}^{\mathrm{2}^{{n}}…
Question Number 16015 by chux last updated on 16/Jun/17 $$\mathrm{Two}\:\mathrm{horses}\:\mathrm{pull}\:\mathrm{horizontally}\:\mathrm{on} \\ $$$$\mathrm{ropes}\:\mathrm{attached}\:\mathrm{to}\:\mathrm{a}\:\mathrm{stump}.\mathrm{The} \\ $$$$\mathrm{two}\:\mathrm{forces}\:\mathrm{F}\:\mathrm{and}\:\mathrm{T}\:\mathrm{that}\:\mathrm{they} \\ $$$$\mathrm{applied}\:\mathrm{to}\:\mathrm{the}\:\mathrm{stump}\:\mathrm{are}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{resultant}\:\mathrm{R}\:\mathrm{has}\:\mathrm{a}\:\mathrm{magnitude} \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{F}\:\mathrm{and}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of} \\ $$$$\mathrm{90}°\:\mathrm{with}\:\mathrm{F}.\mathrm{Let}\:\mathrm{F}=\mathrm{1300N}\:\mathrm{and}\: \\ $$$$\mathrm{R}=\mathrm{1300N}.\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{T}. \\…
Question Number 16012 by chux last updated on 16/Jun/17 $$\mathrm{prove}\:\mathrm{that}\:\mathrm{when}\:\mathrm{light}\:\mathrm{travels}\: \\ $$$$\mathrm{through}\:\mathrm{a}\:\mathrm{triangular}\:\mathrm{glass}\:\mathrm{prism}\: \\ $$$$\mathrm{of}\:\mathrm{angle}\:\mathrm{A} \\ $$$$\mathrm{the}\:\mathrm{refractive}\:\mathrm{index}\:\left(\mathrm{n}\right)\:\mathrm{is}\:\mathrm{given} \\ $$$$\mathrm{by} \\ $$$$\mathrm{n}=\mathrm{sin}\:\left(\frac{\mathrm{A}+\mathrm{D}_{\mathrm{min}} }{\mathrm{2}}\right)/\mathrm{sin}\:\left(\frac{\mathrm{A}}{\mathrm{2}}\right) \\ $$ Commented by…
Question Number 147078 by A8;15: last updated on 17/Jul/21 Commented by Olaf_Thorendsen last updated on 17/Jul/21 $${next}\:{time}\:{write}\:{letters}\:{A},\:{B},\:{C}… \\ $$$${please}\:{mister} \\ $$ Terms of Service Privacy…
Question Number 147068 by tabata last updated on 17/Jul/21 $${find}\:{laplase}\:{transforme}\:{of}\:{e}^{\left({t}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by mathmax by abdo last updated on 17/Jul/21 $$\mathrm{not}\:\mathrm{defined}.. \\ $$…
Question Number 147066 by tabata last updated on 17/Jul/21 $${find}\:{laurant}\:{series}\:{lf} \\ $$$$ \\ $$$$\:\left(\mathrm{1}\right){f}\left({z}\right)=\frac{\mathrm{1}}{{z}−\mathrm{1}}+\frac{\mathrm{1}}{{z}+\mathrm{2}}\:\:,\mid{z}\mid>\mathrm{1} \\ $$$$ \\ $$$$\left(\mathrm{2}\right){f}\left({z}\right)=\frac{\mathrm{1}}{{z}−\mathrm{2}}−\frac{\mathrm{2}}{{z}−\mathrm{3}}\:\:,\mid{z}\mid<\mathrm{3} \\ $$ Answered by mathmax by abdo…
Question Number 15972 by icyfalcon999 last updated on 16/Jun/17 $$\int\mathrm{tan}^{\mathrm{2}} \mathrm{x}\:\mathrm{sec}\:\mathrm{x}\:\mathrm{dx}\: \\ $$ Commented by tawa tawa last updated on 16/Jun/17 $$\int\mathrm{tan}^{\mathrm{2}} \mathrm{x}\:\mathrm{secx}\:\mathrm{dx} \\ $$$$\mathrm{From}\:\mathrm{the}\:\mathrm{trigonometry}\:\mathrm{identity}:\:\mathrm{tan}^{\mathrm{2}}…
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Question Number 146994 by KONE last updated on 17/Jul/21 $${u}_{{n}} ={cos}\sqrt{{n}+\mathrm{1}}−{cos}\sqrt{{n}} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{u}_{{n}} =?? \\ $$ Answered by mathmax by abdo last updated on…